Two-dimensional bimetal-embedded expanded phthalocyanine monolayers: a class of multifunctional materials with fascinating properties

1. Introduction

• The work targets ordered, separately distributed magnetic centers because transition metals can cluster through strong d–d interactions in other 2D systems.The paper identifies Pc as a template whose pores coordinate transition metals with four nitrogen atoms.Source: §1 · p. 2
• The study predicts Sc–Zn TM2EPc monolayers using systematic theoretical investigation of their physicochemical properties.The motivation is the experimentally synthesized expanded-Pc congener with Mo or W bimetal centers.Source: §1 · p. 2
• Predicted outcomes include V2EPc antiferromagnetic Dirac-metal behavior, Cr2EPc ferromagnetic Dirac half-metallicity, and a 25.19% PCE for Ni2EPc/2H-WSe2.The study also reports high magnetic transition temperatures for Cr2-, Mn2-, and Fe2-EPc monolayers.Source: §1 · p. 3

2. Computational methodologies

• Spin-polarized DFT calculations use PAW, PBE, and PBE+U with U = 4 eV and J = 1 eV, plus a 500 eV plane-wave cutoff.Geometries were relaxed to energy and force thresholds of 10^-6 eV and 0.01 eV/Å; DFT-D3 corrections account for van der Waals interactions.Source: §2 · p. 3
• Phonon calculations use DFPT, while 10 ps NVT AIMD simulations at different temperatures assess lattice and thermal stability.The AIMD timestep is 1.0 fs, with temperature controlled by a Nosé–Hoover thermostat.Source: §2 · pp. 3–4
• Molecular-model bonding is analyzed with AdNDP and QTAIM, and periodic bonding patterns with SSAdNDP.Molecular calculations use PBE0/LANL2DZ; solid-state calculations use PBE+U and a def2-TZVP basis for projected plane-wave density.Source: §2 · p. 4
• HSE06 calculations refine electronic band structures because PBE+U does not fully correct band-gap underestimation.The passage attributes the remaining error to PBE errors in single-particle eigenvalues and the lack of derivative discontinuity.Source: §2 · pp. 4–5
• Magnetic ordering is evaluated across FM and three AFM configurations, with exchange interactions and classical-Heisenberg Monte Carlo simulations used to estimate transition temperatures.Spin-polarized charge-density differences are also analyzed to investigate the origin of magnetism.Source: §2 · p. 5
• Optical absorption coefficients are calculated from the frequency-dependent real and imaginary dielectric functions, using 500 bands and a 0.1 complex shift.The shift is used in the Kramers–Kronig transformation between the dielectric-function components.Source: §2 · p. 5

3.1. Geometric structures and ground states of 2D TM2EPc monolayers

• Five systems—Cr2-, Mn2-, Fe2-, Co2-, and Ni2-EPc—are planar Type-A structures, while the other five are buckled Type-B structures.Type-A has space group Cmmm; Type-B has space group Cmm2.Source: §3.1 · pp. 5–6
• Each metal is coordinated by two pyrrole and two amine nitrogen atoms in the macrocycle.The two structural classes differ in whether the central metal and nitrogen atoms remain in-plane or protrude slightly.Source: §3.1 · p. 5
• Sc2- and Ni2- to Zn2-EPc are nonmagnetic; V2EPc is AFM1, Cr2EPc is ferromagnetic, and Ti2- and Mn2- to Co2-EPc prefer AFM3 ordering.Ground-state lattice parameters span 19.67–19.97 Å and 15.20–15.34 Å; the central-metal separation spans 2.42–3.03 Å.Source: §3.1 · p. 7

3.2.1. Lattice dynamic stability

• No imaginary phonon modes appear across the Brillouin zone, and all TM2EPc systems have highest phonon frequencies above 3125 cm–1.A large phonon-frequency gap spans 1600–3125 cm–1; metal contributions occur below 700 cm–1, while frequencies above 3125 cm–1 are almost exclusively from H atoms.Source: §3.2.1 · pp. 7–8

3.2.2. Thermal stability

• All ten monolayers survive simulated annealing above 1200 K for 10 ps, with estimated melting points ranging from 1200 to 1800 K.Above the estimated melting points, the frameworks distort and begin to melt.Source: §3.2.2 · p. 8

3.2.3 Thermodynamic stability

• Formation energies range from –4.98 to 0.80 eV and are negative for all systems except Zn2EPc.Binding energies range from –5.49 to –10.86 eV, and negative Eb + Ec values of –6.22 to –3.65 eV indicate stable embedding and reduced likelihood of metal clustering.Source: §3.2.3 · pp. 8–9

