Theoretical Study on the Electronic Structure of Fe(0)–, Pd(0)–, and Pt(0)–Phosphine–Carbon Dioxide Complexes

Abstract

The activation of carbon dioxide by transition metal complexes is a fundamental process in catalysis and carbon capture. In this study, density functional theory (DFT) calculations, combined with Quantum Theory of Atoms in Molecules (QTAIM) and Natural Orbitals for Chemical Valency (NOCV) analyses, were employed to investigate the bonding characteristics and electronic structure of Fe(0)–, Pd(0)–, and Pt(0)–phosphine complexes with CO₂. The Fe(0) complexes exhibited the strongest CO₂ activation, characterized by substantial C=O bond elongation, significant charge transfer, and strong $\pi$-backdonation. In contrast, Pd(0) complexes showed minimal CO₂ activation, while Pt(0) complexes displayed intermediate behavior. The electronic effects of phosphine ligands were also analyzed, revealing that electron-donating phosphines enhance CO₂ activation, whereas electron-withdrawing phosphines weaken metal–CO₂ interactions. These findings provide key insights into the design of transition-metal-based catalysts for CO₂ conversion and utilization.

1. Introduction

In recent years, the urgent need to address environmental concerns, particularly global climate change and greenhouse gas emissions, has led to significant advancements in the field of green chemistry and sustainable technology. One of the exciting areas of research within this domain is the study of transition metal–carbon dioxide complexes [1,2,3,4]. These complexes offer promising opportunities for both catalysis and carbon capture, potentially paving the way towards a more sustainable future.

Transition metals (TMs) exhibit unique electronic properties due to their partially filled d-orbitals. These properties make them excellent candidates for forming coordination complexes with various ligands, including CO₂. Carbon dioxide, a greenhouse gas notorious for its role in global warming, is challenging to capture and convert [5,6,7,8] due to its inert nature. Transition metal-phosphine complexes have demonstrated the ability to interact with CO₂ and these interactions are mainly governed—in a simplified manner—by the Lewis acid–base chemistry, where the transition metal acts as a Lewis acid, accepting electron pairs from the Lewis base CO₂ [9,10,11,12,13,14,15,16,17]. For instance, the trigonal bipyramidal Fe(η²−CO₂)(depe)₂ complex was synthesized from the dinitrogen complex Fe(N₂)(depe)₂ [18]. Complex Fe(N₂)(depe)₂ was fully characterized by ³¹P NMR spectroscopy, revealing four chemically different phosphorus atoms in the coordination sphere of iron, with chemical shifts in the range of 68.13 to 92.44 ppm, and ddd spin patterns with a large (J = 127 Hz) coupling constant for the P atoms accommodating trans positions. The NMR study of this Fe–CO₂ complex is interesting to compare with that of the oldest reported transition metal–carbon dioxide complex (Aresta-complex, Ni(PCy₃)₂(CO₂)) [19]. In solution, a single sharp resonance at 36.1 ppm was found in the ³¹P NMR spectrum; however, two different isotropic peaks (at 22.0 and 45.2 ppm) were reported for the solid-state CPMAS ³¹P NMR measurement suggesting fluxional behavior only in solution.

Transition metal complexes have shown immense potential as catalysts for the conversion of CO₂ into useful chemicals. One of the most significant achievements in this area is the development of catalytic systems that can selectively reduce CO₂ to carbon monoxide or even further to methanol [20,21,22,23,24]. Both CO and methanol are essential feedstocks in the chemical industry, and their production from CO₂ could significantly reduce greenhouse gas emissions while simultaneously providing valuable resources. The activation of CO₂ using transition metal complexes to facilitate the synthesis of cyclic carbonates has already been also explored [8]. These compounds have applications as solvents, electrolytes, and even in the production of biodegradable plastics, presenting an exciting avenue for sustainable material development. Transition metal complexes have been proved to be effective systems for CO₂ coordination and reduction, offering pathways for converting CO₂ into valuable feedstocks not only as carbon monoxide (CO) and methanol, but cyclic carbonates as well [25,26,27,28].

