Structural resilience in organic–inorganic stacked assemblies: sulfur-mediated self-compensating interaction and metal identity masking in group 10 dithiocarbamate cocrystals with tetracyanobenzene

Abstract

This work investigates the relative influence of metal identity versus ligand environment in determining supramolecular architecture of stacked hybrid organic–inorganic systems. We demonstrate a sulfur-mediated self-compensating mechanism that masks metal-specific electronic differences, enabling ligand-controlled assembly over conventional metal-directed organization. Through systematic investigation of group 10 metal dithiocarbamate cocrystals [M(S₂CNR₂)₂] (M = Ni, Pd, Pt; R₂ = alkyl) with 1,2,4,5-tetracyanobenzene, we reveal structural resilience—identical parallel-displaced supramolecular architectures are maintained across the entire Ni–Pd–Pt triad despite fundamental differences in d_z²-orbital nucleophilicity that typically govern such assemblies. This contradicts established principles where metal variation should produce distinctly different structural outcomes. Comprehensive quantum chemical analysis using QTAIM, IGM, ETS-NOCV, and energy decomposition methods reveals that S atoms from the dithiocarbamate ligands actively neutralize inherent metal-specific properties, creating electronically equivalent {MS₄} building blocks. Despite different metals, remarkably consistent interaction energies (−40.6 to −42.8 kcal mol⁻¹) and metal contributions (13.9–15.9%) demonstrate functional equivalence in the supramolecular recognition. Our study establishes ligand-mediated metal identity masking as a design principle for creating structurally predictable metal-involving materials regardless of metal center.

---

1. Introduction

Stacking plays a crucial role in determining the supramolecular architecture of flat molecular systems. These noncovalent interactions (NCIs) between planar moieties have been extensively studied in supramolecular chemistry, molecular recognition, and materials science.^1–6 The nature of stacking has evolved beyond the classical π⋯π model to encompass more complex phenomena, including π-hole⋯π interactions with strong charge transfer.^7–9 Recent discoveries have revealed a remarkable dichotomy in stacking-directing forces: identical stacked motifs can arise from distinctly different combinations of underlying interactions.^10,11

Hybrid organic–inorganic cocrystals represent a fascinating class of materials that integrate planar molecular systems through stacking to generate emergent properties substantially different from those of individual coformers.^12–14 These characteristics arise from unique intermolecular interactions and electronic environments created within the cocrystal assembly. In these systems, metal sites introduce additional complexity through metal-involving NCIs, such as tetrel bonding via metal d-orbitals, which can significantly influence stacking behavior.^14–17 Such assemblies enable enhanced luminescence,^18,19 improved optoelectronic efficiency,²⁰ novel supramolecular architectures,^14,21,22 and emerging properties including photothermal conversion and circularly polarized luminescence.^23–25

The role of metals in hybrid stacking has been considered particularly profound and structure-determining. Pioneering work by Zarić and colleagues has identified the nature of stacking between organic aromatic compounds and planar metal complexes.^26–35 Our previous investigations have demonstrated that square-planar group 10 metal species participate in structure–determining interactions through their d_z²-metal orbitals with remarkable efficiency.^{15–17,36–38} For instance, {d_z²-M^IIS₄} entities in dithiocarbamate complexes act as integrated five-center nucleophiles toward π-hole donors, forming characteristic reverse sandwich structures.¹⁵ Metal-involved tetrel bonding has been identified as a principal component in stacking interactions between platinum(II) square-planes and perfluorinated aromatics.¹⁶

These studies have consistently established metal identity as the critical and dominant determinant of supramolecular architecture. The electronic properties of the metal center, particularly d_z²-nucleophilicity, have been recognized as primary structure-directing factors, with the progression from Ni^II → Pd^II → Pt^II typically correlating with increasing d_z²-nucleophilicity, leading to predictable variations in interaction strength and resulting crystalline arrangements.³⁹ This metal-centric model has guided rational design in metal-involving crystal engineering (for recent studies see ref. 40–43), with metal selection being considered the primary determinant of structural outcomes.

However, recent investigations into halogen bonding properties of sulfur atoms in dithiocarbamate systems have revealed that ligand environments can play significant roles in modulating intermolecular NCIs.⁴⁴ The sp³-hybridized S atoms have demonstrated remarkable capability as halogen bond acceptors, suggesting that ligand-based interactions might compete with or even override metal-based effects.⁴⁴ This raises a fundamental question that challenges the metal-centric approach: can ligand environments be strategically designed to mask inherent metal-specific differences? Such capability would represent a shift from metal-directed to ligand-controlled assembly, enabling creation of structurally predictable materials regardless of metal identity—a principle we term “metal identity masking”.

The relative influence of metal identity versus ligand compensation effects remains poorly understood, particularly in systems where multiple NCIs compete. Metal dithiocarbamate complexes provide an ideal platform for investigating these issues due to their versatile coordination capabilities and ability to stabilize group 10 metals in square-planar geometries.^45,46 The group 10 metal series (Ni, Pd, Pt) was deliberately selected for this investigation because these metals form square-planar dithiocarbamate complexes with identical coordination geometry, producing isostructural cocrystals that allow for systematic evaluation of metal-centered electronic effects within an essentially invariant supramolecular framework. This design choice enables clear isolation of electronic effects from structural variables.

In this work, we address this fundamental question by investigating cocrystallization behavior of group 10 metal dithiocarbamates [M(S₂CNEt₂)₂] (M = Ni, Pd, Pt) with 1,2,4,5-tetracyanobenzene (TCB) (Fig. 1). Through systematic variation across the Ni–Pd–Pt triad while maintaining identical ligand environments, we probe whether ligand-based interactions can neutralize metal-specific electronic differences that conventionally govern such assemblies.

Fig. 1 Studied coformers.

Our findings reveal unexpected structural resilience that fundamentally challenges the metal-centric model of organic–inorganic assembly. Despite fundamental differences in d_z²-orbital nucleophilicity across the Ni–Pd–Pt series—differences that typically produce distinctly different structural outcomes—all cocrystals maintain identical parallel-displaced supramolecular architectures. We demonstrate that S atoms from dithiocarbamate ligands actively neutralize inherent metal-specific properties through a sulfur-mediated self-compensating mechanism (i.e. mutual electronic compensation between sulfur donor atoms and the metal center, which effectively masks metal-specific electronic characteristics in the resulting supramolecular assemblies), creating electronically equivalent {MS₄} building blocks. This establishes ligand-mediated metal identity masking as a design principle for creating structurally predictable metal-involving materials regardless of metal center, enabling a shift from metal-directed to ligand-controlled supramolecular assembly.

2. Results and discussion

2.1. Cocrystals growth and X-ray structures

Despite systematic variation of metal identity across the Ni–Pd–Pt triad, the resulting cocrystals demonstrate remarkable structural resilience, maintaining nearly identical supramolecular architectures. Dithiocarbamate complexes 1–4 were cocrystallized with TCB in a 1 : 1 molar ratio. The cocrystals were formed by slow evaporation of their solutions at room temperature (RT) (for detailed procedures refer to the Experimental section 4.2). This process yielded cocrystals designated as (1–4)·TCB. The structures of these cocrystals were analyzed using single-crystal X-ray diffractometry (XRD; for details refer to the Experimental section 4.3) and the resulting structural data are presented in Fig. 2 and Fig. S1–S4 (the SI).

Fig. 2 Fragment of crystal packing of 1·TCB (left panel), 2·TCB (middle panel), and 3·TCB (right panel), demonstrating parallel-displaced alternating stacking of 1 (2, or 3) and TCB. Intermolecular metal⋯C short contacts are shown by dotted lines.

We found that among all obtained cocrystals, only 3·TCB displays room-temperature photoluminescence with an emission maximum at 623 nm, while both the isolated complex 3 and other cocrystals show no emission under ambient conditions. Given the modest quantum yield (0.6%), we note this unique emergent property for potential future investigations into supramolecular assembly effects on photophysical behavior, with characterization provided in section S2 of the SI, whereas experimental details provided in section 4.5.

