On the Nature of Luminescence Thermochromism of Multinuclear Copper(I) Benzoate Complexes in the Crystalline State

Abstract

A model luminescent [(PhCO₂)₄Cu₄] (Cu₄) complex in the crystalline state was investigated via combined crystallographic and spectroscopic techniques contributed substantially by theoretical modelling. The complex appeared to exhibit luminescence thermochromism, i.e., red phosphorescence at room temperature which changes to green when lowering the temperature to 90 K. The low-energy emissive state was assigned as a cluster-centred triplet, ³CC. The emission from this state predicted in TDDFT (~635 nm) matches the experimental red band observed at 660–715 nm. In contrast, the nature of the high-energy “green” band was less straightforward. The next reached cluster-centred triplet excited state occurred to be energetically close to the experimental value of ~545 nm. The two excited states also exhibit significant metal-to-ligand and ligand-to-metal charge transfer characteristics, especially for solid-state distorted geometries. In both cases the cluster core was expected to become notably contracted when compared to the ground state. Time-resolved photocrystallographic results supported the computationally predicted core contraction upon excitation. Additionally, the differences between the spectroscopic behaviour of the related tetra- and hexanuclear copper(I) complexes, Cu₄ and Cu₆ (i.e., [(PhCO₂)₆Cu₆]) in the crystalline state were discussed and examined. It appeared that crystal packing may constitute an important factor as far as the lack of luminescence thermochromism in the latter case is concerned. Synopsis: Structure–property relationships characterising a model luminescent [(PhCO₂)₄Cu₄] (Cu₄) complex in the crystalline state were investigated via combined crystallographic and spectroscopic techniques contributed by theoretical modelling, and compared with the properties of the related [(PhCO₂)₆Cu₆] (Cu₆) complex.

1. Introduction

One of the most important current areas in chemistry is developing new functional and controllable materials for technological applications. Therefore, compounds exhibiting specific photoactive properties, either in solution or, even more importantly, in the solid state, are among the most desired materials nowadays. A number of such systems have already found versatile applications in solar-energy conversion [1] and other fields, ranging from molecular electronics [2], light-emitting diodes (LEDs) [3], through photocatalysts [4], to biolabels [5].

Among many photoactive substances, transition-metal complexes seem to be the most interesting ones due to several reasons, two of which are: (i) the presence of metal centres induces spectroscopic properties related to metal-ligand interactions not achievable for purely organic molecules, and (ii) the flexibility in designing new molecules by changing metal centres and organic ligands, which allows fine-tuning of desired properties. In this respect, ${\mathrm{Cu}}^{\mathrm{I}}$ compounds are distinctive, as they provide an attractive alternative to expensive, less abundant, and more toxic heavy-metal-containing complexes [6]. Furthermore, polynuclear ${\mathrm{d}}^{10}$ copper complexes may create diverse molecular assemblies and are often unusually strongly luminescent. Their photochemical properties can be modified by the choice of ligands and by variation of a number of metal centres. Since the ${\mathrm{d}}^{10}$ electronic configuration of ${\mathrm{Cu}}^{\mathrm{I}}$ enforces no stereochemical demands, the coordination sphere, normally four-coordinate, is therefore largely determined by electrostatic and molecular mechanical factors [7]. An advantage of Cu^I systems over many first-row transition metal complexes is also the fact that the luminescence of the latter ones is often bypassed by the presence of low-lying ligand-field excited states (ESs), which may be too short-lived to have measurable emissions [8]. In this context, filled-shell ${\mathrm{d}}^{10}$ systems offer an opportunity to observe other excited states. For instance, tetranuclear cuprous halide clusters usually display thermochromic properties thanks to two distinct emission bands of different emission lifetimes [9,10]. In the literature-reported [Cu₄I₄(py)₄] case (py = pyridine), for example, the strong lower energy emission was assigned to a triplet cluster-centred (³CC) ES, a combination of iodide-to-copper charge transfer (XMCT) and $\mathrm{d}\to \mathrm{s}$ transitions, and the weaker higher-energy band to a triplet halide-to-ligand charge transfer (³XLCT) ES. This subject was well-described in the review by Ford et al. [7].

In the current paper, we will focus our attention on the tetranuclear [(PhCO₂)₄Cu₄] complex (Cu₄, Scheme 1a). This compound has already been studied regarding its structure, interesting reversible interconversion, via sublimation and subsequent recrystallization, into the [(PhCO₂)₆Cu₆] form (Cu₆, Scheme 1b), and some selected aspects of its spectroscopic properties [11]. Nonetheless, our preliminary examination of Cu₄ revealed that the complex additionally exhibits thermochromic emission in its crystal form, which has not been detected in the previous studies. This suggests that, similarly to the mentioned [Cu₄I₄(py)₄] cluster, there exist at least two distinct emissive excited states. These, however, are definitely of different origin than those described for the iodide complex. Interestingly, such properties are not exhibited by the related hexanuclear Cu₆ form, for which, in turn, temperature-induced structural phase transition was observed.

Hence, this paper is devoted to a thorough study of the nature of the luminescence thermochromism found by us for the Cu₄ crystal form, using time-resolved spectroscopic and photocrystallographic methods at different temperatures, largely contributed by theoretical computations. Furthermore, an attempt of understanding the striking difference between the spectroscopic behaviour of the related Cu₄ and Cu₆ complexes in the solid state has been undertaken.

2. Experimental Section

2.1. Synthesis and Crystallisation

The Cu₄ complex was synthesised according to the literature procedure [11]. This procedure yielded a phase pure crystalline powder of the Cu₄ complex. Single rod-shaped crystals of Cu₄ were obtained by slow crystallization of the complex from saturated xylene solution. Additionally, crystals of the Cu₆ complex were obtained, as described in the literature, namely by the sublimation of the Cu₄ powder [11].

2.2. X-ray Diffraction Data Collection and Refinement

All single-crystal X-ray measurements of both compounds were carried out on a classical diffractometer, in all cases equipped with the CCD detector and low-temperature open-flow device to keep the samples at the constant temperature. Data collection strategies determination and optimization, unit cell determination, raw diffraction image integration, and data scaling, were all performed using the appropriate algorithms implemented in the diffractometer software [12,13].