The interaction between CO₂ and a transition metal center is governed by a balance of electrostatic interactions, $\pi -$backdonation, and charge transfer effects. To gain deeper insight into these interactions, Quantum Theory of Atoms in Molecules (QTAIM) [29,30] and Natural Orbitals for Chemical Valency (NOCV) [31,32,33] methods provide an advanced means to analyze metal–ligand interactions at the electronic structure level. This study focuses on Fe(0)–, Pd(0)–, and Pt(0)–phosphine complexes, aiming to understand how metal identity and phosphine ligands influence CO₂ activation.

Our focus on Fe(0), Pd(0), and Pt(0) phosphine systems reflects a design choice to probe CO₂ activation across complementary late-transition-metal manifolds while keeping the ligand class fixed (phosphines). Together with our previous studies [13,14,15,16,17], they span 3d/4d/5d chemistry and distinct d-electron counts (Fe⁰: $d^8$; Pd⁰/Pt⁰: $d^{10}$), allowing us to disentangle metal-identity and ligand-basicity effects under phosphine-saturated conditions. The set is anchored experimentally by structurally and spectroscopically well-characterized Fe(0)–phosphine–CO₂ adducts and through the extensive Pd(0)/Pt(0)–phosphine literature, providing robust external reference points for our computed trends [18].

2. Computational Details

All the structures were optimized without symmetry constraints with tight convergence criteria using the Gaussian suite [34] of programs with the exchange and correlation functional denoted as B97-D3 [35]. For all atoms, the def2-TZVP [36] basis set was employed. According to our previous benchmark studies, this model chemistry proved robust among several DFT methods in terms of predicting vibrational frequencies of TM–carbonyl complexes [37], and for producing reliable geometries and reaction energetics [38]. All IR data were obtained from harmonic vibrational frequency calculations on fully optimized geometries at the same level of theory used for optimization. Analytical second derivatives were evaluated to yield normal-mode frequencies and IR intensities (from dipole-moment derivatives). Each stationary point was verified as a true minimum by the absence of imaginary frequencies.

All singlet structures were optimized with spin-restricted Kohn–Sham (RKS) DFT. For every reported singlet minimum, we ran internal stability analyses in Gaussian (Stable = Opt) and then seeded UKS (singlet) from the converged RKS (Guess = Mix, Stable = Opt). In our four representative cases (Fe, Pt; ligands dmpe, dtfmpe), UKS (singlet) collapsed back to RKS in all instances (identical energies within SCF precision. Triplet-state test calculations were treated with spin-unrestricted Kohn–Sham (UKS) DFT.

For the complexes containing conformationally flexible ligands, conformational analyses have been performed in a similar manner reported earlier and the lowest energy species were considered [14,39]. QTAIM (Quantum Theory of Atoms in Molecules) [29,30] analyses of the wave function were carried out with AIMAll [40] software. For the EDA-NOCV [31,32,33] calculations, the ADF software [41] from the AMS 2025 suite was used, employing the triple-$\zeta$ STO basis set for all atoms with one set of polarization functions (denoted as TZP) and no frozen core [41]. Total and partial density-of-states (TDOS and PDOS) calculations were performed with the Multiwfn program [42,43] using the Hirshfeld method, with the Gaussian broadening function width 1.36057 eV as the full width at half maximum.

3. Results and Discussion

The QTAIM and NOCV analyses provide significant insights into the electronic structure and bonding characteristics of Fe(0)–, Pd(0)–, and Pt(0)–phosphine complexes coordinated with CO₂ (Figure 1). Through a careful examination of electron density distributions, orbital interactions, and charge transfer effects, all governed by the ligand basicity and bite angle, we can discern the relative abilities of these transition metal complexes to activate CO₂ and engage in catalytic transformations.

3.1. QTAIM Analysis: Bonding Trends and Metal—CO₂ Interactions

The QTAIM analysis allowed us to determine how electron density is distributed within the metal–CO₂ complexes, highlighting the bonding strength and activation of CO₂ upon coordination. The electron density (${\rho }_{BCP}$) at the metal-carbon bond critical point (M–C) was highest in Fe(0) complexes, indicating a strong covalent interaction between Fe and CO₂. In contrast, Pd(0) exhibited the weakest interaction, as evidenced by the significantly lower ${\rho }_{BCP}$ values. This suggests that Fe(0) is the most efficient at activating CO₂, whereas Pd(0) plays a relatively passive role in CO₂ coordination. Pt(0), as expected, exhibited intermediate bonding characteristics, forming a moderate interaction with CO₂.