The crystal structures of 1·TCB, 2·TCB, and 3·TCB are isomorphic, exhibiting similar cell parameters and packing motifs (Fig. 2 and Table S1 in the SI). This structural preservation across different metal centers challenges the conventional expectation that metal identity should be the primary structure-directing factor in such assemblies. All these structures comprise seven crystallographically independent units: three TCBs, two complete molecules of 1 (or 2, 3), and two halves of 1 (or 2, 3). Each crystallographically independent molecule is designated by a unique letter code, as shown in Fig. 2. In contrast, 4·TCB consists of one complete molecule of 4, two halves of 4, and two TCBs.

The structures of (1–4)·TCB display similar supramolecular organization: infinite parallel-displaced stacks composed of alternating metal complex and TCB molecules. This consistent stacking behavior, maintained despite metal variation, suggests that ligand-based interactions effectively compensate for inherent metal-specific differences. Within these stacks, the molecules are linked via C⋯M, C⋯S, and CCN⋯CS2C short contacts. The prevalence of C⋯S contacts indicates the significant role of S atoms in mediating intermolecular NCIs. Additionally, in 4·TCB, NCN⋯HCH hydrogen bonds are present. Molecules from neighboring stacks are interconnected through C–H⋯NCN and C–H⋯S hydrogen bonds.

The observed structural similarities across the metal series provide the first indication of a sulfur-mediated compensating mechanism that masks metal identity effects, setting the stage for detailed analysis of the underlying NCIs (section 2.3).

2.2. Noncovalent interactions in the structures of (1–4)·TCB

Analysis of the NCI patterns reveals how S-mediated compensation operates at the molecular level to achieve structural resilience across different metal centers.

Despite similarities in their structure–determining NCIs, the crystallographically independent units in 1·TCB, 2·TCB, and 3·TCB exhibit varying geometric parameters for these contacts. In the structures of (1–4)·TCB, metal complexes and TCB molecules are primarily linked by one C_arene⋯M, two C_arene⋯S_S2C, and two C_CN⋯C_S2C contacts (Fig. 3 and S5–S7). The consistent presence of multiple C⋯S contacts across all structures underscores the pivotal role of S atoms in maintaining uniform intermolecular interactions regardless of metal identity. Slightly different motifs were found in 1·TCB, 2·TCB and 3·TCB: two C_arene⋯S_S2C contacts involve two para-C atoms of the TCB ring (Fig. 3 and S5–S7). In 4·TCB, the stacking occurs via one (C,C_arene)⋯M, one C_arene⋯S_S2C, one C_CN⋯C_S2C, and one C_CN⋯S_S2C contact (Fig. S4 and S7). The parameters of these structure-directing contacts are collected in Tables 1 and 2.

Fig. 3 Stacking in the molecular structure of 1·TCB. Short contacts are shown by dotted lines.

Table 1 Parameters of intermolecular contacts between the stacked complex and TCB in the structures of (1–4)·TCB

Contacting atoms	Carene⋯M, Å	Carene/CN⋯SS2C, Å	CCN⋯CS2C, Å
1 ·TCB
1·TCB-A	Ni1⋯C8A 3.4933(17)	S1⋯C7A 3.7272(17)	C1⋯C6A 3.375(2)
		S3⋯C9A 3.7413(17)	C6⋯C10A 3.532(2)
1·TCB-B	Ni1⋯C3B 3.3175(17)	S2⋯C2B 3.6844(17)	C1⋯C1B 3.381(2)
		S4⋯C4B 3.7124(17)	C6⋯C5B 3.465(2)
1-C·TCB-B	Ni1C⋯C8B 3.3951(17)	S1C⋯C7B 3.8438(17)	C1C⋯C6B 3.389(2)
		S3C⋯C9B 3.7286(17)	C6C⋯C10B 3.424(2)
1-C·TCB-D	Ni1C⋯C3D 3.3326(17)	S2C⋯C2D 3.6398(17)	C1C⋯C1D 3.313(2)
		S3C⋯C9B 3.7820(17)	C6C⋯C5D 3.425(2)
1-E·TCB-A	Ni1E⋯C3A 3.4456(17)	S2E⋯C7A 3.6208(17)	C1E⋯C1A 3.546(2)
		S3C⋯C9B 3.7082(17)	C6C⋯C5D 3.495(2)
1-F·TCB-D	Ni1F⋯C8D 3.660(17)	S1F⋯C7D 3.8332(17)	C1F⋯C6D 3.448(2)
		S2F⋯C9D 3.7395(17)	C1F⋯C10D 3.369(2)
2 ·TCB
2·TCB-A	Pd1⋯C8A 3.515(3)	S1⋯C7A 3.758(3)	C1⋯C6A 3.417(4)
		S3⋯C9A 3.727(3)	C6⋯C10A 3.512(4)
2·TCB-B	Pd1⋯C3B 3.338(3)	S2⋯C2B 3.677(3)	C1⋯C1B 3.386(4)
		S4⋯C4B 3.759(3)	C6⋯C5B 3.513(4)
2-C·TCB-B	Pd1C⋯C8B 3.403(3)	S1C⋯C7B 3.858(3)	C1C⋯C6B 3.416(4)
		S3C⋯C9B 3.707(3)	C6C⋯C10B 3.418(4)
2-C·TCB-D	Pd1C⋯C3D 3.353(3)	S2C⋯C2D 3.620(3)	C1C⋯C1D 3.310(4)
		S3C⋯C9B 3.826(3)	C6C⋯C5D 3.473(4)
2-E·TCB-A	Pd1E⋯C3A 3.463(3)	S2E⋯C7A 3.580(3)	C1E⋯C5A 3.524(4)
		S1E⋯C9A 3.756(3)	C1E⋯C1A 3.541(4)
		S1E⋯C4A 3.738(3)
2-F·TCB-D	Pd1F⋯C8D 3.381(3)	S2F⋯C7D 3.838(3)	C1F⋯C6D 3.477(4)
		S1F⋯C9D 3.721(3)	C1F⋯C10D 3.378(2)
3 ·TCB
3·TCB-A	Pt1⋯C8A 3.536(4)	S1⋯C7A 3.773(4)	C1⋯C6A 3.435(6)
		S4⋯C4A 3.603(4)	C6⋯C10A 3.531(6)
3·TCB-B	Pt1⋯C3B 3.345(4)	S2⋯C2B 3.681(4)	C1⋯C1B 3.398(6)
		S3⋯C4B 3.775(4)	C6⋯C5B 3.514(6)
		S1⋯C1B 3.546(4)
3-C·TCB-B	Pt1C⋯C8B 3.409(4)	S1C⋯C7B 3.856(4)	C1C⋯C6B 3.426(6)
		S3C⋯C9B 3.712(4)	C6C⋯C10B 3.418(6)
3-C·TCB-D	Pt1C⋯C3D 3.361(4)	S2C⋯C2D 3.627(4)	C1C⋯C1D 3.320(6)
		S3C⋯C9B 3.827(4)	C6C⋯C5D 3.491(6)
3-E·TCB-A	Pt1E⋯C3A 3.482(4)	S1E⋯C1A 3.498(4)	C1E⋯C5A 3.550(6)
		S2E⋯C5A 3.667(4)	C1E⋯C5A 3.568(6)
3-F·TCB-D	Pt1F⋯C8D 3.386(4)	S1F⋯C9D 3.730(4)	C1F⋯C6D 3.494(6)
		S2F⋯C7D 3.843(4)	C1F⋯C10D 3.387(6)
4 ·TCB
4·TCB-A	Ni1⋯C3A 3.5421(18)	S2⋯C2A 3.7853(18)	C1⋯C1A 3.532(3)
		S4⋯C4A 3.6664(18)	C6⋯C10A 3.322(3)
4·TCB-B	Ni1⋯C3B 3.4707(18)	S2⋯C7B 3.7598(18)	C1⋯C1B 3.851(3)
		S4⋯C9B 3.4484(18)	C8⋯C5B 3.320(3)
4-C·TCB-A	Ni1C⋯C4A 3.4506(17)	S1C⋯C7A 3.5472(18)	C1C⋯C1A 3.468(3)
	Ni1C⋯C3A 3.5303(17)	S2C⋯C10A 3.7667(19)
4-D·TCB-B	Ni1D⋯C4B 3.7012(18)	S1D⋯C2B 3.5281(19)	C1D⋯C6B 3.645(3)
	Ni1D⋯C9B 3.7160(18)	S2D⋯C5B 3.5268(19)