All structures were solved using a charge-flipping method [14,15,16], as implemented in the SUPERFLIP program [17], and refined with the JANA package [18] within the independent atom model (IAM) approximation. CIF files for each refinement are present in the Supplementary Materials, or can be retrieved from the Cambridge Structural Database [19] (for deposition numbers see Table S1 in the Supplementary Materials). All raw data and associated refinement files are available under the following DOI: 10.18150/repod.0196712 (Repository for Open Data, Interdisciplinary Centre for Mathematical and Computational Modelling, University of Warsaw, Warsaw, Poland).

2.3. Solid-State Spectroscopy

Single-crystal emission spectra and luminescence lifetimes were measured on an in-house -build setup at the Department of Chemistry of the University at Buffalo, NY, USA [20], and on a similar setup recently installed by us at the Department of Chemistry of the University of Warsaw. In the latter case samples were UV-light-excited with the Opotek Vibrant Nd:YAG laser ($\lambda$ = 355 nm, pulse length of about 5 ns). The laser output was delivered to the rear port of an Olympus IX73 (Warsaw, Poland) inverted microscope and focused on the sample using a reflective objective. Any residual or scattered UV-light was cut off from reaching the eyepieces or detector with an appropriate dichroic mirror. The single-crystal samples, placed at the quartz plate with the aid of the Type-F Olympus immersion oil, were mounted inside the microscope cryostage (Cryo Industries of America, Manchester, NH, USA) which allows one to cool the crystal down to 90 K. Emission from the sample was recollected through the reflective objective and delivered to the spectrograph (Acton SP2150; Princeton Instruments; Trenton, NJ, USA) equipped with the time-gated intensified charge-coupled device (ICCD) camera (PI-MAX4, Princeton Instruments). In this setup the laser flash-lamp was used to trigger the CCD camera, which in turn, after a specified time delay triggered the laser Q-switch allowing for a precise control of the detector readout delay throughout the experiment. The experiment was controlled using the LightField software (Princeton Instruments) allowing variations of the time delay and, thus, enabling collecting of the sample emission as a function of time. The luminescence lifetimes were extracted from the intensity decay data by means of the least-squares fitting (Supplementary Materials).

2.4. Theoretical Computations

All non-metal atoms were described using the cc-pVDZ Dunning basis set [21]. For the Cu atoms the cc-pVDZ-PP basis set of Peterson & Puzzarini [22] combined with the relativistic effective core potential of Figgen et al. [23], was employed. The CAM-B3LYP [24] and ωB97XD [25] range-separated exchange-correlation density functional approximations were used, the former supplemented with the pairwise D3 dispersion correction [26].

The quantum-mechanics/molecular mechanics (QM/MM) calculations were performed using the ONIOM approach [27], so as to emulate the crystalline environment [28]. Molecular clusters were prepared with the CLUSTERGEN program [29], based on the experimental data, in which the C–H distances were fixed at the neutron-normalised values. The high-layer encompassed a single Cu₄ molecule, and was calculated at the ωB97XD level. In turn, the electronic embedding was constructed employing Hirshfeld charges obtained at the CAM-B3LYP/cc-pVDZ level of theory. All calculations were conducted using the GAUSSIAN package (GAUSSIAN16 edition) [30]. The analysis of one-particle transition density matrices (1-TDMs) [31,32] was carried out using the THEODORE program package (version 1.2) [33].

2.5. Time-Resolved Laue Studies

The time-resolved laser-pump/X-ray-probe data sets were collected at the 14-ID beamline in the BioCARS station at the Advanced Photon Source (APS; Chicago, Illinois, USA) [34] at a 15 keV undulator setting (polychromatic radiation, $\lambda$ ≈ 0.8–1.0 Å; single X-ray pulse length of about 80 ps). Crystals were mounted on glass fibres using Paratone N oil or epoxy glue, for 90 K and 225 K data set collections, respectively. Optimal laser power was selected on the basis of preliminary short scans and the so-called correlation plot analysis [35]. The 90 K data sets were collected using the Nd:YAG/OPO nanosecond laser setup with a 355 nm excitation wavelength, in turn, the 225 K data sets were collected using a Ti:sapphire laser tuned to 360 nm. The applied laser power varied within 0.7–1.8 mJ·mm⁻² per pulse for different measurements. Light-ON and light-OFF frames were recorded in the prompt succession to minimise the effect of long-range fluctuations in the beam’s position and/or intensity [36,37]. Raw data sets are available under the following DOI: 10.18150/repod.0196712. More details are available from the Supplementary Materials.

Data processing pipeline is based on the so-called RATIO method [38,39]. In this approach the final result of the data reduction are the light-ON and light-OFF reflection intensity ratios ($R_{\mathrm{o}}=I_{\mathrm{o}}^{\mathrm{ON}}/I_{\mathrm{o}}^{\mathrm{OFF}}={\left|F_{\mathrm{o}}^{\mathrm{ON}}\right|}^2/{\left|F_{\mathrm{o}}^{\mathrm{OFF}}\right|}^2$), which are then used to estimate “monochromatic” structure factor amplitudes not spurred by the wavelength dependence present in the original Laue diffraction data. The diffraction spot intensities from the Laue experiment were integrated with our new locally-written software [40], and later indexed by the modified version of the LAUEUTIL software package [41,42]. The resulting intensity ratios were averaged with the SORTAV program [43,44]. Finally, photodifference maps [45] were plotted based on the merged and scaled [46,47] data according to the following general equation:

$$\Delta {𝜚}_{\mathrm{pdiff}}\left(r\right)=\frac{1}{V}{\displaystyle \sum }_k\left(\sqrt{R_{\mathrm{o},k}}·\left|F_{\mathrm{o},k}^{\mathrm{mOFF}}\right|-\left|F_{\mathrm{o},k}^{\mathrm{mOFF}}\right|\right)e^{\mathrm{i}{\varphi }_{\mathrm{c},k}^{\mathrm{mOFF}}}{e}^{2\pi \mathrm{i}{h}_k·r}$$

(1)

where $R_{\mathrm{o},k}$ are synchrotron-derived intensity ratio values, $F_{\mathrm{o}}^{\mathrm{mOFF}}$ are the reference observed structure factors from the monochromatic light-OFF measurement, while ${\varphi }_{\mathrm{c}}^{\mathrm{mOFF}}$ constitute the calculated structure factor phases from the same monochromatic data. More details are available from the Supplementary Materials.