3.3. Chemical bonding analysis

• Molecular analyses find no TM–TM bonding; metal–organic bonding instead occurs through eight 2c-2e TM–N σ-bonds per molecule.The molecular models also contain four locally π-aromatic C6-ring fragments and two π-conjugated C2N3 chains.Source: §3.3 · p. 9
• The Ni2EPc monolayer has four TM–N σ-bonds per metal center, six delocalized 5c-2e π-bonds in C2N3 fragments, and six 6c-2e π-bonds in C6 rings.The organic framework also contains 46 2c-2e σ-bonds and six 2c-2e π-bonds.Source: §3.3 · p. 9
• Across the monolayers, the main bonding-pattern difference is the number of metal d-type lone pairs, identified as the fundamental origin of differing magnetic moments.The Ni2EPc pattern is reported to be similar to those of the other TM2EPc monolayers.Source: §3.3 · pp. 9–10
• In planar structures, the C–N bond near the nitrogen coordinated to two metals is shorter than a single C–N bond; in buckled structures it is slightly elongated, except in Zn2EPc.The authors attribute the elongation to extra electrons contributing to antibonding C–N orbitals.Source: §3.3 · p. 10

3.4.1. Intrinsic magnetism without biaxial strain

• Cr2EPc is ferromagnetic with TC about 221 K, while Mn2EPc and Fe2EPc are antiferromagnetic with TN about 217 and 325 K; other systems have transition temperatures below room temperature.The reported ground states include AFM1 for V2EPc and FM for Cr2EPc; Ti2EPc and Mn2EPc through Co2EPc favor AFM3.Source: §3.4.1 · pp. 14–15
• Magnetic moments mainly originate on central TM atoms, while neighboring N and C atoms acquire smaller, ordering-dependent spin polarization.In Cr2EPc, each Cr carries 3.29 μB; neighboring N atoms carry −0.28 μB and coordinated C atoms 0.02 μB.Source: §3.4.1 · pp. 15–16
• Cr2EPc’s short 2.55 Å Cr–N–Cr superexchange is strongly ferromagnetic, whereas competing direct and superexchange interactions yield antiferromagnetic Fe2EPc.The long-range Cr pathways also favor ferromagnetism; Fe’s third-nearest-neighbor pathway is weakly ferromagnetic.Source: §3.4.1 · pp. 18–19

3.4.2. Effect of biaxial strain on magnetism

• At −10%, −4%, −4%, and −6% strain, transition temperatures reach 150, 270, 295, and 350 K for V2EPc, Cr2EPc, Mn2EPc, and Fe2EPc, respectively.Mn2EPc, Ti2EPc, and Co2EPc retain antiferromagnetic ground states across the full −10% to 10% strain range.Source: §3.4.2 · p. 21

3.4.3. The microscopic mechanism of modulation of magnetism via biaxial strain

• Spin-density plots serve as a graph descriptor for magnetic states and moments, while d-orbital electron occupation tracks spin-channel crossings and phase transitions.For V2EPc, the spin plots indicate six transitions across seven magnetic states, consistent with the electron-occupation plot.Source: §3.4.3 · pp. 22, 24

3.5.1. Intrinsic electronic properties without biaxial strain modulation

• Cr2EPc is a ferromagnetic half-metal with a 1.416 eV spin-up gap at HSE06 level, while V2EPc is an antiferromagnetic metal; both exhibit Dirac cones.The Cr2EPc cone remains nearly unchanged at HSE06, while V2EPc's cone changes considerably and moves to a crossing at the Fermi level.Source: §3.5.1 · pp. 25, 26, 29
• Cr2EPc Fermi velocities are 4.06 × 10^5 and 4.79 × 10^5 m/s along Γ→Y and Y→Γ; V2EPc values are 3.18 × 10^5 and 5.68 × 10^5 m/s.The direction-dependent values reflect anisotropic band slopes near the Dirac points.Source: §3.5.1 · p. 26
• The ten systems divide into nonmagnetic semiconductors (Sc2-, Ni2-, Cu2-, Zn2-EPc), an antiferromagnetic metal (V2EPc), a ferromagnetic half-metal (Cr2EPc), and antiferromagnetic semiconductors (Ti2-, Mn2-, Fe2-, Co2-EPc).HSE06 calculations identify Zn2EPc as a semiconductor with a 0.245 eV gap.Source: §3.5.1 · p. 29