All structures considered in this study were singlet-state complexes. Triplet-state structures were only obtained for the species with strong electron-donating phosphines. With less basic ligands, such as dtfmpe, or dppe, the carbon dioxide ligand left the metal center during geometry optimization. Interestingly, the adducts Fe(dmpe)₂(CO₂) and Pt(dmpe)(CO₂) possess a CO₂ ligand coordinated in a ${\eta }^1$ manner (see Figure S1 in the Supporting Information). These structures are, however, not feasible energetically, as their relative free energies are higher by 6.7 and 30.8 kcal/mol, respectively, compared to their singlet-state counterparts.

Further evidence for CO₂ activation was obtained from the analysis of C=O bond weakening upon coordination. The ${\rho }_{BCP}$ values for the C=O bonds decreased significantly in Fe(0) complexes, demonstrating the strongest activation and partial reduction of CO₂. This trend correlates with the ability of Fe(0) to donate electron density into the antibonding orbitals of CO₂. On the other hand, Pd(0) retained high ${\rho }_{BCP}$ values for C=O bonds, suggesting that CO₂ remains largely unactivated in these complexes upon coordination.

According to the delocalization indices, the change in bite angle (i.e., going from bis-dimethylphosphino methane (dmpm) to bis-dimethylphosphino propane (dmpp)) results in a decrease in bond orders inside the CO₂ ligands. On the other hand, the metal–carbon bond order shows a minimum for the ethandiphos-type ligands, that is, when the diphosphine forms a five-membered ring with the metal. A notable exception is the electron-withdrawing dtfmpe ligand, when attached to platinum, as it reveals the strongest metal–CO₂ bond order compared to the other ligands containing trifluoromethyl substituents.

The V/G value, that is, the ratio of the potential and kinetic energy densities provided additional insights into the nature of the bonding. Fe(0) complexes exhibited the highest V/G values (1.55–1.56), confirming a stronger covalent component in the Fe–CO₂ interaction. Conversely, Pd(0) had the lowest V/G values (1.45–1.50), indicating a somewhat more ionic character. Pt(0) complexes displayed intermediate values, consistent with their moderate CO₂ activation capability (

Table 1. QTAIM parameters of the CO₂ complexes (in atomic units).