3. Results and Discussion

3.1. Crystal Structures of the Cu₄ and Cu₆ Complexes

The studied tetranuclear Cu₄ complex (i.e., [(PhCO₂)₄Cu₄]) crystallises in the triclinic $P\overline{1}$ space group with two molecules in the asymmetric unit (Figure 1). These molecules differ somewhat in the geometry of the metal core (

Table 1. Selected geometrical parameters describing the molecular cores of both independent molecules present in the Cu₄ crystal structure at different temperatures.

Molecule	$\mathrm{Bond} \mathrm{Distance}, \mathit{d}$/Å	$\mathrm{Temperature}, \mathit{T}$/K
		90	225	250	RT ¶
A	Cu1−Cu3	2.7061(9)	2.7140(5)	2.7141(6)	2.719(2)
	Cu1−Cu4	2.7335(7)	2.7564(7)	2.7547(6)	2.7625(9)
	Cu2−Cu3	2.7129(7)	2.7324(7)	2.7323(6)	2.7391(9)
	Cu2−Cu4	2.7325(9)	2.7573(5)	2.7592(6)	2.769(2)
	Cu1⋯Cu2 ¥	2.8726(8)	2.9251(7)	2.9351(6)	2.958(1)
	Cu3⋯Cu4 ‡	4.622(1)	4.6335(6)	4.6272(7)	4.630(2)
B	Cu5−Cu7	2.7256(9)	2.7401(6)	2.7426(7)	2.751(2)
	Cu5−Cu8	2.7025(7)	2.7199(8)	2.7182(7)	2.7264(9)
	Cu6−Cu7	2.7118(7)	2.7266(8)	2.7239(7)	2.7315(9)
	Cu6−Cu8	2.7113(9)	2.7215(6)	2.7240(7)	2.727(2)
	Cu5⋯Cu6 ¥	3.0797(9)	3.1450(6)	3.1527(7)	3.185(2)
	Cu7⋯Cu8 ‡	4.4668(8)	4.4560(8)	4.4509(7)	4.444(1)
Molecule	Valence Angle, θ/°	Temperature, T/K
		90	225	250	RT ¶
A	Cu3−Cu1−Cu4	116.37(2)	115.77(2)	115.58(2)	115.27(2)
	Cu3−Cu2−Cu4	116.17(2)	115.13(2)	114.83(2)	114.40(2)
	Cu1−Cu3−Cu2	64.03(2)	64.97(2)	65.22(1)	65.63(2)
	Cu1−Cu4−Cu2	63.41(2)	64.08(2)	64.32(1)	64.65(2)
B	Cu7−Cu5−Cu8	110.75(2)	109.39(2)	109.19(2)	108.47(2)
	Cu7−Cu6−Cu8	110.91(2)	109.75(2)	109.57(2)	109.01(2)
	Cu5−Cu7−Cu6	69.00(2)	70.24(2)	70.44(2)	71.04(2)
	Cu5−Cu8−Cu6	69.34(2)	70.62(2)	70.80(2)	71.47(2)

^¶ Room temperature. ^¥ Short diagonal. ^‡ Long diagonal.

), but they share the general structural features. The metal core of the molecule A is characterised by, on the average, slightly longer Cu−Cu bonds, however, the shorter diagonal of the formed rhomboid can still be classified as a metal-metal bond at 90 K (based on the van der Waals radii criteria), which is not the case as far as the second symmetry-independent molecule B is concerned. The metal core of the molecule A is also more regular and resembles a parallelogram with two longer (ca. 2.73 Å at 90 K) and two shorter edges (ca. 2.71 Å at 90 K). For the purpose of this study, the Cu₄ crystal structure was determined also at 225 K, 250 K, and RT in order to catch any structural changes which could be related to the temperature spectroscopic behaviour of the system. It appeared that, the analysed crystal structure does not undergo any phase transition in the temperature range between 90 K and room temperature (RT). In general, temperature influences the lattice and geometrical parameters in a typical way. Regarding the core shapes, the copper–copper distances get elongated except for the longer diagonal in the B molecule, which shortens with temperature rise. Furthermore, both metal cores become slightly more ‘square-like’, i.e., the obtuse angles diminish, whereas the acute ones increase (the average changes though do not exceed about 2°).

As already mentioned, the crystal structure of the Cu₆ complex (Figure 2) behaves unlike that of Cu₄ with changes of temperature. Although it also forms the triclinic $P\overline{1}$ crystal lattice, it is differently packed depending on temperature (Figure 2). Below 253 K the asymmetric unit contains a half of the Cu₆ molecule, which is located at the centre of symmetry. Between 253 K and 263 K a phase transition is observed, as described in the literature [11], leading to two independent halves of the Cu₆ complex comprising the asymmetric unit at higher temperatures (Figure 2). The crystal packing similarities and differences between the 293 K and at 173 K crystal structures of Cu₆ have already been discussed by Filatov et al. [11]. Our X-ray diffraction measurement conducted at 90 K confirms that there are no other phase transitions down to this temperature point. Geometrical parameters characterising the Cu₆ copper cores at 90 K and at RT are collected in

Table 2. Selected bond distances describing the metal cores’ geometries in the Cu₆ crystal structures at different temperatures.

$\mathrm{Bond} \mathrm{Distance}, \mathit{d}$/Å	$\mathrm{Temperature}, \mathit{T}$/K
	90	290 ¶	290 ¥
Cu1−Cu2	2.6817(5)	2.700(1)	2.693(1) §
Cu1−Cu3 ‡	2.7131(4)	2.747(1)	2.760(1) §
Cu2−Cu3	2.6687(4)	2.689(1)	2.697(1) §

1st molecule in ASU (contains Cu1, Cu2, and Cu3 atoms). ^¥ 2nd molecule in ASU (contains Cu4, Cu5, and Cu6 atoms). ^§ Values given for respective bonds of 2nd molecule as in the 1st molecule in ASU. ^‡ Symmetry transformations: −x + 1, −y + 2, −z + 1 (for molecule at 90 K), −x, −y + 2, −z + 1 (for 1st molecule at 290 K), −x + 2, −y + 1, −z (for 2nd molecule at 290 K).

. Again, the copper–copper distances tend to elongate with increasing temperature. The Cu₆ molecules do not exhibit the inter-core Cu⋯Cu short diagonal contacts, as indicated by the respective distances. The Cu−Cu bonds in Cu₆, however, are on average shorter than in the case of Cu₄. Additionally, in the case of the high-temperature phase, the symmetry-independent molecules are very much alike, in contrast to two molecules comprising ASU in the Cu₄ crystal structure. Furthermore, the geometries of all the Cu₆ species at both high- and low-temperature crystal forms resemble each other more than the Cu₄ symmetry-independent molecules.