3.5.2. Effect of elastic strain engineering on electronic properties

• From −6% to 2% strain, Cr2EPc retains Dirac half-metallicity, while Fe2EPc becomes a half-metal under −6% to −10% compression.Cr2EPc's spin-up gap in this strain range varies from 0.60 to 0.99 eV.Source: §3.5.2 · p. 30
• V2EPc is an AFM Dirac metal at −2% to 2% strain, becomes an FM metal at −4% and 4%, then an AFM semiconductor at −6% and 6%.Source: §3.5.2 · p. 30
• Strain drives Mn2EPc and Ti2EPc between semiconductor and metal states, while Co2EPc remains semiconducting across −10% to 10%.Mn2EPc becomes metallic at 4% to 8% tensile strain; Ti2EPc is semiconducting from 0% to 6% tensile strain and metallic at 8%.Source: §3.5.2 · p. 30

3.6.1. Optical absorption coefficients

• The yy absorption component generally exceeds xx, and every monolayer responds to visible light; Sc2-, Ti2-, Mn2-, Cu2-, and Zn2-EPc also absorb strongly in ultraviolet and infrared regions.Source: §3.6.1 · p. 31
• Visible-light absorption ranges from 1.70 × 10^5 to 5.32 × 10^5 cm–1, with Cu2EPc highest; ultraviolet absorption exceeds 3.0 × 10^5 cm–1 in every system.Ni2EPc's ultraviolet absorption exceeds 5.0 × 10^5 cm–1.Source: §3.6.1 · pp. 31–32
• At −8% strain, Ni2EPc ultraviolet absorption rises to 6.66 × 10^5 cm–1 and visible absorption to 5.06 × 10^5 cm–1.The reported strain response also includes a gradually increasing infrared response under compression.Source: §3.6.1 · pp. 32–33

3.6.2. Power conversion efficiency

• Only Fe2EPc, Co2EPc, and Ni2EPc meet the type-II alignment, conduction-band-offset, and energy-gap criteria with SnC, GeS, and 2H-WSe2 after screening 100 materials.Source: §3.6.2 · p. 33
• 25.19% for Ni2EPc/2H-WSe2, 19.89% for Co2EPc/GeS, and 16.25% for Fe2EPc/SnC are the calculated power conversion efficiencies.Source: §3.6.2 · pp. 34–35

• All ten predicted monolayers survive simulated annealing above 1200 K for 10 ps, and chemical bonding analysis finds isolated metal centers linked to the organic framework by four TM–N σ-bonds.Five structures are planar and five are buckled; TM–TM bonding is absent.Source: §4 · p. 36
• V2EPc is an antiferromagnetic Dirac metal and Cr2EPc a ferromagnetic Dirac half-metal; other systems are predicted as nonmagnetic or antiferromagnetic semiconductors.Source: §4 · p. 36
• Cr2EPc retains ferromagnetic half-metallicity from −6% to 2% strain, Fe2EPc becomes a ferromagnetic half-metal under −6% to −10% compression, and predicted transition temperatures reach 325 K for Fe2EPc.Cr2-, Mn2-, and Fe2EPc transition temperatures are reported as 221, 217, and 325 K, respectively.Source: §4 · p. 36
• The monolayers have strong visible and ultraviolet optical responses, and Ni2EPc/2H-WSe2 is predicted to reach 25.19% power conversion efficiency.Source: §4 · p. 36

• Supplementary structural and stability materials include optimized ground-state structures, phonon spectra and densities of states, and 10 ps AIMD simulations at different temperatures.Source: Supporting Information · p. 37
• The supplementary analyses also cover formation, cohesive, and binding energies; molecular bonding; exchange parameters; magnetic transition temperatures; and spin densities.Source: Supporting Information · p. 37
• Additional band structures and strain-dependent electronic and optical results are listed for the TM2EPc systems.These include band gaps and magnetic ground states under −10% to 10% biaxial strain and optical absorption under strain for Fe2-, Co2-, and Ni2-EPc.Source: Supporting Information · p. 37

“For Table of Contents Use Only”

• Embedding diverse 3d transition metals can tune TM2EPc monolayers among metallic, Dirac half-metallic, and semiconducting states.The approach also tunes magnetism and optical absorption.Source: “For Table of Contents Use Only” · p. 42
• Strong coordination between the metal atoms and EPc substrate accounts for the monolayers’ excellent structural stability.Source: “For Table of Contents Use Only” · p. 42
• Strong visible-light absorption and high power conversion efficiency point to potential optoelectronic and photovoltaic applications.Source: “For Table of Contents Use Only” · p. 42