---

Table 2 Angular stacking parameters in (1–4)·TCB

Structure	MS4/C6 plane-to-plane fold angle, °
1 ·TCB
1·TCB-A	5.99(4)
1·TCB-B	15.13(4)
1-C·TCB-B	15.80(4)
1-C·TCB-D	17.99(4)
1-E·TCB-A	6.25(4)
1-F·TCB-D	17.10(4)
2 ·TCB
2·TCB-A	3.82(7)
2·TCB-B	13.26(7)
2-C·TCB-B	13.75(7)
2-C·TCB-D	15.91(7)
2-E·TCB-A	4.58(7)
2-F·TCB-D	14.73(7)
3 ·TCB
3·TCB-A	3.19(10)
3·TCB-B	13.18(10)
3-C·TCB-B	13.29(10)
3-C·TCB-D	15.57(10)
3-E·TCB-A	4.28(10)
3-F·TCB-D	14.30(10)
4 ·TCB
4·TCB-A	1.42(4)
4·TCB-B	7.42(5)
4-C·TCB-A	3.72(5)
4-D·TCB-B	2.76(4)

---

Despite the similarities in NCI patterns across all four cocrystals, the lengths of these contacts vary significantly. However, these variations do not translate into fundamentally different supramolecular architectures, demonstrating the self-compensating nature of the interaction network. In the structures of 1·TCB and 4·TCB, the distances Ni⋯C (3.32–3.50, 3.42, and 3.45–3.72 Å, respectively) and also Pd⋯C separation in 2·TCB (3.34–3.52 Å) are greater than or on the borderline of Bondi van der Waals radii sum (∑_BvdWNi + C and ∑_BvdWPd + C = 3.33 Å), but noticeable smaller than Alvarez van der Waals radii sum (∑_AvdWNi + C = 4.17 Å, ∑_AvdWPd + C = 3.92 Å).

In 3·TCB, Pt⋯C separations (3.35–3.54 Å) lie close around to Bondi van der Waals radii sum (∑_BvdWPt + C = 3.45 Å) and smaller than Alvarez van der Waals radii sum (∑_AvdWPt + C = 4.06 Å). The relatively narrow range of M⋯C distances across the Ni–Pd–Pt series (3.32–3.72 Å) suggests that the ligand environment effectively normalizes metal-specific electronic differences.

In (1–4)·TCB, almost all C_CN⋯C_S2C separations (3.31–3.85 Å) are close to the borderline of ∑_BvdWC + C (3.40 Å) or ∑_AvdWC + C (3.54 Å). The C_arene/CN⋯S_S2C intraatomic distances (Table 1) are rather long (∑_BvdWC + S = 3.50 Å; ∑_AvdWC + S = 3.66 Å) and such comparison indicates that these interactions are quite weak. Despite their individual weakness, the cumulative effect of multiple C⋯S contacts appears to provide sufficient stabilization to maintain consistent stacking patterns across all metal variants. Analysis of interatomic distances reveals that the formation of infinite alternating stacks is primarily determined by two major components: (i) arene carbon-centered π-hole interactions between TCB and the metal; (ii) and π-C_CN-hole interactions between TCB and the nucleophilic sites of the dithiocarbamate ligand.

In the stacks, the alternating metal complexes and TCB molecules are parallel-displaced but not perfectly coplanar. The angles of deviation between these planes, listed in Table 2, are relatively small. This deviation appears to correlate qualitatively with the steric hindrance of the amide substituent in the dithiocarbamate ligand. 1·TCB, 2·TCB, and 3·TCB, featuring the Et₂N group, exhibit greater deviations as compared to 4·TCB, which bears the cyclic substituent C₆H₁₂N.

In different subunits of 4, the bulky cyclic substituents C₆H₁₂N exhibit varying orientations relative to the NiS₄ coordination plane. Specifically, two subunits (denoted as 4-C and 4-D, Fig. S4) have their amide groups oriented in opposite directions relative to the coordination plane; one subunit (4, Fig. S4) has both amide groups located on the same side of the plane (Fig. S4). These different orientations of the bulky amide substituents in 4, 4-C, and 4-D result in substantially different NCIs between the various subunits of 4 and TCB.

Despite observed differences in supramolecular packing motifs, all five structures exhibit similar extended parallel-displaced stacks of alternating complexes and TCB molecules. These stacks are held together by several types of noncovalent contacts. Among these, the most common types are M⋯C (M = Ni, Pd, Pt) and C_CN⋯C_S2C interactions. The prevalence of S-involving interactions across all structures provides experimental evidence for the metal identity masking mechanism proposed in this work.

To better understand the formation of these supramolecular aggregates, and to elucidate the electronic basis of the observed structural resilience, we theoretically examined the nature and energetic contributions of these contacts. This analysis focused on three isomorphic structures, 1·TCB, 2·TCB, and 3·TCB (section 2.3).

2.3. Theoretical considerations

To understand the electronic basis of the observed structural resilience and to quantify the sulfur-mediated self-compensating mechanism that masks metal identity differences, comprehensive theoretical calculations of (1–3)·TCB have been performed (for details refer to the Experimental section 4.4). The part of stacks bearing three metal complex molecules and two TCB molecules were selected as computational models. Full geometry optimization of these supramolecular clusters preserved the general stacking structure. This computational validation of the experimental stacking motifs confirms that the observed structural similarities reflect intrinsic energetic preferences rather than crystal packing artifacts.

All organic and inorganic planar molecules became nearly parallel to each other in the optimized structures, and the average distances between planes formed by TCB and a metal complex slightly decreased from 3.7–3.9 to 3.3–3.4 Å. The consistent optimization outcomes across different metal centers provide computational evidence for the ligand-controlled assembly mechanism, where the dithiocarbamate environment effectively homogenizes the electronic properties of the {MS₄} units regardless of metal identity.

2.3.1. Quantum theory of atoms in molecules (QTAIM) analysis. The topological analysis of the electron density distribution indicates several bond critical points (BCPs) which correspond to the Ni(Pd,Pt)⋯C, S⋯C and N⋯H interactions between the central complex 1 (2 or 3) and two TCB molecules at each side (Fig. 4 and S10). The narrow range of these topological parameters across the Ni–Pd–Pt series suggests that the ligand environment successfully normalizes the electronic characteristics of metal-involving interactions, creating functionally equivalent {MS₄} building blocks. The relatively low values of the electron density, ρ_b, (0.0042–0.0108 au) and kinetic and potential energy densities, G_b and V_b, (0.0034–0.0066 and −0.0023–(−0.0059) au, respectively) at the BCPs and positive Laplacian values, ∇²ρ_b, (0.0174–0.0326 au) are typical for weak noncovalent interactions (Table S2). This corroborates with results of the electron localization function (ELF) analysis which reveal the ELF values between the metal complex and TCB molecules lower than 0.1 (Fig. 4B). The ρ_b values are similar for all types of the short contacts being slightly higher for the S⋯C ones. Several cage critical points which are one of the indicators of the π⋯π stacking interactions were also found (Fig. 4A).

Fig. 4 Bond paths with bond (yellow) and cage (green) critical points (A), ELF distribution (B), sign(λ₂)ρ(r) function mapped on the δg^inter isosurface (δg^inter = 0.004 au and blue-cyan-green-yellow-red color scale −0.015 < sign(λ₂)ρ(r) < 0.015, the atoms of Ni, S, N, C and H are in green, yellow, blue, gray and light gray, respectively) (C), scatter map of the IGMH δg^atom signatures for the Ni (red), sulfur (blue), thiocarbamate carbon (green), nitrogen (pink) atoms and ethyl groups (black) (D) and overall atomic percentage contribution in the 1⋯TCB interactions (blue-cyan-green-yellow-red color scale, blue corresponding to 0% and red corresponding to 15%) (E) in the optimized structure of 1·TCB.