M	Ligand	${\mathit{\rho }}_{\mathit{BCP}}$ C=${\mathrm{O}}^1$	${\mathit{\rho }}_{\mathit{BCP}}$ C=${\mathrm{O}}^2$	DI C=${\mathrm{O}}^1$	DI C=${\mathrm{O}}^2$	${\mathit{\rho }}_{\mathit{BCP}}$ M–C	DI M–C	V/G
Fe	dmpp	0.3521	0.4059	1.0571	1.2453	0.1224	0.7303	1.538
Fe	dmpe	0.3551	0.4068	1.0699	1.2542	0.1061	0.6014	1.555
Fe	dmpm	0.3574	0.4061	1.0808	1.2562	0.1252	0.7247	1.561
Fe	dtfmpp	0.3628	0.4228	1.0708	1.2941	0.1145	0.6682	1.550
Fe	dtfmpe	0.3755	0.4314	1.1077	1.3367	0.0971	0.5710	1.478
Fe	dtfmpm	0.3737	0.4300	1.1070	1.3341	0.1044	0.6038	1.516
Fe	depp	0.3498	0.4044	1.0451	1.2340	0.1234	0.7384	1.536
Fe	depe	0.3522	0.4041	1.0631	1.2407	0.1260	0.7313	1.554
Fe	depm	0.3544	0.4048	1.0733	1.2525	0.1274	0.7356	1.560
Fe	dppp	0.3519	0.4057	1.0498	1.2365	0.1329	0.7847	1.586
Fe	dppe	0.3562	0.4140	1.0524	1.2531	0.1238	0.7295	1.563
Fe	dppm	0.3527	0.4100	1.0534	1.2574	0.1266	0.7394	1.566
Pd	dmpp	0.3911	0.4195	1.1933	1.3006	0.1039	0.5968	1.481
Pd	dmpe	0.3898	0.4208	1.1897	1.3077	0.1061	0.6014	1.492
Pd	dmpm	0.3918	0.4256	1.1898	1.3186	0.1098	0.6135	1.515
Pd	depp	0.3895	0.4177	1.1896	1.2946	0.1058	0.6068	1.488
Pd	depe	0.3884	0.4193	1.1861	1.3000	0.1079	0.6102	1.500
Pd	depm	0.3895	0.4235	1.1845	1.3108	0.1103	0.6211	1.510
Pd	dppp	0.3896	0.4225	1.1884	1.3100	0.1028	0.5862	1.463
Pd	dppe	0.3889	0.4228	1.1849	1.3140	0.1028	0.5882	1.455
Pd	dppm	0.3922	0.4251	1.1900	1.1341	0.1096	0.6116	1.499
Pt	dmpp	0.3664	0.4178	1.1132	1.2979	0.1312	0.7320	1.709
Pt	dmpe	0.3632	0.4201	1.1050	1.3089	0.1324	0.7346	1.712
Pt	dmpm	0.3649	0.4242	1.1045	1.3157	0.1349	0.7428	1.731
Pt	dtfmpp	0.3840	0.4351	1.1519	1.3583	0.1035	0.5684	1.550
Pt	dtfmpe	0.3793	0.4352	1.1402	1.3605	0.1089	0.5906	1.582
Pt	dtfmpm	0.3952	0.4465	1.1722	1.3792	0.1014	0.5435	1.504
Pt	depp	0.3586	0.4187	1.0891	1.3022	0.1314	0.7504	1.68
Pt	depe	0.3616	0.4191	1.1015	1.3061	0.1333	0.7401	1.713
Pt	depm	0.3636	0.4213	1.1030	1.3045	0.1364	0.7499	1.737
Pt	dppp	0.3616	0.4207	1.0990	1.3070	0.1295	0.7263	1.680
Pt	dppe	0.3626	0.4198	1.1015	1.3035	0.1302	0.7281	1.684
Pt	dppm	0.3668	0.4227	1.1080	1.3046	0.1363	0.7445	1.738

).

3.2. Geometric and IR Trends: CO₂ Activation Efficiency

The extent of CO₂ activation can also be understood from the geometric parameters of the complexes. The CO₂ bond angle is a key indicator of activation, as a larger deviation from linearity suggests a stronger interaction with the metal center. Fe(0) complexes exhibited the smallest bond angles (132–142°), indicating substantial activation, while Pd(0) and Pt(0) complexes retained larger bond angles (145–152°), implying weaker activation (

Table 2. Geometric parameters of the different carbon dioxide complexes. Bond lengths are in Å, bond angles are in degrees.

M	Ligand	Bond Angle CO2	Bond Length C=${\mathrm{O}}^1$	Bond Length C=${\mathrm{O}}^2$	Bond Length M–C
Fe	dmpp	133.40	1.286	1.223	1.916
Fe	dmpe	134.76	1.282	1.222	1.915
Fe	dmpm	135.27	1.279	1.223	1.907
Fe	dtfmpp	138.82	1.274	1.204	1.948
Fe	dtfmpe	142.43	1.258	1.195	2.014
Fe	dtfmpm	142.25	1.260	1.196	1.985
Fe	depp	132.34	1.289	1.225	1.914
Fe	depe	133.92	1.286	1.225	1.906
Fe	depm	134.70	1.283	1.224	1.900
Fe	dppp	132.95	1.285	1.223	1.892
Fe	dppe	134.76	1.279	1.218	1.915
Fe	dppm	134.25	1.284	1.218	1.903
Pd	dmpp	143.55	1.240	1.208	2.095
Pd	dmpe	143.95	1.242	1.206	2.086
Pd	dmpm	145.81	1.239	1.201	2.067
Pd	depp	142.85	1.242	1.210	2.089
Pd	depe	143.33	1.243	1.208	2.079
Pd	depm	144.69	1.242	1.203	2.066
Pd	dppp	144.09	1.241	1.204	2.097
Pd	dppe	144.01	1.242	1.203	2.095
Pd	dppm	145.71	1.239	1.201	2.066
Pt	dmpp	139.19	1.271	1.210	2.057
Pt	dmpe	139.33	1.275	1.208	2.052
Pt	dmpm	140.59	1.273	1.204	2.041
Pt	dtfmpp	146.00	1.250	1.191	2.153
Pt	dtfmpe	145.55	1.255	1.191	2.131
Pt	dtfmpm	152.43	1.238	1.180	2.144
Pt	depp	137.55	1.280	1.210	2.053
Pt	depe	138.82	1.277	1.209	2.050
Pt	depm	139.70	1.275	1.207	2.038
Pt	dppp	138.80	1.276	1.207	2.059
Pt	dppe	138.83	1.276	1.208	2.057
Pt	dppm	140.65	1.271	1.205	2.036

and Figure 2).