3.2. Single-Crystal Luminescence Characterisation

In order to quantitatively relate spectroscopic features with the X-ray-derived crystal structures, multi-temperature time-resolved single-crystal spectroscopic experiments were performed for the studied systems. Such proceedings also eliminated problems encountered for powder samples which may contain amorphous phase impurities that affect their properties (e.g., excited states’ lifetimes). Our experiments revealed that crystals of the Cu₄ complex exhibit two emission bands in the visible-light spectral region, namely the red band, ~680 nm, and the green band, 546 nm (Figure 3,

Table 3. The Cu₄ complex solid-state luminescence lifetimes ($\tau$) and emission peak maxima (${\lambda }_{\mathrm{em}}$) obtained from the least-squares fit at various temperatures ($T$). ${\tau }_{\mathrm{l}}$ and ${\tau }_{\mathrm{s}}$ denote longer and shorter lifetime, respectively; “r” and “g” superscripts denote parameters for red- and green-light emission maxima, respectively.

$\mathit{T}$/K	${\mathit{\tau }}_s^r/\mathsf{\mu }\mathbf{s}$	${\mathit{\tau }}_l^r/\mathsf{\mu }\mathbf{s}$	${\mathit{\lambda }}_{\mathrm{em}}^r/\mathrm{nm}$	${\mathit{\tau }}_s^g/\mathsf{\mu }\mathbf{s}$	${\mathit{\tau }}_l^g/\mathsf{\mu }\mathbf{s}$	${\mathit{\lambda }}_{\mathrm{em}}^g/\mathrm{nm}$
90	11.6(3)	66.4(5)	718	15.3(4)	111.0(6)	547
150	5.2(1)	61.3(3)	682	10.4(2)	61.0(4)	546
200	2.5(3)	35.5(2)	673	5.4(1)	27.6(6)	546
250	2.13(4)	10.16(4)	668	− b	− b	− b
RT a	0.47(2)	1.65(2)	660	− b	− b	− b

^a RT—room temperature. ^b Impossible to determine with current experimental setup (emission decay is very fast).

). At high-temperature, the emission is clearly orange (250 K) to red (RT), but at lower temperatures it becomes yellow, yellow-green to intensively green at 90 K (Figure S1, Supplementary Materials [48]). Indeed, when taking a closer look at the emission spectra at different temperatures, at RT almost exclusively the low-energy red band is visible, whereas the very weak green-band signal can be spotted only in the short time scale. In turn, while the temperature is being decreased, the high-energy green band gradually becomes stronger. At 200 K, the green band is still much less intensive than the other one, however, below 150 K it is clearly dominant. At 90 K, the high-energy band is very strong, while the low-energy band is almost fully suppressed, which is reflected in a brightly green emission of the sample (Supplementary Materials). The numerical parameters describing the emission maxima and the estimated emission decay lifetimes at different temperatures are presented in Table 3.

It appears that the emission decay can be efficiently modelled by a bi-exponential function in the case of both band types. The temperature influences strongly the emission decay lifetimes, which are significantly shorter at high temperatures. The green band maximum does not shift with temperature, while the red band maximum shifts notably from about 715 nm at 90 K to 660 K determined at RT.

Interestingly, in the case of the related Cu₆ compound, crystals of which undergo the phase transition between 253 and 263 K, the emission maximum shifts only from 586 nm at 90 K to 577 nm at RT (Figure 4). Furthermore, the temperature has also weaker effect on the emission decay lifetime when compared to Cu₄ (

Table 4. The Cu₆ complex solid-state luminescence lifetimes ($\tau$) and emission peak maxima (${\lambda }_{\mathrm{em}}$) obtained from the least-squares fit at various temperatures ($T$). ${\tau }_{\mathrm{l}}$ and ${\tau }_{\mathrm{s}}$ denote longer and shorter lifetime, respectively.

$\mathit{T}$/K	${\mathit{\tau }}_s/\mathsf{\mu }\mathbf{s}$	${\mathit{\tau }}_l/\mathsf{\mu }\mathbf{s}$	${\mathit{\lambda }}_{\mathrm{em}}/\mathrm{nm}$
90	17.4(4)	117.9(7)	586
RT a	13.0(4)	79.0(3)	577

^a RT—room temperature.

).

Finally, it should be noted that significant Stokes shift and relatively long emission decay times (μs regime) observed for the studied complexes’ crystals, i.e., Cu₄ and Cu₆, suggest that in both cases, the emissive state is of triplet nature.

3.3. Theoretical Modelling

For the purpose of the described emission bands’ nature investigation, theoretical modelling and computations were performed. At first, it was checked how the ground state optimised molecular geometries compare to those found in the crystal lattice. The ground-state geometry optimizations were conducted using crystal structures as a starting point. Two approaches were compared, i.e., optimization of a single Cu₄ moiety in the gas phase and optimization of both Cu₄ molecules forming the asymmetric unit in the QM/MM approach using the ONIOM electronic embedding to emulate the effect of the crystal environment. The results of theoretical calculations are shown in

Table 5. Selected distances and angles for Cu₄: in ground state (S₀): comparison of experiment and theory. 90 K denotes experimental results (Table 1); QM/MM denotes modelled solid-state structures; CAM-B3LYP denotes theoretical isolated-molecule results (shown only once for molecule A entries).