2.3.2. Independent gradient model (IGM) analysis. This analysis in the IGMH version demonstrates the extended regions of the negative sign(λ₂)ρ(r) function on the δg^inter isosurface and, thus, confirms the multiple attractive interactions between the metal complex and TCB which involve the whole these molecules (Fig. 4C and S11). To estimate the relative contribution of individual atoms of the metal complexes in the interactions with TCB, the δg^atom signatures were calculated. The δg^atom descriptor is the sum of all paired contributions of a given atom of one molecule with all atoms of another molecule. The δg^atom signatures for different atoms are completely overlapped on the scatter map of δg^atomversus the sign(λ₂)ρ(r) function (Fig. 4D and S12). In 1·TCB, the S⋯TCB and Et⋯TCB interactions are characterized by the higher δg^atom maximum values than other interactions including the metal⋯TCB ones. Correspondingly, the S⋯C interactions represent three paired interactions with the highest percentage contribution (Table 3). In 2·TCB and 3·TCB, δg^atom of Et⋯TCB and metal⋯TCB are predominant, and the highest percentage contribution corresponds to the metal⋯C paired interaction. The progressive shift from S-dominated interactions in the Ni system to metal dominant interactions in the Pd and Pt systems illustrates the adaptive nature of the compensating mechanism across the metal series.

Table 3 Highest atomic pair and overall atomic contributions (%) in the interactions of complexes 1–3 with two TCB molecules (optimized structures)

Atomic pair percentage contributions				Overall atomic percentage contribution
Contact	%	Contact	%	Atom	%	Atom	%
1 ·TCB
S⋯C	1.21	Ni⋯C	1.03	Ni	14.77	S	8.02
S⋯C	1.13	S⋯C	1.03	S	10.17	C	5.50
S⋯C	1.09	S⋯C	1.01	S	9.98	C	5.36
Ni⋯C	1.09	S⋯C	1.00	S	8.11	H	2.63
2 ·TCB
Pd⋯C	1.75	Pd⋯C	1.12	Pd	13.92	S	7.22
S⋯C	1.22	Pd⋯C	1.08	S	11.36	C	5.51
S⋯C	1.17	S⋯C	1.07	S	10.17	C	5.47
Pd⋯C	1.13	N⋯H	1.03	S	7.95	H	3.03
3 ·TCB
Pt⋯C	1.71	N⋯H	1.04	Pt	15.87	S	7.17
S⋯C	1.22	S⋯C	1.04	S	10.72	C	5.37
Pt⋯C	1.15	Pt⋯C	1.03	S	9.97	C	5.29
Pt⋯C	1.13	N⋯H	1.02	S	8.07	H	2.79

---

Meanwhile, the metal atom has the highest overall percentage contribution in the interactions between the metal complexes and TCB (13.9–15.9%) followed by the S atoms (7.2–11.4%) (Fig. 4E and Table 3). This indicates that the metal atoms play an important role in construction of supramolecular architecture of the cocrystals under study. Meanwhile, the narrow range of metal contributions of 2% suggests the ligand-controlled assembly mechanism in creating structurally resilient supramolecular systems.

2.3.3. Electrostatic potential (ESP). One of the most important factors which governs intermolecular NCIs is the electrostatic factor. The ESP distribution in molecules 1–3, and TCB demonstrates the presence of an extensive zone of the negative potential above the {MS₄} moiety of the metal complexes and the region of the positive potential above the phenyl ring of TCB (Fig. 5 and S13). Additionally, ESP is positive around the ethyl groups of the dithiocarbamate ligands in 1, 2 and 3 and it is negative at the terminus of the nitrile groups of TCB. Such a distribution perfectly explains the π⋯π stacking interaction between the metal complexes and TCB molecules from electrostatic viewpoint.

Fig. 5 Distribution of ESP in the optimized structures of 1 (top panel) and TCB (bottom panel) (electron density isosurfaces 0.002 au, blue-cyan-green-yellow-red color scale from −0.05 to 0.05).

2.3.4. Charge transfer (CT). Another factor which may provide some contribution to the intermolecular NCIs is charge transfer. Analysis of the natural bond orbitals (NBOs) demonstrates that CT is quite weak for the co-crystals under study. The 1(2,3) → TCB charge transfer mostly involves the LP(S) → π*(CC/CN) transitions with the total second-order perturbation energy E(2) of 5.3–8.1 kcal mol⁻¹ for the interactions of the metal complex with two TCBs at both sides. The TCB → 1(2,3) back-CT is even lower with the total E(2) value of 2.6–6.7 kcal mol⁻¹ for the LP(N) → π*(CC)/σ*(CH) and π(CN/CC) → π*(CN/CC) transitions. The overall NBO charge on the central metal complex in the model cluster is +0.09e for 1, +0.07e for 2 and +0.08e for 3 indicating the general charge transfer from the metal complexes to TCB.

The electron density difference (EDD) distribution in the M(1)M(2)N(1) and S(1)S(2)S(3) planes of cocrystals demonstrates some increase of the electron density between the metal or sulfur atoms of the central complex and the TCB molecule (Fig. 6 and S14). However, the integrated charge displacement function (CDF) shows only small 1(2) → TBC CT at the isoboundary line between these molecules (3 me for 1 and 6 me for 2). For cocrystal 3·TCB, very weak TBC → 3 CT was found at the isoboundary line (2 me). The low CT in the systems under study mitigates the importance of the d_z² orbital nature in the NCIs.

Fig. 6 EDD contour plots for the Ni(1)Ni(2)N(1) (top panel) and S(1)S(2)S(3) (bottom panel) planes (isovalues from −0.01 to 0.01 au, red solid contours – charge concentration, blue dashed contours – charge depletion, atomic numbering from Fig. 4A) and CDF function along the Ni(1)Ni(2) axis (top panel) in the optimized structure 1·TCB (the gray vertical lines identifies the boundary between two molecules).

The extended transition state-natural orbital for chemical valence (ETS-NOCV) method allows the calculation of individual orbital interaction contributions in EDD. This analysis shows that the main type of the orbital interactions responsible for CT corresponds mostly to the S → C transitions which are mixed with the metal → C transitions in 2·TCB and 3·TCB (Δρ₁ and Δρ₂, Fig. 7 and S15, S16). The orbital energy of both these NOCV pairs is −4.9, −3.8 and 3.9 kcal mol⁻¹ for 1·TCB, 2·TCB and 3·TCB, respectively, that comprises 16.9, 23.7 and 22.9% of the total orbital interaction energy (Table 4). Another intermolecular orbital interaction revealed by this analysis is the metal → C transition (Δρ₅ for 1⋯TCB and Δρ₃ for 2⋯TCB and 3⋯TCB) with the energy of −1.0–(−1.4) kcal mol⁻¹ and contribution to ∑E^orb_int of 3.4–8.2%. Other two NOCV pairs among five the most energetic ones correspond to the intramolecular CT within 1, 2 or 3. The metal involvement in CT slightly increases from M = Ni to Pd and then to Pt.

Fig. 7 ETS-NOCV deformation densities for the optimized structure 1·TCB (electron transfer occurs from the zones of the charge density depletion (cyan) to those of the charge density concentration (green), isovalues ±0.0001 au for Δρ₁–Δρ₅ and ±0.0006 au for Δρ_total).