The C=O bond lengths further reinforced this trend, as they were most elongated in Fe(0) complexes, signifying strong $\pi$-backdonation from Fe to CO₂. Pd(0) complexes exhibited minimal elongation, indicating a notably weaker electronic interaction.

As expected, the asymmetric CO₂ stretching frequencies show strong correlation with the Lewis-basicity of the diphosphine ligands. For instance, in the presence of the basic depe ligand, a stretching frequency of 1695 cm⁻¹ was calculated. Comparing the ligands with a similar bite angle, but different basicity, the $\nu$(CO₂) value increased to 1718, 1731, and 1899 cm⁻¹ for dmpe, dppe, and dtfmpe, respectively.

3.3. EDA-NOCV Analysis: Charge Transfer and Orbital Interactions

The EDA-NOCV analysis (energy decomposition analysis in combination with the natural orbitals of chemical valence methodology) provides critical insight into the charge transfer mechanisms that govern metal-ligand interactions, in our case the CO₂ coordination.

As it was reported previously [13,14,15,16,17] the dominating contribution of the orbital interaction energy is the back-donation part, initiated by a d-orbital of the metal center directing towards the ${\pi }^{*}$ orbitals of the CO₂ ligand. Depending on the metal, and on the spectator ligands, the back-donation interaction energy can exceed −100 kcal/mol, whereas the $\pi$-donation component originating from carbon dioxide towards a low-population orbital of the metal is usually weaker than −20 kcal/mol.

The orbital interaction energy ($\mathrm{\Delta }{E}_{orb}$) was highest in Fe(0) complexes (−156.9 kcal/mol for Fe–dmpe), indicating a significant charge transfer between Fe and CO₂. Pt(0) complexes showed a lower interaction energy (−131.5 kcal/mol), and Pd(0) exhibited the weakest charge transfer (−109 kcal/mol). As the Pd(0)-CO₂ complexes were found to be the least stable according to our QTAIM studies [17], we restrict here our NOCV studies to the Pt and Fe complexes, taking one example each for strong electron-donating spectator ligands (dmpe) and one as an electron withdrawing ligand (dtfmpe).

The deformation densities from the ETS-NOCV (Figure 3) analysis revealed that Fe(0) exhibited the largest $\pi$-backdonation component (−77.1 and −121.3 kcal/mol, for ligands dtfmpe and dmpe, respectively), confirming that bisligated Fe(diphosphine)₂ types of complexes donate electron density efficiently into the antibonding ${\pi }^{*}$ orbitals of CO₂. With a single coordinated diphosphine, Pt(0) displayed moderate charge flow for the back-donation interaction (−65.1 and −97.8 kcal/mol, respectively) (

Table 3. Ziegler-Rauk energy decomposition analyses for selected complexes. Energies are given in kcal/mol.

M	Ligand	$\mathrm{\Delta }{\mathit{E}}_{\mathit{int}}$	$\mathrm{\Delta }{\mathit{E}}_{\mathit{Pauli}}$	$\mathrm{\Delta }{\mathit{E}}_{\mathit{elstat}}$	$\mathrm{\Delta }{\mathit{E}}_{\mathit{orb}}$
Fe	dmpe	−81.8	154.6	−76.7	−155.4
Fe	dtfmpe	−35.8	130.1	−53.5	−107.9
Pt	dmpe	−65.3	166.8	−98.6	−130.9
Pt	dtfmpe	−42.4	129.2	−75.8	−95.8

).

The influence of phosphine ligands was also apparent for the other energy components, such as Pauli-repulsion and electrostatic contribution (

Table 4. Orbital energy decomposition values for the leading deformation density contributions (NOCV), and Hirshfeld charges of the CO₂ fragment. Energies are given in kcal/mol.

