Reparameterization of PM6 Applied to Organic Diradical Molecules

We have performed a reparameterization of PM6 (called rPM6) to compute open-shell species, specifically organic diradical molecules, within a framework of the spin-unrestricted semiempirical molecular orbital (SE-UMO) method. The parameters for the basic elements (hydrogen, carbon, nitrogen, and oxygen) have been optimized simultaneously using the training set consisting of 740 reference data. On the basis of the GMTKN30 database, the mean absolute error of rPM6 is decreased from 16.1 to 14.1 kcal/mol, which reassures its accuracy for ground-state properties. Applications of the spin-unrestricted rPM6 (UrPM6) method to small diradicals and relatively large polycyclic aromatic hydrocarbons have provided substantial improvement over the standard SE-UMO methods like UAM1, UPM3, and the original UPM6. The UrPM6 calculation is much less susceptible to spin contamination and, therefore, reproduces geometric parameters and adiabatic singlet–triplet energy gaps obtained by UDFT (UB3LYP and/or UBHandHLYP) at much lower computational cost

A Density Functional Theory Based Protocol to Compute the Redox Potential of Transition Metal Complex with the Correction of Pseudo-Counterion: General Theory and Applications

We propose an accurate scheme to evaluate the redox potential of a wide variety of transition metal complexes by adding a charge-dependent correction term for a counterion around the charged complexes, which is based on Generalized Born theory, to the solvation energy. The mean absolute error (MAE) toward experimental redox potentials of charged complexes is considerably reduced from 0.81 V (maximum error 1.22 V) to 0.22 V (maximum error 0.50 V). We found a remarkable exchange-correlation functional dependence on the results rather than the basis set ones. The combination of Wachters+f (for metal) and 6-31++G­(d,p) (for other atoms) with the B3LYP functional gives the least MAE 0.15 V for the test complexes. This scheme is applicable to other solvents, and heavier transition metal complexes such as M₁(CO)₅(pycn) (M₁ = Cr, Mo, W), M₂(mnt)₂ (M₂ = Ni, Pd, Pt), and M₃(bpy)₃ (M₃ = Fe, Ru, Os) with the same quality

Quantum Master Equation Approach to Singlet Fission Dynamics of Realistic/Artificial Pentacene Dimer Models: Relative Relaxation Factor Analysis

The singlet fission (SF) dynamics of realistic/artificial pentacene dimer models are investigated using the quantum master equation method in order to obtain new insight into the SF dynamics and its rational design guidelines. We comprehensively clarify the effects of the energy offsets of diabatic Frenkel exciton (FE) and charge transfer (CT) exciton states to the double-triplet (TT) exciton state, excitonic couplings, and state-dependent vibronic couplings on the exciton population dynamics using relative relaxation factors (RRFs) between the adiabatic exciton states. As shown in previous studies, efficient sequential/superexchange CT-mediated SF is observed in the energy level matching region (<i>E</i>(TT) – <i>E</i>(FE) < 0). On the other hand, it is predicted that almost the perfect energy level matching (<i>E</i>(TT) – <i>E</i>(FE) ∼ 0) causes the significant reduction of TT yields though exhibits remarkably fast SF rates, when the corresponding adiabatic double-triplet (TT′) and Frenkel exciton (FE′) states are near-degenerate to each other with common diabatic configurations. The excitonic coupling is also found to have a possibility of causing significant change of SF dynamics when it has a large amplitude comparable to those of the other electronic coupling elements. Furthermore, the large vibronic coupling of CT state shows striking enhancement of SF rates with keeping high TT yields in the CT-mediated superexchange region, while the large vibronic couplings of FE and TT states do not show such striking enhancement. These features are understood by analyzing their RRFs, which are proportional to the product of the square of common diabatic exciton configuration coefficients in the concerned two adiabatic exciton states, multiplied by the spectral density (vibronic coupling)

Origin of the Enhancement of the Second Hyperpolarizabilities of Metal–Carbon Bonds