Table 4 Charge transfer types corresponding to the first five NOCV pairs with the paired orbital interaction energies (E^orb_int, kcal mol⁻¹) and their percentage contribution in the total orbital interaction energy for the optimized structures 1·TCB, 2·TCB, and 3·TCB

Structure	NOCV	E ^orbint (%)
1·TCB	Δρ1: LP(S) → π*(CC)	−3.4 (11.7)
	Δρ2: LP(S) → π*(CC)	−1.5 (5.2)
	Δρ3: intramolecular	−1.2 (4.1)
	Δρ4: intramolecular	−0.8 (2.8)
	Δρ5: dz^2(Ni) → π*(CC)	−1.0 (3.4)
2·TCB	Δρ1: LP(S) → π*(CC)	−2.1 (13.1)
	Δρ2: LP(S) → π*(CC)	−1.7 (10.6)
	Δρ3: dz^2(Pd) → π*(CC)	−1.1 (6.9)
	Δρ4: intramolecular	−1.0 (5.6)
	Δρ5: intramolecular	−0.8 (5.0)
3·TCB	Δρ1: LP(S)/dxy(Pt) → π*(CC)	−2.3 (13.5)
	Δρ2: LP(S)/dz^2(Pt) → π*(CC)	−1.6 (9.4)
	Δρ3: dz^2(Pt) → π*(CC)	−1.4 (8.2)
	Δρ4: intramolecular	−1.0 (5.8)
	Δρ5: intramolecular	−0.9 (5.3)

---

2.3.5. Interaction energy. The energy of interaction between the central complex 1(2,3) in the model cluster and both TCB⋯1(2,3) fragments (E_int) was calculated in accord with procedure described in Computational details section. The calculated BSSE-corrected values are −40.6, −41.7, and −42.8 kcal mol⁻¹ for cocrystals 1·TCB, 2·TCB, and 3·TCB, respectively. This corresponds to quite efficient interactions between the metal complex and TCB due to multiple contacts forming the π⋯π stacking. The remarkably narrow range of the interaction energies across the Ni–Pd–Pt triad once again confirms the proposed self-compensating mechanism, where ligand-mediated effects successfully mask the inherent d-orbital differences that would otherwise lead to significantly different binding strengths.

The interaction energy was then decomposed into its electrostatic (E_ele), exchange and repulsion (E_exrep), polarization (E_pol), dispersion (E_disp) and electron correlation (E_corr) components using the generalized Kohn–Sham energy decomposition analysis (GKS-EDA) (Table 5). The results indicate that the dominant components in the interactions are electrostatic and dispersion ones together comprising approx. 67% of the attractive part of E_int regardless of metal identity. The polarization term including charge transfer is although visible but clearly less significant (10–11% of contribution). This energetic uniformity demonstrates that the dithiocarbamate ligand environment successfully homogenizes the fundamental interaction mechanisms, creating functionally equivalent {MS₄} units that exhibit identical assembly behavior despite containing metals with fundamentally different electronic properties. This energetic equivalence provides the mechanistic foundation for the observed structural resilience and supports the paradigm shift from metal-directed to ligand-controlled supramolecular assembly.

Table 5 Calculated interaction energies between 1(2,3) and two TCB molecules (E_int) and their decomposition to principal components (in kcal mol⁻¹)

Structure	ΔEele	ΔEexrep	ΔEpol	ΔEdisp	ΔEcorr	E int
1·TCB	−38.6	71.0	−11.0	−36.4	−25.3	−40.2
2·TCB	−37.1	67.0	−11.5	−36.4	−23.6	−41.6
3·TCB	−39.5	71.1	−13.0	−37.4	−23.9	−42.7

---

3. Conclusions

This work demonstrates a novel approach to controlling supramolecular assembly through systematic compositional variations in hybrid organic–inorganic systems. Using group 10 metal dithiocarbamate-TCB cocrystals as a model platform, we reveal design principles that provide a foundation for engineering robust metal-involved flat supramolecular systems.

Our key discovery is the unexpected structural resilience exhibited by these metal-containing assemblies. Despite systematic variations across the Ni–Pd–Pt triad, the cocrystals maintain virtually identical stacking motifs. This contradicts expectations based on the previous studies of hybrid organic–inorganic flat assemblies that d-orbital nucleophilicity differences are the principal structure-directing force for such assemblies.

Comprehensive quantum chemical analysis reveals the underlying mechanism through sulfur-mediated electronic compensation. Independent gradient model calculations demonstrate substantial metal center contributions to intermolecular interactions (13.9–15.9%), confirming that d-orbital differences between group 10 metals are electronically distinct and this distinction is readily detectable. However, sulfur atoms from the dithiocarbamate ligands effectively neutralize this variation through a leveling effect that overwhelms inherent d-orbital differences. Consequently, the {MS₄} units function as electronically equivalent building blocks, with S atoms masking metal-specific properties to produce identical stacking architectures regardless of metal identity.

Energy decomposition analysis reveals remarkably consistent energetic profiles across all systems—electrostatic and dispersion forces account for ∼70% of attractive interactions while charge transfer contributes minimally (∼10%). This energetic uniformity, enabled by sulfur-mediated compensation, explains the observed structural preservation: assembly forces remain constant because the ligand environment homogenizes electronic properties around different metal centers.

The broader significance extends beyond this specific system family. Our findings demonstrate that ligand environments can be strategically designed to either amplify or neutralize metal-specific properties in supramolecular assemblies. Understanding how ligand's donor atoms compensate for metal differences provides opportunities for creating metal-based materials with predictable assembly behavior.

4. Experimental section

4.1. General

1,2,4,5-Tetracyanobenzene and all solvents were obtained from commercial sources and used without further purification. Complexes 1–4 were synthesized according to literature procedures.^39,47

4.2. Cocrystallization of 1–4 with TCB

A mixture of a metal complex (0.028 mmol) and TCB (0.056 mmol), placed in a closed vial, was dissolved in a dichloromethane : acetonitrile mixture (2.5 : 0.5 mL) on heating (approx. 40 °C) and ultrasonic treatment until TCB was completely dissolved (∼10 min). The formed mixture was filtered off from small amount of undissolved solid material through a PTFE syringe filter (0.45 μm). The filtrate was then left to stand at RT for slow evaporation. Dark brownish green crystals of (1,4)·TCB and yellow crystals of (2,3)·TCB suitable for XRD were obtained after 2–4 days.

4.3. X-ray structure determinations

XRD studies were performed at 100(2) K on a Rigaku XtaLAB Synergy-S (1·TCB and 4·TCB) and on a Rigaku Supernova (2·TCB and 3·TCB) diffractometers using CuKα (λ = 0.154184 nm) radiation. The structures were solved with the ShelXT⁴⁸ structure solution program using intrinsic phasing and refined with the ShelXL⁴⁹ refinement program using least-squares minimization. All these programs were incorporated in Olex2 ⁵⁰ program package. Hydrogen atoms in all structures were placed in ideally calculated positions determined according to the neutron diffraction statistical data⁵¹ and then refined as colliding atoms with the parameters of relative isotropic displacement. Table S1 provide an overview of the crystal structures and refinement data. All structures have been deposited at Cambridge Crystallographic Data Centre (CCDC numbers 2482470–2482473).

4.4. Computational details

Full geometry optimization of the structures was carries out at the DFT level of theory with the PBE0 functional^52,53 and the atom-pairwise dispersion correction with the Becke–Johnson damping scheme D3BJ.^54,55 The Gaussian 09 program package⁵⁶ was used. Cartesian d and f basis functions (6d, 10f) were used in all calculations. The def2-SVP basis set was used for the geometry optimization while the def2-TZVP basis set⁵⁷ with the Douglas–Kroll–Hess second-order scalar relativistic correction (DKH)^58,59 was applied in following single point calculations for the analyses of the intermolecular bonding nature.

The topological analysis of the electron density distribution with help of the AIM method of Bader^60,61 was performed using the program AIMAll.⁶² The ELF,^63,64 IGMH,^65,66 EDD, CDF⁶⁷ and ETS-NOCV⁶⁸ analyses were performed using the Multiwfn 3.8 ⁶⁹ and VMD⁷⁰ software. Such studies represent a toolbox of different bonding descriptors and have been termed as complementary bonding analysis.⁷¹ The bond orbital nature was analyzed by using the NBO partitioning scheme.⁷² The GKS-EDA calculations⁷³ were carried out at the PBE0-D3BJ/def2-TZVP level by using the GAMESS-US software (version 2021-R2 patch 1)^74,75 with application of the XEDA patch.^76,77

The interaction energies between the metal complex and TCB molecules in 1(2,3)⋯TCB⋯1(2,3)⋯TCB⋯1(2,3) model clusters were calculated as the energy difference E_int = E[1(2,3)⋯TCB⋯1(2,3)⋯TCB⋯1(2,3)] − E{1(2,3)}_central − E{1(2,3)⋯TCB}_left − E{1(2,3)⋯TCB}_right where structures in square brackets are fully optimized while the structures in curly brackets have unrelaxed geometries. The basis set superposition error (BSSE) was estimated using the counterpoise method.⁷⁸

4.5. Photophysical measurements

Emission spectrum of cocrystal 3·TCB (section S2, the SI) was measured on a Fluorolog 3 (Horiba Jobin Yvon) spectrofluorimeter, λ_ex = 400 nm. The photoluminescence quantum yield was defined as the number of photons emitted per photon absorbed by the system and was measured with an integrating sphere by a reported method.⁷⁹

Author contributions

Lev E. Zelenkov – methodology, investigation, conceptualization; Sergey V. Baykov – conceptualization, formal analysis, funding acquisition, writing – original draft; Maxim L. Kuznetsov – methodology, data curation, resources, writing – original draft; Evgeny Kh. Sadykov – investigation, formal analysis; Pavel V. Nikulshin – investigation; Eugene V. Ignatov – investigation, writing – original draft; Nadezhda A. Bokach – conceptualization, supervision, project administration, writing – review & editing; Vadim Yu. Kukushkin – conceptualization, methodology, supervision, writing – review & editing.

