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. 2020 Sep 14;5(38):24520–24525. doi: 10.1021/acsomega.0c02992

Theoretical Investigations of Electronic Structure and Magnetic and Optical Properties of Transition-Metal Dinuclear Molecules

Indukuru Ramesh Reddy 1, Kartick Tarafder 1,*
PMCID: PMC7528315  PMID: 33015469

Abstract

graphic file with name ao0c02992_0006.jpg

In this work, we have reported the electronic structure, spin state, and optical properties of a new class of transition-metal (TM) dinuclear molecules (TM = Cr, Mn, Fe, Co, and Ni). The stability of these molecules has been analyzed from the vibration spectra obtained by using density functional theory (DFT) calculations. The ground-state spin configuration of the tetra-coordinated TM atom in each molecule has been predicted from the relative total energy differences in different spin states of the molecule. The DFT + U method has been used to investigate the precise ground-state spin configuration of each molecule. We further performed time-dependent DFT calculations to study the optical properties of these molecules. The planar geometric structure remains intact in most of the cases; hence, these molecules are expected to be well adsorbed and self-assembled on metal substrates. In addition, the optical characterization of these molecules indicates that the absorption spectra have a large peak in the blue-light wavelength range; therefore, it could be suitable for advanced optoelectronic device applications. Our work promotes further computational and experimental studies on TM dinuclear molecules in the field of molecular spintronics and optoelectronics.

Introduction

Quinonoids are promising molecules, well known for their application in several chemical and biological process.1,2 This class of molecules and their derivatives are highly pH-selective and pH-sensitive.3−5 Their presence in organic thin films may significantly enhance the charge carrier concentration of films. As a result highly conductive interface can be formed by adsorbing these molecules and their derivatives on metal/semiconducting surfaces.6 These ascribe that considering quinonoids and their derivatives as active centers, one can take part in developing new functional materials. In addition, metal–organic quinonoid molecules are potential building blocks in coordination polymers as well as many other materials which are useful for catalysis, surface chemistry, and molecular spintronics.7,8 In transition-metal-quinonoid (TM-quinonoid), the valence electrons are primarily from the partially filled d-orbitals of the TM. Therefore, they can be stabilize in various spin-state configurations depending on the local environment of the TM present in the molecule. As a result, this class of materials could exhibit reversible spin state switching under the influence of suitable external parameters such as temperature, pressure, electric, and magnetic field. Molecules which exhibit reversible spin switching are useful for memory storage devices and molecular switches. Mixed valence and valence tautomerism in TM-quinonoid complexes have already been reported and can be exploited in molecular switching applications.8 Recently, a multifunctional Ni-quinonoid molecule has been reported in which a Ni atom connects two quinonoid molecules, exhibits a reversible color change, and undergoes structural transformation upon methanol adsorption.9 In one of our previous report, we have shown that the Ni-quinonoid molecule chemisorbed on the Co(100) surface, coupled ferromagnetically with the substrate, in which the Ni spin state switches from low spin (LS) to high spin (HS).10 Several quinonoid-based organometallic compounds have been synthesized in the past few years, aiming to their application in spintronics. Kar et al.11 have recently reported quinonoid-based homo- and hetero-dinuclear complexes, where the two noble metals (PtII and/or PdII) are linked through a quinonoid molecule. They have also reported that the metal center can be replaced with TM by using suitable precursor during the synthesis process. Herein, we modeled a set of TM homo-dinuclear organometallics similar to the reported PtII-dinuclear complex, by replacing both the noble metals in the molecule with different TM atoms and carried out theoretical investigations of their stability, electronic structure, magnetic, and optical properties by using density functional theory (DFT) calculations.

Computational Methodology

TM dinuclear molecules were modeled according to the reported structure of the PtII-dinuclear complex.11 Electronic structure and optical absorption spectra of these molecules were obtained by using DFT calculations implemented in the GAUSSIAN 09 package.12 The all-electron Gaussian basis set developed by Ahlrichs and co-workers13 was employed for all the elements in each system. Prediction of proper ground-state spin configuration of organometallic molecules is a challenging task as the total energy difference could be very small for such complex in different spin-state configuration.14 Recent studies showed that the meta-GGA hybrid functional (TPSSh functional)15,16 which uses 10% Hartree–Fock exchange to approximate the exchange correlation functional for TM atoms works excellently and predicts accurate spin configurations in TM-organometallic complexes.17 Hence, we have used the TPSSh functional with the large triple-ζ basis set13 along with polarization function for all the atoms. The geometric structure of all the molecules were optimized using this functional. Bernys optimization algorithm which involves redundant internal coordinates was used to optimize the molecular geometry.