M	Ligand	$\mathrm{\Delta }{\mathit{E}}_{\mathit{bd}}$	$\mathrm{\Delta }{\mathit{E}}_{\mathit{d}}$	QH
Fe	dmpe	−131.4 (1.27)	−14.6 (0.43)	−0.532
Fe	dtfmpe	−86.6 (1.12)	−17.2 (0.46)	−0.338
Pt	dmpe	−105.3 (1.06)	−19.7 (0.42)	−0.374
Pt	dtfmpe	−72.0 (0.92)	−20.3 (0.40)	−0.252

). Electron-donating phosphines (e.g., dmpe, depe) enhanced CO₂ activation by increasing the overall interaction energy. In contrast, electron-withdrawing phosphines (e.g., dtfmpe) reduced $\mathrm{\Delta }{E}_{int}$, thus results in a weaker meta–CO₂ interaction.

Overall, the combination of QTAIM and NOCV analyses reveals Fe(0) as the most effective metal center for CO₂ activation, with Pt(0) as a moderate activator and Pd(0) as the least effective, providing valuable insights for designing CO₂-reducing catalysts.

The Hirshfeld charge of a fragment is an indicator for the charge transfer capability of a metal-containing fragment strongly influenced by its spectator ligands. In Table 3, the Hirshfeld charge (Q_H) is also displayed for the dmpe and dtfmpe ligands in the case of the iron and platinum centers. The difference in the Lewis-basicity of the diphosphines is clearly reflected by the almost 0.2 difference in Q_H for both metals. As expected, CO₂ is more negative in the Fe(0) complexes where there are two diphosphines to increase the electron density on the metal.

3.4. DOS/PDOS Analysis: Electronic Structure Depending on Phosphine Substituents

Figure 4 compares the total and projected densities of states (DOS/PDOS) for two Fe–CO₂ complexes containing diphosphines with either electron-donating (methyl, EDG, top) or electron-withdrawing (trifluoromethyl, EWG, bottom) substituents. The dashed line marks the HOMO edge, and representative HOMO–1/HOMO/LUMO isosurfaces are shown.

Replacing EDGs by EWGs shifts the Fe-centered PDOS envelope to lower energies relative to the Fermi-level ($E_F$). This stabilization of the d-manifold is the expected response to reduced $\sigma$ donation and enhanced ligand electronegativity. Conversely, EDGs raise the metal d levels, rendering the Fe center more electron-rich. Near the frontier region, the overlap of Fe (red) and CO₂ (blue) PDOS is markedly larger for EDGs. In the EDG complex, the carbon dioxide intensity that appears in the LUMO region tracks with a non-negligible red (Fe) contribution, and the LUMO isosurface shows clear mixing of Fe d with the CO₂${\pi }^{*})$ framework. In contrast, for EWGs, the blue peak nearest to the LUMO is weaker and less coincident with Fe intensity; the LUMO is more ligand-localized with the diminished Fe admixture.

Stronger back-donation (EDG case) implies a more activated CO₂: greater O–C–O bending, longer C–O bonds, and a lower $\nu$(C=O) stretching frequency. The EWG complex should display the opposite: less bending/elongation and higher $\nu$(C=O). These trends are consistent with the qualitative frontier-orbital pictures shown (HOMO/HOMO-1 bearing more Fe–phosphine character, LUMO with larger CO₂${\pi }^{*})$ weight for EDGs).

4. Conclusions

This study highlights the critical role of transition metal identity and phosphine ligand effects in CO₂ activation. The Fe(0) complexes demonstrated the strongest CO₂ activation, as evidenced by the significant elongation of C=O bonds, high charge transfer, and substantial $\pi$-backdonation. In contrast, Pd(0) complexes exhibited the weakest CO₂ activation, indicating limited catalytic potential for CO₂ reduction. Pt(0) complexes displayed an intermediate degree of activation, suggesting their potential for selective CO₂ functionalization. Furthermore, the choice of a phosphine ligand was shown to be crucial, with electron-donating phosphines enhancing CO₂ activation, whereas electron-withdrawing phosphines weakened the metal–CO₂ interaction. These findings provide valuable insights for designing transition metal catalysts optimized for CO₂ reduction and conversion, contributing to the advancement of sustainable chemistry.