Molecule	$\mathrm{Bond} \mathrm{Distance}, \mathit{d}$/Å	90 K	QM/MM	CAM-B3LYP
A	Cu1−Cu3	2.7061(9)	2.735	2.738
	Cu1−Cu4	2.7335(7)	2.722	2.738 *
	Cu2−Cu3	2.7129(7)	2.734	2.738 *
	Cu2−Cu4	2.7325(9)	2.758	2.738 *
	Cu1⋯Cu2 ¥	2.8726(8)	2.846	2.911
	Cu3⋯Cu4 ‡	4.622(1)	4.677	4.638
	Cu1−O1	1.867(1)	1.872	1.853
	Cu2−O8	1.876(1)	1.881	1.853 *
	Cu3−O7	1.844(1)	1.843	1.844
	Cu4−O2	1.855(2)	1.851	1.844 *
B	Cu5−Cu7	2.7256(9)	2.690	−
	Cu5−Cu8	2.7025(7)	2.704	−
	Cu6−Cu7	2.7118(7)	2.746	−
	Cu6−Cu8	2.7113(9)	2.732	−
	Cu5⋯Cu6 ¥	3.0797(9)	3.128	−
	Cu7⋯Cu8 ‡	4.4668(8)	4.445	−
	Cu5⋯O16	1.855(1)	1.854	−
	Cu6⋯O11	1.852(2)	1.853	−
	Cu7⋯O15	1.864(1)	1.868	−
	Cu8⋯O12	1.864(1)	1.865	−
Molecule	Valence Angle, θ/°	90 K	QM/MM	CAM-B3LYP
A	Cu3−Cu1−Cu4	116.37(2)	117.97	115.77
	Cu3−Cu2−Cu4	116.17(2)	116.76	115.77
	Cu1−Cu3−Cu2	64.03(2)	62.71	64.23
	Cu1−Cu4−Cu2	63.41(2)	62.56	64.23
B	Cu7−Cu5−Cu8	110.75(2)	111.00	−
	Cu7−Cu6−Cu8	110.91(2)	108.47	−
	Cu5−Cu7−Cu6	69.00(2)	70.26	−
	Cu5−Cu8−Cu6	69.34(2)	70.27	−

^¥ Short diagonal. ^‡ Long diagonal. * These bonds are identical in the gas-phase-optimised molecule.

, and in the Supplementary Materials.

In general, the agreement between the experiment and theory appears to be satisfactory. Both tested range-separated functionals, ωB97XD and CAM-B3LYP, yielded similar optimised gas-phase geometry of the ¹A ground state exhibiting the $D_2$ symmetry ($222$ in crystallographic notation), which closely resembles the experimental geometries. In turn, QM/MM correctly imitates distortions from the $D_2$ symmetry of both independent molecules constituting the asymmetric unit (the A and B molecules), including different shapes of the Cu4-cores. The most significant differences between the gas phase and QM/MM results, however, concern the organic ligands, as illustrated in Figure 5.

Having received the above overview of the approach and functional performance for the ground-state of Cu₄, lowest excited states of the studied complex were derived using the TDDFT method.

Table 6. Lowest-energy triplet excited states computed for a single Cu₄ molecule for both the isolated molecule and QM/MM results. Symmetry labels refer to the isolated-molecule CAM-B3LYP results for the complex exhibiting $D_2$ point-group symmetry.

State	Method & Excitation Energy/eV
	CAM-B3LYP (isol.)	QM/MM (mol. A)	QM/MM (mol. B)
13A	3.12	3.21	3.16
13B1	3.27	3.32	3.35
13B2	3.27	3.35	3.36
23A	3.28	3.36	3.37
13B3	3.28	3.37	3.37
23B1	3.32	3.39	3.46
23B2	3.55	3.65	3.57
33A	4.12	4.12	4.14
23B3	4.15	4.22	4.16
33B1	4.23	4.26	4.23

presents the first ten triplet excited states calculated for the Cu₄ species, both in the gas phase and in the molecular environment.

The excitation energies obtained for the isolated complex in the $D_2$ symmetry are comparable to these derived for the embedded complexes with distorted-core geometries. The first excited ³A state involves excitations from HOMO, HOMO-1, and HOMO-2 to LUMO and several higher-lying orbitals. The frontier molecular orbitals of Cu₄ are shown in Figure 6, i.e., HOMO of the antibonding character and the bonding LUMO (see also Figure S5). As indicated by the orbital population analysis, both the initial and final molecular orbitals are composed mainly of copper d orbitals, which suggests that ³A has a distinct cluster-centred character. Directly above 1³A, there is a set of close-lying excited states, three of the ³B symmetry and one of the ³A symmetry. The corresponding excitation amplitudes are distributed among configurations of a ligand-ligand and core-ligand character.

To gain insight into the nature of the computed excited states, the one-particle transition density matrix (1-TDM) obtained at the TDDFT level of theory was analysed. In particular, the concept of charge transfer numbers introduced by Plasser & Lishka [31] was employed, as well as its extension to a transition-metal complex case [32]. When two molecular fragments A and B are considered, the charge transfer number is defined as:

$${\mathsf{\Omega }}_{\mathrm{AB}}=\frac{1}{2}{\displaystyle \sum }_{\mu \in \mathrm{A}}{\displaystyle \sum }_{\nu \in \mathrm{B}}\left[{\left(D^{0I}S\right)}_{\mu \nu }{\left(S{D}^{0I}\right)}_{\mu \nu }+D_{\mu \nu }^{0I}{\left(S{D}^{0I}S\right)}_{\mu \nu }\right]$$

(2)

where the sum runs over all atomic basis functions $\mu$ and $\nu$ on fragments A and B, respectively. $D^{0I}$ stands for 1-TDM, while $S$ is the overlap matrix. The total charge transfer (CT) character is given as the sum of the off-diagonal elements of the CT matrix:

$${\omega }_{\mathrm{CT}}=\frac{1}{\mathsf{\Omega }}{\displaystyle \sum }_{\mathrm{B}\ne \mathrm{A}}{\mathsf{\Omega }}_{\mathrm{AB}}$$

(3)

where the $\mathsf{\Omega }={{\displaystyle \sum }}_{\mathrm{AB}}{\mathsf{\Omega }}_{\mathrm{AB}}$ normalization factor corresponds to the squared norm of 1-TDM. The matrix can be visualized in a direct manner yielding the so-called electron-hole correlation plots ($\mathsf{\Omega }$-matrix plots) [49]. The ${\omega }_{\mathrm{CT}}$ index may be partitioned into metal centred (MC), ligand centred (LC), metal-to-ligand (MLCT), ligand-to-metal (LMCT), and ligand-to-ligand (LLCT) charge-transfer contributions [32]. Consequently, the total CT index can be expressed as follows: ${\omega }_{\mathrm{CT}}={\omega }_{\mathrm{MLCT}}+{\omega }_{\mathrm{LMCT}}+{\omega }_{\mathrm{LLCT}}$. For the purpose of the described analysis, a single Cu₄ molecule was divided into five fragments, i.e., the Cu₄ metal core and four benzoic acid ligands. In Figure 7 the obtained electron-hole correlation plots for the first ten triplet excited states of the gas-phase-optimised Cu₄ complex are presented, while Table S3 contains the corresponding excitation energies and the 1-TDM analysis results.