The detailed magnetic structure of TM-organometallics was obtained by using the plane wave, pseudopotential method as implemented in the Vienna Ab initio Simulation Package (VASP)18 with projected augmented plane wave potential.19 Generalized gradient approximation (GGA) was used with Perdew–Burke–Ernzerhof parameterization for exchange–correlation function.20 We have used DFT + U technique21 to obtain the precise spin state of the organometallic by capturing the strong electron–electron correlation effect in the partially filled 3d shell of TM atoms and missing correlation effect beyond GGA. We have tested with different on-site Coulomb parameter (U) and exchange parameter (J) for TM atoms. This method has already been proven to be very accurate in similar systems.22−25 A detailed description is given in Supporting Information. A plane wave kinetic energy cutoff of 500 eV was considered. The convergence criterion was set to 10–5 eV for the self-consistent electronic minimization. Forces on each atom were estimated using the Hellmann–Feynman theorem, and subsequently, structural optimization was carried out using the conjugate gradient method until force on each atom was reduced to 0.01 eV/Å.

Results and Discussion

Optimized Geometric Structure

The molecular structure of the TM dinuclear molecule consist of two TM atoms, one quinonoid and two bipyridine ligands. Each one of two TM atoms in the molecule is attached with a bipyridine ligand. TM atoms are further connected through a quinonoid. The modeled structure of the TM dinuclear molecule is shown in Figure 1a. In order to proceed further, we first optimized the geometric structure and investigated the vibrational spectra of each modeled molecule to test their structural stability.26,27 The calculated IR spectra of TM dinuclear molecules is given in Figure S1. The absence of any negative frequencies in vibration spectra confirms that the optimized structures of molecules are stable. Although the basic structure of all these molecules are same, there are conformal changes, clearly visible in the molecule with different TM atoms. The average TM–ligand bond lengths (ΔTM – L) are 2.05, 2.09, 1.95, 1.93, and 1.90 Å for Cr, Mn, Fe, Co, and Ni dinuclear molecules, respectively. We observed distortion of the molecular planer structure around the TM atom site, which is different in different molecules depending on the TM atom. The distortion from a square-planar to a tetrahedral structure can be indexed with the τ4 parameter; τ4 is 0 for the perfect square-planar and 1 for the perfect tetrahedral geometry. The τ4 parameter in the tetra-coordinated geometry of molecules was calculated from the relation τ4 = (360° – (θ + Φ))/141°, where θ (O–TM–C) and Φ [N(1)–TM–N(2)] are the two largest angles in the tetra-coordinated geometry. The τ4 parameter for the distortion in the tetra-coordinated TM of the molecules is tabulated in Table 1.

Figure 1.

Figure 1

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(a) Modelled structure of the TM dinuclear molecule; TM, O, N, C, and H atoms are represented by orange, red, blue, black, and light pink colored balls, respectively. (b–f) Optimized structure of the CrII-, MnII-, FeII-, CoII-, and NiII-dinuclear molecules. Cr, Mn, Fe, Co, and Ni atoms are represented by magenta, yellow, turquoise, and bronze, respectively, whereas other atoms are shown same as in (a).

Table 1. Calculated Average TM–Ligand Bond Lengths (in Å) and the Distortion Parameter in the Optimized Geometry of TM Dinuclear Molecules.