The spin-unrestricted coupled-cluster method was employed to investigate the origin of the second hyperpolarizabilities (γ) in model systems involving metal–carbon bonds with various bond lengths as a function of their diradical character (<i>y</i>) and charge transfer (CT). These systems exhibit unique features: (i) σ electrons give the dominant contribution to γ, (ii) the π electrons contribution to γ is negative, (iii) when the bond length increases, γ exhibits two positive extrema, which are associated with the CT nature and the intermediate diradical character, respectively, (iv) and one negative extremum corresponding to intermediate CT and diradical character, and (v) in the bond stretching process, the maximum γ amplitude per σ bond is about 7 times larger than that per π bond. These features are significantly different from those observed in pure organic systems

Dissymmetric Bis(dipyrrinato)zinc(II) Complexes: Rich Variety and Bright Red to Near-Infrared Luminescence with a Large Pseudo-Stokes Shift

Bis­(dipyrrinato)­metal­(II) and tris­(dipyrrinato)­metal­(III) complexes have been regarded as much less useful luminophores than their boron difluoride counterparts (4,4-difluoro-4-bora-3a,4a-diaza-<i>s</i>-indacenes, BODIPYs), especially in polar solvent. We proposed previously that dissymmetry in such metal complexes (i.e., two different dipyrrinato ligands in one molecule) improves their fluorescence quantum efficiencies. In this work, we demonstrate the universality and utility of our methodology by synthesizing eight new dissymmetric bis­(dipyrrinato)­zinc­(II) complexes and comparing them with corresponding symmetric complexes. Single-crystal X-ray diffraction analysis, ¹H and ¹³C NMR spectroscopy, and high-resolution mass spectrometry confirm the retention of dissymmetry in both solution and solid states. The dissymmetric complexes all show greater photoluminescence (PL) quantum yields (ϕ_PL) than the corresponding symmetric complexes, allowing red to near-infrared emissions with large pseudo-Stokes shifts. The best performance achieves a maximum PL wavelength of 671 nm, a pseudo-Stokes shift of 5400 cm^–1, and ϕ_PL of 0.62–0.72 in toluene (dielectric constant ε_s = 2.4), dichloromethane (ε_s = 9.1), acetone (ε_s = 21.4), and ethanol (ε_s = 24.3). The large pseudo-Stokes shift is distinctive considering BODIPYs with small Stokes shifts (∼500 cm^–1), and the ϕ_PL values are higher than or comparable to those of BODIPYs fluorescing at similar wavelengths. Electrochemistry and density functional theory calculations illustrate that frontier orbital ordering in the dissymmetric complexes meets the condition for efficient PL proposed in our theory

Diradical and Ionic Characters of Open-Shell Singlet Molecular Systems

The diradical and ionic natures of open-shell singlet systems have been investigated using new definitions of the diradical and ionic characters as well as of their densities within the valence configuration interaction (VCI) model with two electrons in two active orbitals. The two-site symmetric and asymmetric diradical models are examined by using these diradical/ionic characters. For realistic compounds, we investigate a diradicaloid diphenalenyl and a rectangular graphene nanoflake in the presence of an external static electric field, as well as π-stacked phenalenyl-derivative dimers with varying the intermonomer distance, where the central carbon atoms in the phenalenyl rings are substituted by boron (B) and nitrogen (N) atoms, respectively. It is found that the increase of charge asymmetricity induced by the static electric field decreases the diradical character and finally induces an ionic character in the ground state, while the first excited state is changed from pure ionic to diradical-dominant as the field amplitude increases. On the other hand, when increasing the intermonomer distance, the B/N substitution in the phenalenyl dimer changes the electronic state from open-shell singlet with small diradical character to closed-shell with large ionic character. These results indicate that the application of a static electric field to diradicaloids and the asymmetric substitution of a pancake bonded π-dimer combined with the variation of intermonomer distance could tune the diradical/ionic characters and therefore control the nonlinear optical responses