Based on the information from 1-TDM, it can be concluded that two types of triplet states are distinguishable. The first type gathers the core-centred states with significant contributions from the metal-to-ligand charge-transfer excitations. The second type includes states of Frenkel exciton nature involving $\mathsf{\pi }\to {\mathsf{\pi }}^{*}$ excitation localised on the ligands (Figure 7).

In this view, the lowest-lying ³A triplet together with states from 6th to 9^th can be classified as the first type, i.e., they all share the dominant core-centred character, which is reflected in the notable ${\omega }_{\mathrm{MC}}$ values ranging from 0.7 to 0.8, and in the MLCT contributions being above 0.1. The mixed charge transfer character is also supported by the number of participating fragments (referred to as PR) ranging between 1.21 and 2.56. The largest CT index, indicated by grey off-diagonal elements in the $\mathsf{\Omega }$-matrix plot (Figure 7), is observed for the 9th state. In turn, deviation from the $D_2$ symmetry results in a stronger CT character of all these states calculated for the QM/MM geometries, manifested by larger MLCT and LMCT contributions (for details see Table S3). In particular, in the first excited state ${\omega }_{\mathrm{MLCT}}$ amounts to 0.202, whereas it equals 0.165 in the $D_2$ case. The delocalisation of the excitation from the complex’s core to one of the ligands affects also the PR value, which increases from 1.3 to 2.0.

The second type of triplet states encompasses states from the 2nd to 5th, as well as, the 10th triplet state. The local character of these excitations can be deduced from the electron-hole correlation plots dominated by diagonal elements, the ${\omega }_{\mathrm{CT}}$ values being close to zero, and the number of participating fragments around 3.5 (Figure 7, Table S3).

The nature of excited states may also be analysed by inspection of natural transition orbitals (NTOs). NTOs are obtained from the singular value decomposition of 1-TDM:

$$D^{0I,\left[\mathrm{MO}\right]}=U·\mathrm{diag}\left(\sqrt{{\lambda }_1},\sqrt{{\lambda }_2},\dots \right)·V^T$$

(4)

where matrices $U$ and $V$ contain hole (initial) and particle (final) orbitals, respectively. The advantage of NTOs over canonical orbitals is that the former provide a more compact representation of the excitation, i.e., typically only a few configurations are needed to describe the electronic transition. In Figure 8 we present the dominant NTO pairs for the 1³A and 1³B₁ states. Examination of NTOs corroborates the character of triplet excitations as deduced from the $\mathsf{\Omega }$-matrix plots. In the ³CC states the electron and hole are localised primarily in the core region, and the antibonding-to-bonding transition is clearly visible. The contributions from 2p orbitals of oxygen atoms correspond to the MLCT transitions. In turn, visual inspection of NTOs computed for the 1³B₁ state confirms the $\mathsf{\pi }\to {\mathsf{\pi }}^{*}$ character of excitations localised on the benzoic acid fragments.

Finally, to model the most probable structural changes occurring during the excitation, two lowest-lying triplets were optimised using the analytic gradients from the TDDFT calculations. The selected optimised geometrical parameters are presented in

Table 7. Comparison of selected ground (${\mathrm{S}}_0$) and excited triplet-state (${\mathrm{T}}_1$ & ${\mathrm{T}}_2$) geometries. QM/MM denotes modelled solid-state structures; CAM-B3LYP denote theoretical isolated-molecule results (shown only once for molecule A entries). See also Figures S3 and S4 in the Supplementary Materials.

Molecule	$\mathrm{Bond} \mathrm{Distance}, \mathit{d}$/Å	QM/MM	QM/MM	CAM-B3LYP	CAM-B3LYP	CAM-B3LYP
		${\mathrm{S}}_0$	${\mathrm{T}}_1$	${\mathrm{S}}_0$	${\mathrm{T}}_1$	${\mathrm{T}}_2$
A	Cu1−Cu3	2.735	2.438	2.738	2.498	2.665
	Cu1−Cu4	2.722	2.579	2.738 *	2.498 *	2.665 *
	Cu2−Cu3	2.734	2.452	2.738 *	2.498 *	2.665 *
	Cu2−Cu4	2.758	2.636	2.738 *	2.498 *	2.665 *
	Cu1⋯Cu2 ¥	2.846	2.608	2.911	2.623	2.372
	Cu3⋯Cu4 ‡	4.677	4.325	4.638	4.252	4.773
	Cu1−O1	1.872	1.946	1.853	1.864	1.917
	Cu2−O8	1.881	1.955	1.853 *	1.864 *	1.917 *
	Cu3−O7	1.843	1.874	1.844	1.852	1.932
	Cu4−O2	1.851	1.841	1.844 *	1.852 *	1.932 *
B	Cu5−Cu7	2.690	2.441	−	−	−
	Cu5−Cu8	2.704	2.524	−	−	−
	Cu6−Cu7	2.746	2.480	−	−	−
	Cu6−Cu8	2.732	2.547	−	−	−
	Cu5⋯Cu6 ¥	3.128	2.724	−	−	−
	Cu7⋯Cu8 ‡	4.445	4.188	−	−	−
	Cu5⋯O16	1.854	1.907	−	−	−
	Cu6⋯O11	1.853	1.933	−	−	−
	Cu7⋯O15	1.868	1.892	−	−	−
	Cu8⋯O12	1.865	1.859	−	−	−
Molecule	Valence Angle, θ/°	QM/MM	QM/MM	CAM-B3LYP	CAM-B3LYP	CAM-B3LYP
		${\mathbf{S}}_{\mathbf{0}}$	${\mathbf{T}}_{\mathbf{1}}$	${\mathbf{S}}_{\mathbf{0}}$	${\mathbf{T}}_{\mathbf{1}}$	${\mathbf{T}}_{\mathbf{2}}$
A	Cu3−Cu1−Cu4	117.97	119.10	115.77	116.65	127.15
	Cu3−Cu2−Cu4	116.76	116.40	115.77	116.65	127.15
	Cu1−Cu3−Cu2	62.71	64.46	64.23	63.35	52.85
	Cu1−Cu4−Cu2	62.56	60.01	64.23	63.35	52.85
B	Cu7−Cu5−Cu8	111.00	115.01	−	−	−
	Cu7−Cu6−Cu8	108.47	112.80	−	−	−
	Cu5−Cu7−Cu6	70.26	67.22	−	−	−
	Cu5−Cu8−Cu6	70.27	64.97	−	−	−

^¥ Short diagonal. ^‡ Long diagonal. * All bonds are identical because the molecule is symmetric.