Conflicts of interest

There are no conflicts to declare.

Data availability

The data available within the article or its SI can be provided in raw format upon request.

Supplementary information (SI) is available: X-ray diffraction studies, Photophysical Properties and Measurements, Calculation details. See DOI: https://doi.org/10.1039/d5qi01980j.

CCDC 2482470–2482473 ((1–4)·TCB) contain the supplementary crystallographic data for this paper.^80a–d

Acknowledgements

Authors thank the Russian Science Foundation for support of this study (project no. 22-73-10031-P). X-ray diffraction experiments were performed at the Center for X-ray Diffraction Studies of Saint Petersburg State University. Computational part of this work was supported by Fundação para a Ciência e a Tecnologia (FCT), Portugal, [UIDB/00100/2020 (https://doi.org/10.54499/UIDB/00100/2020), UIDP/00100/2020 (https://doi.org/10.54499/UIDP/00100/2020) of Centro de Química Estrutural and LA/P/0056/2020 (https://doi.org/10.54499/LA/P/0056/2020) of Institute of Molecular Sciences projects].

References

1. S. V. Baykov, E. A. Katlenok, A. V. Semenov, S. O. Baykova, V. P. Boyarskiy, N. A. Bokach and V. Y. Kukushkin, Different Stacking Types in a Single Hybrid Cocrystal System: π⋯π- and π–Hole-Based Organic–Inorganic Planar Assemblies, Inorg. Chem., 2025, 64, 4005–4016.
2. R. Bu, Y. Xiong and C. Zhang, π–π Stacking Contributing to the Low or Reduced Impact Sensitivity of Energetic Materials, Cryst. Growth Des., 2020, 20, 2824–2841.
3. T. Chen, M. Li and J. Liu, π–π Stacking Interaction: A Nondestructive and Facile Means in Material Engineering for Bioapplications, Cryst. Growth Des., 2018, 18, 2765–2783.
4. S. Jena, J. Dutta, K. D. Tulsiyan, A. K. Sahu, S. S. Choudhury and H. S. Biswal, Noncovalent Interactions in Proteins and Nucleic Acids: Beyond Hydrogen Bonding and π-Stacking, Chem. Soc. Rev., 2022, 51, 4261–4286.
5. S. Yang, Y. Qu, L. Liao, Z. Jiang and S. Lee, Research Progress of Intramolecular Π–Stacked Small Molecules for Device Applications, Adv. Mater., 2022, 34, 2104125.
6. S. V. Baykov, D. M. Ivanov, S. O. Kasatkina, B. Galmés, A. Frontera, G. Resnati and V. Y. Kukushkin, Stacking Interactions: A Supramolecular Approach to Upgrade Weak Halogen Bond Donors, Chem. – Eur. J., 2022, 28, e202201869.
7. W. Wang, W. X. Wu, Y. Zhang and W. J. Jin, Perfluoroaryl⋯aryl Interaction: The Most Important Subset of π -Hole⋯ π Bonding, Chem. Phys. Rev., 2024, 5, 031303.
8. D. P. Malenov, G. V. Janjić, V. B. Medaković, M. B. Hall and S. D. Zarić, Noncovalent Bonding: Stacking Interactions of Chelate Rings of Transition Metal Complexes, Coord. Chem. Rev., 2017, 345, 318–341.
9. C. J. Pace and J. Gao, Exploring and Exploiting Polar−π Interactions with Fluorinated Aromatic Amino Acids, Acc. Chem. Res., 2013, 46, 907–915.
10. E. A. Katlenok, A. V. Rozhkov, M. L. Kuznetsov, V. V. Suslonov and V. Y. Kukushkin, Dichotomy of π-Stacking-Directing Noncovalent Forces in Organic–Inorganic Planar Assemblies: The Case of Halo-Substituted Benzoquinones π-Stacked with a Platinum(II) Square-Plane, Inorg. Chem. Front., 2024, 11, 1252–1265.
11. K. Molčanov, V. Milašinović and B. Kojić-Prodić, Contribution of Different Crystal Packing Forces in π-Stacking: From Noncovalent to Covalent Multicentric Bonding, Cryst. Growth Des., 2019, 19, 5967–5980.
12. F. Nie and D. Yan, Photo–Controllable Ultralong Room–Temperature Phosphorescence: State of the Art, Chem. – Eur. J., 2024, 30, e202303611.
13. J.-C. Christopherson, K. P. Potts, O. S. Bushuyev, F. Topić, I. Huskić, K. Rissanen, C. J. Barrett and T. Friščić, Assembly and Dichroism of a Four-Component Halogen-Bonded Metal–Organic Cocrystal Salt Solvate Involving Dicyanoaurate(I) Acceptors, Faraday Discuss., 2017, 203, 441–457.
14. M. Sun, O. Anhalt, M. B. Sárosi, M. Stolte and F. Würthner, Activating Organic Phosphorescence via Heavy Metal–π Interaction Induced Intersystem Crossing, Adv. Mater., 2022, 34, 2207331.
15. L. E. Zelenkov, A. A. Eliseeva, S. V. Baykov, D. M. Ivanov, A. I. Sumina, R. M. Gomila, A. Frontera, V. Y. Kukushkin and N. A. Bokach, Inorganic–Organic {dz²-M^IIS₄}⋯π-Hole Stacking in Reverse Sandwich Structures: The Case of Cocrystals of Group 10 Metal Dithiocarbamates with Electron-Deficient Arenes, Inorg. Chem. Front., 2022, 9, 2869–2879.
16. E. A. Katlenok, M. L. Kuznetsov, A. V. Cherkasov, D. M. Kryukov, N. A. Bokach and V. Y. Kukushkin, Metal-Involved C⋯dz²-Pt^II Tetrel Bonding as a Principal Component of the Stacking Interaction between Arenes and the Platinum(II) Square-Plane, Inorg. Chem. Front., 2023, 10, 3916–3928.
17. S. V. Baykov, E. A. Katlenok, S. O. Baykova, A. V. Semenov, N. A. Bokach and V. P. Boyarskiy, Conformation-Associated C⋯dz²-Pt^II Tetrel Bonding: The Case of Cyclometallated Platinum(II) Complex with 4-Cyanopyridyl Urea Ligand, Int. J. Mol. Sci., 2024, 25, 4052.
18. V. V. Sivchik, A. I. Solomatina, Y.-T. Chen, A. J. Karttunen, S. P. Tunik, P.-T. Chou and I. O. Koshevoy, Halogen Bonding to Amplify Luminescence: A Case Study Using a Platinum Cyclometalated Complex, Angew. Chem., Int. Ed., 2015, 54, 14057–14060.
19. M. I. García, S. Burguera, A. Lázaro, A. Pinto, J. S. Ward, K. Rissanen, L. Rodríguez and A. Frontera, Halogen-Bonded Cocrystals for Tunable Phosphorescence Emission of Pt Complexes, Inorg. Chem., 2025, 64, 10772–10779.
20. Y. Zhuo, T. Zheng, S. Cao, S. Luo, Z. Bi, Y. Zheng, B. Z. Taye, X. Chen, L. G. Gutsev, V. V. Ozerova, N. A. Emelianov, S. G. Vasil'ev, A. F. Shestakov, H. Li, C. Wang, Y. Mo, G. L. Gutsev and B. R. Ramachandran, et al., Mitigating Trap States in Halide Perovskite Solar Cells through the Synergy of Coordination, Hydrogen and Halogen Types of Bonding, J. Mater. Chem. A, 2025, 13, 21589–21600.
21. T. Chen, Z. Sun, S. Zhao, C. Ji and J. Luo, An Organic–Inorganic Hybrid Co-Crystal Complex as a High-Performance Solid-State Nonlinear Optical Switch, J. Mater. Chem. C, 2016, 4, 266–271.