    average TM–ligand bond length in (Å)
 τ4
molecule TM TPSSh GGA + U TPSSh GGA + U
CrII Cr-1 2.05847 2.07833 0.16 0.16
  Cr-2 2.05846 2.07840 0.16 0.16
MnII Mn-1 2.09841 2.14652 0.75 0.38
  Mn-2 2.09840 2.14627 0.75 0.38
FeII Fe-1 1.95588 1.96381 0.15 0.16
  Fe-2 1.95589 1.96376 0.15 0.16
CoII Co-1 1.93057 1.92874 0.17 0.17
  Co-2 1.93058 1.92900 0.17 0.17
NiII Ni-1 1.90151 1.90319 0.16 0.16
  Ni-2 1.90148 1.90323 0.16 0.16
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Our investigation shows that the tetra-coordinated Mn atoms in MnII-dinuclear molecule is more distorted toward tetrahedral geometry compared to other TM dinuclear molecules, which are nearly in the square-planar geometry. According to the well-known Irving–Williams order,28 the stability of the TM increases in the order MnII < FeII < CoII < NiII. Therefore, the distortion in the MnII-dinuclear molecule could be ascribed because of less ligand field stabilization energy.29 Optimized geometry for each of these molecules is shown in Figure 1b–f.

Electronic Structure and Magnetic Properties

The magnetic behavior of TM dinuclear molecules depends on the coordination of TM and their local environment. In general, tetra-coordinated (square-planar) TM centers with more than half-filled d-orbitals do not exhibit the HS state because of a large John–Tellar effect.9 Therefore, depending on the number of electrons present in d-orbitals of the TM atom, the spin state of the magnetic center of these organometallic molecules are expected to be either intermediate spin (IS) or LS state. Hence one of singlet, triplet, and quintuplet would be the possible spin states (or spin multiplicities) for the molecule with an even number of electrons in the d-orbitals, whereas the doublet, quartet, or sextet would be the possible spin states for those with an odd number of electrons in the d-orbitals. The ground-state spin configuration of the organometallic molecules was determined by comparing the total energies of the molecule calculated in all the possible spin-state configurations. The difference in total energy with respect to the ground-state energy in different spin states is listed in Table 2. Our calculations show that the CrII- and MnII-dinuclear molecules are in HS state configuration, FeII-dinuclear is in IS state configuration, and CoII- and NiII-dinuclear molecules are in LS state configuration in their respective ground state. The obtained average TM-ligand bond lengths (ΔTM – L) of the optimized structures for the LS and HS states are in the range of 1.90–1.93 and 2.07–2.15 Å, respectively, and ≈1.96 Å for the IS state (see Supporting Information), and these values are in good agreement with the reported ΔTM – L values for the respective spin state of the organometallic molecules.22,30 Note that the energy change because of the change of the spin state in the TM atom in the molecule is significantly high; this is mainly because of the local environment of the TM atom in the optimized structure of the molecule, which strongly affects on the occupation of d-orbitals.

Table 2. Calculated Total Energy Difference in the Possible Spin States with Respect to the Ground Spin-State Energy of the TM-Dinuclear Molecules in eVa.

  relative total energy and spin state (in eV)
molecule LS IS HS
CrII 5.08 (singlet) 1.263 (triplet) 0 (quintuplet)
MnII 2.19 (doublet) 0.296 (quartet) 0 (sextet)
FeII 2.22 (singlet) 0 (triplet) 0.92 (quintuplet)
CoII 0 (doublet)   0.63 (quartet)
NiII 0 (singlet)   1.86 (triplet)
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a

Total energy = 0 eV represents the ground-state spin configuration. Corresponding spin multiplicity of TM is given in parentheses.

In order to have a clear insight into the predicted spin state, we further performed the GGA + U calculations and obtained detailed atom-specific spin moments of molecules. The obtained magnetic moment on the both the TM atoms in each molecule is listed in Table 3.

Table 3. Calculated Magnetic Moments and Spin State (in Parenthesis) on the TM Atoms in TM Dinuclear Molecules.

  magnetic Moment (in μB)
  
molecule TM-1 TM-2 total magnetic moment of the molecule (in μB)
CrII 3.730 (S = 2) 3.730 (S = 2) 8.0
MnII 4.598 (S = 5/2) 4.598 (S = 5/2) 10.0
FeII 2.149 (S = 1) 2.149 (S = 1) 4.0
CoII 1.083 (S = 1/2) 1.083 (S = 1/2) 2.0
NiII –0.012 (S = 0) –0.012 (S = 0) 0.0
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To understand the electron occupation in the d-orbitals, we have obtained the spin and d-orbital resolved density of states (DOSs) for each molecule, as plotted in Figure 2a–e. TM atoms in molecules are tetra-coordinated and bonded with O, N, and C atoms of molecular ligands in the xy-plane. Therefore, σ-type hybridization between the in-plane 3d and 2p orbitals will originate the crystal field effect in d-orbitals of TM atoms. The coulomb repulsion along with strong σ-type hybridization will lead to a splitting of the d-orbital into t2g and eg orbitals. On the other hand, in the absence of vertical co-ordination of TM, the degenerated eg orbitals will further split into two states, in which the dz2–r2 orbital will be lower in energy compared to dx2–y2.