. The calculations were carried out both in the gas phase and in the crystal environment, where possible. In each case, frequency calculations confirmed the presence of the minima. The first excited ${\mathrm{T}}_1$ state structures obtained in different approaches remain in close agreement. The second excited state, denoted as ${\mathrm{T}}_2$, was determined only for the $D_2$ symmetry (gas phase) Cu₄ complex. The ${\mathrm{T}}_2$ optimisation was conducted using two approaches, which led to identical results, i.e., either by converging the 6th root in TDDFT, or by optimisation of the unrestricted Kohn-Sham (UKS) determinant with a deformed Cu₄-core as a starting point. It was not possible to reach the excited state minima corresponding to the $\mathsf{\pi }\to {\mathsf{\pi }}^{*}$ excitations, for which geometrical changes should occur primarily on the organic parts of the ligands.

It appeared that both ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ states involve significant changes in the Cu₄ core compared to ${\mathrm{S}}_0$ (Table 7, Figure S3), which is consistent with the ³CC character of the first and 6th excited states predicted from the 1-TDM analysis (Figure 7 and Figure 8). Among these, the core contraction was estimated to be notably larger for the ${\mathrm{S}}_0\to {\mathrm{T}}_1$ transition, for which the Cu−Cu distance is shortened by 0.240 Å upon excitation (for the gas-phase-optimised Cu₄ geometries; for ${\mathrm{T}}_2$ it is shortened by 0.073 Å; Table 7). In the case of ${\mathrm{T}}_2$, the changes in the metal core were predicted to be smaller, however, more significant elongation of the Cu−O bonds with respect to the ${\mathrm{S}}_0$ state was observed (1.93 Å vs. 1.85 Å, respectively; Table 7). This finding supports the presence of non-negligible MLCT and/or LMCT contribution to the ³CC state.

The TDDFT excitation energies from the ground state to the first triplet state (referred to as 1st ${\mathrm{S}}_0\to \mathrm{T}$) calculated for the optimised geometries of the ${\mathrm{S}}_0$, ${\mathrm{T}}_1$, and ${\mathrm{T}}_2$ states are gathered in

Table 8. The TDDFT-computed excitation energies from the ground state to the first triplet state calculated for the optimised geometries of the ${\mathrm{S}}_0$, ${\mathrm{T}}_1$, and ${\mathrm{T}}_2$ states. CAM-B3LYP denotes theoretical isolated-molecule results, and QM/MM denotes modelled solid-state structures; $\Delta \mathrm{SCF}$ is the difference between the electronic energy of the triplet state and energy singlet states (both calculated at the triplet minimum-energy geometry).

Method	State	$1^{\mathrm{st}} S_0\to T/\mathrm{eV}$	$1^{\mathrm{st}} S_0\to T/\mathrm{nm}$	$\Delta \mathrm{SCF}/\mathrm{nm}$
CAM-B3LYP (isol.)	${\mathrm{T}}_1$ (13A)	1.952	635	592
CAM-B3LYP (isol.)	${\mathrm{T}}_2$ (23B1)	2.149	578	523
QM/MM (mol. A)	${\mathrm{T}}_1$	2.077	597	−
QM/MM (mol. B)	${\mathrm{T}}_1$	2.001	618	−

. Additionally, the $\Delta \mathrm{SCF}$ values, i.e., the difference between the electronic energy of the triplet state and the energy of respective singlet states (both energies calculated at the triplet minimum-energy geometry), are reported. In the case of the ${\mathrm{T}}_1$ geometry, the lowest triplet excited state occurs at 1.952 eV (635 nm), while the corresponding $\Delta \mathrm{SCF}$ value is equal to 592 nm. The QM/MM calculations predicted this state at 2.077 eV (597 nm) for the A molecule, while at 2.001 eV (618 nm) for B. The emission from the ${\mathrm{T}}_1$ state computed using the TDDFT approach matches the experimental low-energy band observed at 660−715 nm. The identification of the second emitting state is less straightforward. In the case of the ${\mathrm{T}}_2$ geometry the lowest triplet state was placed by TDDFT at 2.149 eV (578 nm), while the $\Delta \mathrm{SCF}$ amounted to 523 nm. Thus, the anticipated emission from ${\mathrm{T}}_2$ in the ${\mathrm{D}}_2$ symmetry is close to the experimental value of 546 nm. It should be noted, however, that upon distortion of the $D_2$ symmetry, which is observed in crystals, as well as in the QM/MM-optimized structures, the two types of states gain significantly more MLCT and LMCT contributions. Furthermore, it was not possible to identify a minimum on the excited potential energy surfaces complying with the states dominated by the $\mathsf{\pi }\to {\mathsf{\pi }}^{*}$ excitations.

3.4. Time-Resolved X-ray Laue Diffraction Results

Determination of geometry changes occurring in the Cu₄ complex in the crystal form at 90 K and 225 K upon excitation may provide us some indication about the nature of the dominant excited states at low and high temperatures. This goal can be realised via a time-resolved laser-pump/X-ray-probe Laue technique, especially for heavier atoms rich in electrons [50]. Nevertheless, even some information on the copper core deformation would be of help, as the changes in the cluster-centre geometry confronted with the theoretical results could give us premises about the emission origins.