22. S. Soldner, M. Sun, O. Anhalt, M. B. Sárosi, M. Stolte and F. Würthner, Room–Temperature Phosphorescence of Cocrystals of Aromatic Bisimides and Triplet Sensitizer Pt(Acac)₂, Adv. Funct. Mater., 2025, 35, 2412843.
23. X. Wang, Z. Wang, X. Wang, F. Kang, Q. Gu and Q. Zhang, Recent Advances of Organic Cocrystals in Emerging Cutting–Edge Properties and Applications, Angew. Chem., Int. Ed., 2024, 63, e202416181.
24. S. Ren, G.-Y. Qiao and J.-R. Wu, Supramolecular-Macrocycle-Based Functional Organic Cocrystals, Chem. Soc. Rev., 2024, 53, 10312–10334.
25. Y. Ding, Y. Zhao and Y. Liu, Organic Cocrystals: From High–performance Molecular Materials to Multi–functional Applications, Aggregate, 2024, 5, e626.
26. D. P. Malenov and S. D. Zarić, Stacking Interactions of Aromatic Ligands in Transition Metal Complexes, Coord. Chem. Rev., 2020, 419, 213338.
27. D. P. Malenov and S. D. Zarić, Stacking Interactions between Indenyl Ligands of Transition Metal Complexes: Crystallographic and Density Functional Study, Cryst. Growth Des., 2020, 20, 4491–4502.
28. D. P. Malenov and S. D. Zarić, Strong Stacking Interactions at Large Horizontal Displacements of Tropylium and Cyclooctatetraenide Ligands of Transition Metal Complexes: Crystallographic and DFT Study, CrystEngComm, 2020, 22, 3831–3839.
29. D. P. Malenov, I. S. Antonijević, M. B. Hall and S. D. Zarić, Stacking of Cyclopentadienyl Organometallic Sandwich and Half-Sandwich Compounds. Strong Interactions of Sandwiches at Large Offsets, CrystEngComm, 2018, 20, 4506–4514.
30. J. P. Blagojević Filipović, M. B. Hall and S. D. Zarić, Stacking Interaction Potential Energy Surfaces of Square-Planar Metal Complexes Containing Chelate Rings, in Advances in Inorganic Chemistry, 2019, vol. 73, pp. 159–189.
31. D. N. Sredojević, Z. D. Tomić and S. D. Zarić, Evidence of Chelate−Chelate Stacking Interactions in Crystal Structures of Transition-Metal Complexes, Cryst. Growth Des., 2010, 10, 3901–3908.
32. D. Sredojević, Z. Tomić and S. Zarić, Influence of Metal and Ligand Types on Stacking Interactions of Phenyl Rings with Square-Planar Transition Metal Complexes, Cent. Eur. J. Chem., 2007, 5, 20–31.
33. D. P. Malenov and S. D. Zarić, Strong Stacking Interactions of Metal–Chelate Rings Are Caused by Substantial Electrostatic Component, Dalton Trans., 2019, 48, 6328–6332.
34. D. P. Malenov and S. D. Zarić, Recognizing New Types of Stacking Interactions by Analyzing Data in the Cambridge Structural Database, Chemistry, 2023, 5, 2513–2541.
35. D. P. Malenov, D. Z. Vojislavljević-Vasilev and S. D. Zarić, Stacking Interactions of Organometallic Sandwich and Half-Sandwich Compounds: Crystallographic Evidence and Quantum Chemical Support, Crystallogr. Rev., 2025, 31, 1–36.
36. S. V. Baykov, S. I. Filimonov, A. V. Rozhkov, A. S. Novikov, I. V. Ananyev, D. M. Ivanov and V. Y. Kukushkin, Reverse Sandwich Structures from Interplay between Lone Pair−π-Hole Atom-Directed C⋯dz²[M] and Halogen Bond Interactions, Cryst. Growth Des., 2020, 20, 995–1008.
37. A. V. Rozhkov, M. A. Krykova, D. M. Ivanov, A. S. Novikov, A. A. Sinelshchikova, M. V. Volostnykh, M. A. Konovalov, M. S. Grigoriev, Y. G. Gorbunova and V. Y. Kukushkin, Reverse Arene Sandwich Structures Based upon π-Hole⋯[M^II] (d⁸M=Pt, Pd) Interactions, Where Positively Charged Metal Centers Play the Role of a Nucleophile, Angew. Chem., Int. Ed., 2019, 58, 4164–4168.
38. Y. V. Torubaev, I. V. Skabitsky, A. V. Rozhkov, B. Galmés, A. Frontera and V. Y. Kukushkin, Highly Polar Stacking Interactions Wrap Inorganics in Organics: Lone-Pair–π-Hole Interactions between the PdO 4 Core and Electron-Deficient Arenes, Inorg. Chem. Front., 2021, 8, 4965–4975.
39. L. E. Zelenkov, A. A. Eliseeva, S. V. Baykov, V. V. Suslonov, B. Galmés, A. Frontera, V. Y. Kukushkin, D. M. Ivanov and N. A. Bokach, Electron Belt-to-σ-Hole Switch of Noncovalently Bound Iodine(I) Atoms in Dithiocarbamate Metal Complexes, Inorg. Chem. Front., 2021, 8, 2505–2517.
40. D. M. Kryukov, A. A. Khrustaleva, S. V. Baykov, R. M. Gomila, A. Frontera, V. Y. Kukushkin, A. V. Rozhkov and N. A. Bokach, Cooperativity of chalcogen and halogen bonding in cocrystals of Pd^II and Pt^II acetylacetonates with perfluoroarene selanes: Impact of the arene iodination on supramolecular architecture, Inorg. Chem. Commun., 2025, 182, 115288.
41. A. A. Eliseeva, D. M. Ivanov, A. V. Rozhkov, V. Y. Kukushkin and N. A. Bokach, Engineering metal site behavior: electrophilic-nucleophilic dualism in square-planar platinum(II) through geometry-controlled switching Engineering metal site behavior: electrophilic-nucleophilic dualism in square-planar platinum(II) through geometry-controlled switching, Dalton Trans., 2025, 54, 9076–9087.
42. A. Amonov and S. Scheiner, Semicoordinate versus σ-Hole Bonding of Group 10 Metal Atoms in a Square Planar Motif, Inorg. Chem., 2025, 64, 18577–18587.
43. S. Scheiner, Semicoordinate and halogen bonding to group 10 and group 8 metals, Phys. Chem. Chem. Phys., 2025, 27, 12416–12426.
44. V. Nemec and D. Cinčić, The Halogen Bonding Proclivity of the sp³ Sulfur Atom as a Halogen Bond Acceptor in Cocrystals of Tetrahydro-4H-Thiopyran-4-One and Its Derivatives, Cryst. Growth Des., 2022, 22, 5796–5801.
45. D. Pugh and G. Hogarth, Addressing Misconceptions in Dithiocarbamate Chemistry, Dalton Trans., 2025, 54, 11464–11494.
46. S. M. Lee and E. R. T. Tiekink, A Structural Survey of Poly-Functional Dithiocarbamate Ligands and the Aggregation Patterns They Sustain, Inorganics, 2021, 9, 7.
47. E. V. Ignatov, L. E. Zelenkov, S. V. Baykov, M. K. Shurikov, A. V. Semenov, N. A. Bokach, P. S. Postnikov and V. Y. Kukushkin, Controlled Mono- and Double-Insertion of Sulfonamide Fragments into Ni–S Bonds of Nickel(II) Dithiocarbamate Complexes via Sulfonyl Azide Reactivity, Inorg. Chem., 2025, 64, 11867–11879.
48. G. M. Sheldrick, SHELXT – Integrated Space-Group and Crystal-Structure Determination, Acta Crystallogr., Sect. A: Found. Adv., 2015, 71, 3–8.
49. G. M. Sheldrick, Crystal Structure Refinement with SHELXL, Acta Crystallogr., Sect. C: Struct. Chem., 2015, 71, 3–8.