Figure 2.

Figure 2

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d-orbital projected DOS of the TM atom in (a) CrII-, (b) MnII-, (c) FeII-, (d) CoII-, and (e) NiII-dinuclear molecule. Spin-up and spin-down DOS are shown by positive and negative values, respectively.

Relatively, shorter TM–ligand bond lengths in Fe-, Co-, and Ni-dinuclear will induce strong ligand field and affect the in-plane d-orbitals of the TM atom that will further rise the in-plane orbital energy levels. As a result, electron distribution in the d-orbital for 3d6–3d8 electronic configurations will violate the Hund’s rule. Electrons will be forced to occupy the dxz, dyz, dz2–r2, and dxy orbitals first to saturate these orbitals, leaving the dx2–y2 orbital completely unoccupied. The d-orbital-projected DOSs for the system with 3d6–3d8 configurations are shown in the Figure 2a,c–e, which clearly shows that both the up and down spin dx2–y2 states are in the conduction band. In the case of the FeII-dinuclear complex, the dxz and dxy orbitals are completely occupied, and dyz and dz2–r2 orbitals are partially filled with spin-up electrons. As a result, the spin state of the FeII atom turned out to be S = 1 (See Figure 2c). In a similar way, only the dyz orbital in CoII-complex is partially filled with spin-up electron and all three dxz, dxy, dz2–r2 orbitals are completely occupied. Thus, the spin state of the CoII atom is S = 1/2 (see Figure 2d). In the case of NiII-dinuclear, all four dxz, dyz, dz2–r2, and dxy orbitals are completely occupied and the dx2–y2 orbital is completely unoccupied, leading to S = 0 spin state for this system (see Figure 2e), whereas in the case of the CrII-dinuclear molecule, these four orbitals are partially occupied with the spin-up electrons giving rise to S = 2 (see Figure 2a) spin state in this system. Interestingly, MnII-dinuclear does not follow this rule. Because the tetra-coordinated Mn atoms in MnII-dinuclear molecule are more distorted towards tetrahedral geometry, also, the average TM–ligand bond length is increased. Therefore, realignment of the d-orbitals according to the tetrahedral co-ordination is expected. As a result, all the d-orbitals including the in-plane dx2–y2 orbital of Mn in the MnII-dinuclear molecule are singly occupied with spin-up electrons, and the spin-down channel is completely empty. Hence, the spin state of the tetra-coordinated MnII atom in the molecule is turned out to be S = 5/2 (see Figure 2b).

Optical Properties

Optical response is a useful tool to understand the proper electronic behavior of molecules. Therefore, considering the optimized structure of TM dinuclear molecules, we have performed time-dependent density functional theory (TD-DFT) calculations by using the PBE0 functional.31 The reconstructed LANL2DZ basis set has been considered for TM atoms, which are known to provide accurate excitation and ionization energies.32,33 We have calculated electronic transitions and absorption spectra in the UV–visible range. The optical absorption spectra of different TM dinuclear molecules are plotted in Figure 3. We observed that there are two major peaks in the absorption spectra. The first one is in the range of 410–450 nm which has maximum intensity and the second one is in the range of 560–590 nm which is less intense and wide. The position of the maximum intensity peaks, band transition energy, and transition probabilities of TM dinuclear molecules are listed in the Table 4. Maximum intensity of the first peak is observed from the Ni-dinuclear molecule. A similar but slightly less intensity peak is found for the Co-dinuclear molecule. For other three TM dinuclear molecules, the absorption band is quite broad. In the case of the Fe-dinuclear molecule, the first and second peaks appear near 545 and 680 nm wavelength regions, respectively. From the optical absorption spectra, we can predict that the dinuclear molecule containing Cr, Ni, Co, and Mn atoms would be useful for blue light-emitting diode applications, in which the Ni-dinuclear molecule will show maximum efficiency. However, the Fe-dinuclear molecule would be useful for yellow light emission.