In the studied case, the full response-ratio refinement [51] was unfortunately not possible, most probably due to the rather low completeness of the collected data (35% and 17% for 90 K and 225 K data, respectively), as a result of low conversion, low space-group symmetry of the sample and the examined crystals’ shape. Nevertheless, some meaningful qualitative conclusions can still be drawn. The obtained photodifference maps, computed for the copper cores, are presented in Figure 9. The negative peaks, as expected, are localised on copper atoms’ positions, which shows that these atoms shifted/moved upon excitation. The similarity of photodifference maps obtained from two independent measurements at both 90 and 225 K is striking. This suggests the same excited state was captured in both experiments and also indicates good reproducibility of the results. Since the pump-probe delay was set to several ns, while the studied excited state lifetimes are in the μs regime (Table 3), such explanation is rational. The measurement could have been faster than the conversion to the final emissive state. In such a case, either some singlet excited state was captured, or the high-energy (“green”) triplet excited state. It also seems that most of the peaks are located closer to the centre of the cluster core, especially for molecule B (see, e.g., the large peak next to the Cu7 atom), which suggests its contraction. For this molecule, more peaks are visible than for A when the same isocontour values are applied. This suggests that the molecule B, exhibiting longer “short” diagonal Cu⋯Cu contact, should undergo more pronounced core contraction when excited, which is indeed observed in the ${\mathrm{T}}_1$ QM/MM results. Nevertheless, the experimental geometrical changes are not straightforward. Regarding the theoretical results, one may conclude that the low-energy excited state should be characterised by more significant changes of the copper core shape which becomes more quadratic (Table 7), whereas the high-energy excited state is expected to exhibit more emphasized Cu−O bond elongation and less notable copper atoms’ distortions from the GS geometry (Supplementary Materials). For both ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$ states, the contraction of all Cu−Cu bonds is observed and also the shorter diagonal gets contracted (Table 7).

3.5. Cu₄ and Cu₆ Comparison

As already mentioned, despite the similarity of Cu₄ and Cu₆, no luminescence thermochromism was observed in the latter case. In an attempt to explain such behaviour, the first few excited states of the Cu₆ complex were calculated and analysed. It appears that the nature of the first singlet and triplet states obtained for Cu₄ and Cu₆ is qualitatively very much alike. Namely, the triplet states have either a core-centred or ligand-centred character (see the discussion in Section 3.3, and Figures S6, S11 and S12 and Tables S6 and S7), whereas the first singlets are core-centred with significant MLCT charge-transfer contributions (Figures S7, S9 and S10 and Tables S3 and S5). Clearly, without direct probing of the excited-state dynamics, it is not straightforward to establish whether thermochromism occurs for a single Cu₄ molecule. If this was the case, the lack of this phenomenon in Cu₆ could be attributed, for instance, to a lower energy barrier between the emissive triplet states. Another possibility is that the thermochromism arises due to crystal packing effects, which are markedly different in the studied structures.

In order to explore the role of molecular packing in the Cu₄ and Cu₆ crystals, two closest-neighbour complex molecules were selected in both structures. The lowest-lying excited triplet states of such Cu₄ and Cu₆ dimers characterised in terms of natural transition orbitals and electron-hole correlation plots are shown in Figure 10. The dimer geometries were taken directly from the crystal structures. Inspection of Figure 10 reveals different characteristics of the excited states in the Cu₄ and Cu₆ dimers. In the former case excitations are localised on the separate monomers, whereas in the latter they are delocalised on both monomers forming exciton resonance states (no charge transfer between the monomers is observed, and each excited state of the Cu₆ dimer is doubly degenerate). Analogous behaviour was confirmed for singlet states (Figures S8, S13 and S14 and Tables S8 and S9).

The significant difference between the nature of excited states of Cu₄ and Cu₆ dimers indicates that the distinct spectroscopic behaviour of the two complexes in the solid state could be to some extent attributed to the mutual molecular arrangement in the crystal lattice. Nevertheless, the impact of such intermolecular interactions remains debatable due to the lack of unequivocal evidence on the matter.

4. Summary and Conclusions

Although temperature-dependent phosphorescence observed and characterised by us for crystals of the studied tetranuclear copper complex Cu₄ is similar to the luminescence thermochromism reported for the Cu₄I₄-core-containing compounds [52,53,54,55], its nature differs substantially between the two systems due to cluster cores chemical and geometrical features. In Cu₄, four copper atoms form almost flat parallelogram-like cluster centre instead of a cubane copper-iodine core characteristic for the Cu₄I₄-type molecules. In the latter case, the dual emission was attributed to excited states of different character: the low-energy band was assigned to the low-lying emissive ³CC state involving pronounced core geometry relaxation, whereas the high-energy band to a halide-to-ligand charge transfer (³XLCT) state, in which only minor geometrical changes occur in the core region. In the case of the studied ${\mathrm{Cu}}^{\mathrm{I}}$ benzoate crystals, a similar low-lying cluster-centred triplet excited state was identified, ${\mathrm{T}}_1$. The emission from the ${\mathrm{T}}_1$ state predicted in TDDFT (~635 nm) matches the experimental red band observed at 660–715 nm. In contrast, the indication of the high-energy “green” emissive state, active at low temperature, appeared to be much more problematic. First of all, it was not possible to identify a minimum on the excited potential energy surfaces complying with the states dominated by the $\mathsf{\pi }\to {\mathsf{\pi }}^{*}$ excitations, lying directly above the 1³A₁ (³CC) state. The next reached excited state, ${\mathrm{T}}_2$ in the ${\mathrm{D}}_2$ symmetry, occurred energetically close to the experimental value of 546 nm. It should be noted, however, that upon distortion of the ${\mathrm{D}}_2$ symmetry, which is observed in crystals, the two types of states gain significantly more MLCT and LMCT contributions. In both states, ${\mathrm{T}}_1$ and ${\mathrm{T}}_2$, the cluster core is notably contracted when compared to the ground state, which is more emphasised in the case of ${\mathrm{T}}_1$. Photocrystallographic results supported the computationally predicted core contraction upon excitation.

Another issue was the lack of luminescent thermochromism in the case of the related Cu₆ crystal structure. Single-molecule computations of the first few excited states provided results analogous to these obtained for Cu₄. The differences between the two solid-state systems appeared not until molecular closest dimers from crystal structures were computationally examined. In Cu₆, the exciton delocalisation in resonance states was predicted, which was not the case for Cu₄. Clearly, without direct probing of the excited-state dynamics, it is not straightforward to establish whether thermochromism occurs for a single Cu₄ molecule. Furthermore, it would also be very challenging, if at all possible, to verify a single Cu₄ or Cu₆ molecule’s spectroscopic behaviour experimentally. If a single Cu₄ cluster is emissive, the lack of this phenomenon in Cu₆ could be attributed, for instance, to a lower energy barrier between the emissive triplet states. On the other hand, the excited states’ delocalisation over dimers expected for Cu₆ in a crystal lattice could facilitate, or strengthen, the possible transition between the high- and low-energy states, resulting in its shorter time-scale, or enhanced coupling between the excited states, leading to the observed low-energy emission band. Nevertheless, the mechanism behind the luminescent behaviour of the Cu₄ and Cu₆ complexes remains disputable at places due to the lack of unequivocal evidence.