π‑Conjugated Trinuclear Group‑9 Metalladithiolenes with a Triphenylene Backbone

Previously, we synthesized π-conjugated trinuclear metalladithiolene complexes based on benzenehexathiol (<i>J. Chem. Soc., Dalton Trans.</i> <b>1998</b>, 2651; <i>Dalton Trans.</i> <b>2009</b>, 1939; <i>Inorg. Chem.</i> <b>2011</b>, <i>50</i>, 6856). Here we report trinuclear complexes with a triphenylene backbone. A reaction with triphenylenehexathiol and group 9 metal precursors in the presence of triethylamine gives rise to trinuclear complexes <b>9</b>–<b>11</b>. The planar structure of <b>11</b> is determined using single crystal X-ray diffraction analysis. The ligand-to-metal charge transfer bands of <b>9</b>–<b>11</b> move to longer wavelengths compared with those of mononuclear <b>12</b>–<b>14</b>. Electrochemical measurements disclose that the one-electron and two-electron reduced mixed-valent states are stabilized thermodynamically. UV–vis–NIR spectroscopy for the reduced species of <b>9</b> identifies intervalence charge transfer bands for <b>9</b>^– and <b>9</b>^2–, substantiating the existence of electronic communication among the three metal nuclei. These observations prove that the triphenylene backbone transmits π-conjugation among the three metalladithiolene units

Bis(dipyrrinato)zinc(II) Complex Chiroptical Wires: Exfoliation into Single Strands and Intensification of Circularly Polarized Luminescence

One-dimensional (1D) coordination polymers (CPs) experiences limitations in exfoliation into individual strands, which hamper their utility as functional 1D nanomaterials. Here we synthesize chiral 1D-CPs that feature the bis­(dipyrrinato)­zinc­(II) complex motif. They can be exfoliated into single strands upon sonication in organic media, retaining lengths of up to 3.19 μm (ca. 2600 monomer units). Their chiroptical structure allows the exfoliated wires to show circularly polarized luminescence at an intensity 5.9 times that of reference monomer complexes

Comparison of the Magnetic Anisotropy and Spin Relaxation Phenomenon of Dinuclear Terbium(III) Phthalocyaninato Single-Molecule Magnets Using the Geometric Spin Arrangement

Herein we report the synthesis and characterization of a dinuclear Tb^III single-molecule magnet (SMM) with two [TbPc₂]⁰ units connected via a fused-phthalocyaninato ligand. The stable and robust complex [(obPc)­Tb­(Fused-Pc)­Tb­(obPc)] (<b>1</b>) was characterized by using synchrotron radiation measurements and other spectroscopic techniques (ESI-MS, FT-IR, UV). The magnetic couplings between the Tb^III ions and the two π radicals present in <b>1</b> were explored by means of density functional theory (DFT). Direct and alternating current magnetic susceptibility measurements were conducted on magnetically diluted and nondiluted samples of <b>1</b>, indicating this compound to be an SMM with improved properties compared to those of the well-known [TbPc₂]^−/0/+ and the axially symmetric dinuclear Tb^III phthalocyaninato triple-decker complex (Tb₂(obPc)₃). Assuming that the probability of quantum tunneling of the magnetization (QTM) occurring in one TbPc₂ unit is <i>P</i>_QTM, the probability of QTM simultaneously occurring in <b>1</b> is <i>P</i>_QTM², meaning that QTM is effectively suppressed. Furthermore, nondiluted samples of <b>1</b> underwent slow magnetic relaxation times (τ ≈ 1000 s at 0.1 K), and the blocking temperature (<i>T</i>_B) was determined to be ca. 16 K with an energy barrier for spin reversal (<i>U</i>_eff) of 588 cm^–1 (847 K) due to <i>D</i>_4<i>d</i> geometry and weak inter- and intramolecular magnetic interactions as an exchange bias (<i>H</i>_bias), reducing QTM. Four hyperfine steps were observed by micro-SQUID measurement. Furthermore, solution NMR measurements (one-dimensional, two-dimensional, and dynamic) were done on <b>1</b>, which led to the determination of the high rotation barrier (83 ± 10 kJ/mol) of the obPc ligand. A comparison with previously reported Tb^III triple-decker compounds shows that ambient temperature NMR measurements can indicate improvements in the design of coordination environments for SMMs. A large <i>U</i>_eff causes strong uniaxial magnetic anisotropy in <b>1</b>, leading to a χ_ax value (1.39 × 10^–30 m³) that is larger than that for Tb₂(obPc)₃ (0.86 × 10^–30 m³). Controlling the coordination environment and spin arrangement is an effective technique for suppressing QTM in TbPc₂-based SMMs