50. O. V. Dolomanov, L. J. Bourhis, R. J. Gildea, J. A. K. Howard and H. Puschmann, OLEX2: A Complete Structure Solution, Refinement and Analysis Program, J. Appl. Crystallogr., 2009, 42, 339–341.
51. F. H. Allen and I. J. Bruno, Bond Lengths in Organic and Metal-Organic Compounds Revisited: X—H Bond Lengths from Neutron Diffraction Data, Acta Crystallogr., Sect. B: Struct. Sci., 2010, 66, 380–386.
52. J. P. Perdew, K. Burke and M. Ernzerhof, Generalized Gradient Approximation Made Simple, Phys. Rev. Lett., 1996, 77, 3865–3868.
53. C. Adamo and V. Barone, Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model, J. Chem. Phys., 1999, 110, 6158–6170.
54. S. Grimme, J. Antony, S. Ehrlich and H. Krieg, A Consistent and Accurate Ab Initio Parametrization of Density Functional Dispersion Correction (DFT-D) for the 94 Elements H-Pu, J. Chem. Phys., 2010, 132, 154104.
55. S. Grimme, S. Ehrlich and L. Goerigk, Effect of the Damping Function in Dispersion Corrected Density Functional Theory, J. Comput. Chem., 2011, 32, 1456–1465.
56. M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, Ö. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski and D. J. Fox, Gaussian 09, Revision C.01, Gaussian, Inc., Wallingford, CT, 2016.
57. B. P. Pritchard, D. Altarawy, B. Didier, T. D. Gibson and T. L. Windus, New Basis Set Exchange: An Open, Up-to-Date Resource for the Molecular Sciences Community, J. Chem. Inf. Model., 2019, 59, 4814–4820.
58. M. Douglas and N. M. Kroll, Quantum Electrodynamical Corrections to the Fine Structure of Helium, Ann. Phys., 1974, 82, 89–155.
59. B. A. Hess, Applicability of the No-Pair Equation with Free-Particle Projection Operators to Atomic and Molecular Structure Calculations, Phys. Rev. A, 1985, 32, 756–763.
60. R. F. W. Bader, A Quantum Theory of Molecular Structure and Its Applications, Chem. Rev., 1991, 91, 893–928.
61. P. S. V. Kumar, V. Raghavendra and V. Subramanian, Bader's Theory of Atoms in Molecules (AIM) and Its Applications to Chemical Bonding, J. Chem. Sci., 2016, 128, 1527–1536.
62. T. A. Keith, AIMAll (Version 19.02.13), TK Gristmill Software, Overland Park, KS, USA, 2019.
63. Z. Liu, T. Lu and Q. Chen, An Sp-Hybridized All-Carboatomic Ring, Cyclo[18]Carbon: Bonding Character, Electron Delocalization, and Aromaticity, Carbon, 2020, 165, 468–475.
64. A. D. Becke and K. E. Edgecombe, A Simple Measure of Electron Localization in Atomic and Molecular Systems, J. Chem. Phys., 1990, 92, 5397–5403.
65. C. Lefebvre, G. Rubez, H. Khartabil, J.-C. Boisson, J. Contreras-García and E. Hénon, Accurately Extracting the Signature of Intermolecular Interactions Present in the NCI Plot of the Reduced Density Gradient versus Electron Density, Phys. Chem. Chem. Phys., 2017, 19, 17928–17936.
66. C. Lefebvre, H. Khartabil, J.-C. Boisson, J. Contreras-García, J.-P. Piquemal and E. Hénon, The Independent Gradient Model: A New Approach for Probing Strong and Weak Interactions in Molecules from Wave Function Calculations, ChemPhysChem, 2018, 19, 724–735.
67. G. Ciancaleoni, F. Nunzi and L. Belpassi, Charge Displacement Analysis—A Tool to Theoretically Characterize the Charge Transfer Contribution of Halogen Bonds, Molecules, 2020, 25, 300.
68. M. P. Mitoraj, A. Michalak and T. Ziegler, A Combined Charge and Energy Decomposition Scheme for Bond Analysis, J. Chem. Theory Comput., 2009, 5, 962–975.
69. T. Lu and F. Chen, Multiwfn: A Multifunctional Wavefunction Analyzer, J. Comput. Chem., 2012, 33, 580–592.
70. W. Humphrey, A. Dalke and K. Schulten, VMD: Visual Molecular Dynamics, J. Mol. Graphics, 1996, 14, 33–38.
71. Complementary Bonding Analysis, ed. S. Grabowsky, De Gruyter, Berlin, 2021.
72. A. E. Reed, L. A. Curtiss and F. Weinhold, Intermolecular Interactions from a Natural Bond Orbital, Donor-Acceptor Viewpoint, Chem. Rev., 1988, 88, 899–926.
73. P. Su, Z. Jiang, Z. Chen and W. Wu, Energy Decomposition Scheme Based on the Generalized Kohn–Sham Scheme, J. Phys. Chem. A, 2014, 118, 2531–2542.
74. G. M. J. Barca, C. Bertoni, L. Carrington, D. Datta, N. De Silva, J. E. Deustua, D. G. Fedorov, J. R. Gour, A. O. Gunina, E. Guidez, T. Harville, S. Irle, J. Ivanic, K. Kowalski, S. S. Leang, H. Li, W. Li, J. J. Lutz, I. Magoulas, J. Mato, V. Mironov, H. Nakata, B. Q. Pham, P. Piecuch, D. Poole, S. R. Pruitt, A. P. Rendell, L. B. Roskop, K. Ruedenberg, T. Sattasathuchana, M. W. Schmidt, J. Shen, L. Slipchenko, M. Sosonkina, V. Sundriyal, A. Tiwari, L. L. Galvez Vallejo, B. Westheimer, M. Włoch, P. Xu, F. Zahariev and M. S. Gordon, Recent Developments in the General Atomic and Molecular Electronic Structure System, J. Chem. Phys., 2020, 152, 154102.
75. M. W. Schmidt, K. K. Baldridge, J. A. Boatz, S. T. Elbert, M. S. Gordon, J. H. Jensen, S. Koseki, N. Matsunaga, K. A. Nguyen, S. Su, T. L. Windus, M. Dupuis and J. A. Montgomery, General Atomic and Molecular Electronic Structure System, J. Comput. Chem., 1993, 14, 1347–1363.
76. P. Su, Z. Tang and W. Wu, Generalized Kohn–Sham Energy Decomposition Analysis and Its Applications, Wiley Interdiscip. Rev.: Comput. Mol. Sci., 2020, 10, e1460.
77. Z. Tang, Y. Song, S. Zhang, W. Wang, Y. Xu, D. Wu, W. Wu and P. Su, XEDA, a Fast and Multipurpose Energy Decomposition Analysis Program, J. Comput. Chem., 2021, 42, 2341–2351.
78. S. F. Boys and F. Bernardi, The Calculation of Small Molecular Interactions by the Differences of Separate Total Energies. Some Procedures with Reduced Errors, Mol. Phys., 1970, 19, 553–566.
79. C. Würth, M. Grabolle, J. Pauli, M. Spieles and U. Resch-Genger, Relative and Absolute Determination of Fluorescence Quantum Yields of Transparent Samples, Nat. Protoc., 2013, 8, 1535–1550.
80. (a) CCDC 2482470: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2pb6py; (b) CCDC 2482471: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2pb6qz; (c) CCDC 2482472: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2pb6r0; (d) CCDC 2482473: Experimental Crystal Structure Determination, 2025,  DOI:10.5517/ccdc.csd.cc2pb6s1.

---