Figure 3.

Figure 3

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UV–vis absorption spectra of all TM dinuclear molecules obtained from TD-DFT calculations.

Table 4. Calculated Transition Energies, Absorption Wavelength, and Corresponding Transition Probabilities for TM-Dinuclear Molecules.

molecule transition energy (eV) transition wavelength (λ) (nm) transition probability
CrII 2.9807 415.95 0.0967
MnII 3.0063 412.42 0.1033
FeII 2.2483 551.45 0.2076
CoII 2.7883 444.67 0.4664
NiII 2.9584 419.09 0.6207
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To understand the nature of inter-/intraband transitions under the influence of photon absorption, we plotted the frontier orbitals for each system. Molecular orbital plots clearly indicate that π-electrons in quinonoid (Q2–) adopt a zwitterionic form with two delocalized subunits, that is, trimethine oxonol (OCCCO) and trimethine cyanine (NCCCN) in each molecule. Higher occupied orbitals especially the highest occupied molecular orbital (HOMO) and HOMO – 1 are mainly contributed either from NCCCN or OCCCO subunit orbitals in most of the cases. On the other hand, lower unoccupied orbitals are localized mainly on the electron deficient C–C single bond of the quinonoid ligand. Excitation wavelengths and their corresponding oscillator strengths which originates the absorption bands for Ni- and Co-dinuclear molecule are marked with arrows in Figure 4a,b, respectively.

Figure 4.

Figure 4

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HOMO, HOMO – 1, and LUMO orbital plots for (a) NiII- and (b) CoII-dinuclear molecule obtained from DFT calculations using the PBE0 functional. These are the main molecular orbital in which transition take places during the photo-absorption. Transition wavelength and corresponding transition probabilities are indicated near arrow marks.

The intense peaks in the absorption spectra of Ni-dinuclear and Co-dinuclear molecules are at λ = 420 nm and at λ = 446 nm, respectively, and are mainly attributed to the (HOMO – 1)–LUMO transition in both cases. However, the HOMO–LUMO transition in both cases corresponds to the broad absorption band which are at λ = 566 nm and at λ = 577 nm for Ni- and Co-molecules, respectively.

Conclusions

To conclude, we have studied the electronic structure, magnetic, and optical properties of a set of TM dinuclear molecules using DFT calculations. The geometric structure of molecules is optimized in the gas phase, and their structural stability were analyzed by studying vibrational properties. The proper ground-state spin configuration of the tetra-coordinated TM atom in each molecule was estimated by comparing total energies of the molecule in different possible spin-state configurations. We observed that the TM atoms in Cr-, Mn-, Fe-, Co-, and Ni-dinuclear molecules are in S = 2, S = 5/2, S = 1, S = 1/2 and S = 0 spin state, respectively, in the ground state. Apart from Mn-dinuclear, the planer structure remains intact in all other molecules and expected to be well adsorbed and self-assembled on metal substrates. Therefore, we anticipate that this class of molecules would be very suitable for molecular spintronic applications. The optical properties of TM dinuclear molecules are calculated using the TD-DFT method. We observe that in the case of Cr-, Mn-, Co-, and Ni-dinuclear molecules, the absorption takes place mainly near blue light wavelength range; therefore, it could be suitable for optoelectronic device applications. Our present work promotes further theoretical and experimental studies on the TM-dinuclear organometallic molecules for their future application in optoelectronics and molecular spintronics.

Acknowledgments

K.T. would like to acknowledge NITK-high performance computing facility and also would like to thank DST-SERB (project no. SB/FTP/PS-032/2014) for the financial support.

Supporting Information Available

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsomega.0c02992.

  • Calculated magnetic moment on TM atoms in the modelled TM dinuclear molecules with different U values, calculated TM–ligand bond length (in Å) in the geometry of tetra-coordinated TM for the modelled TM dinuclear molecules, calculation of the distortion parameter, and calculated vibrational spectra (PDF)

The authors declare no competing financial interest.

Supplementary Material

ao0c02992_si_001.pdf (1.6MB, pdf)

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