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Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano
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Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano

A special issue of Chemistry (ISSN 2624-8549). This special issue belongs to the section "Theoretical and Computational Chemistry".

Deadline for manuscript submissions: closed (31 January 2025) | Viewed by 16044

Special Issue Editors

Prof. Dr. Takashi Kubo

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Guest Editor
Graduate School of Science, The University of Osaka, Machikaneyama 1-1, Toyonaka 560-0043, Osaka, Japan
Interests: structural and physical organic chemistry; syntheses and properties of polycyclic aromatic compounds with open-shell character; development of cooperative proton and electron transfer systems based on π-conjugated molecules and transition metal complexes
Prof. Dr. Yasutaka Kitagawa

E-Mail Website
Guest Editor
Graduate School of Engineering Science, The University of Osaka, Machikaneyama 1-3, Toyonaka 560-8531, Osaka, Japan
Interests: quantum chemistry and theoretical chemistry; properties of degenerate and open-shell systems; d-π conjugated systems; metal complexes; metal clusters
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Manabu Abe

E-Mail Website
Guest Editor
Graduate School of Advanced Science and Engineering, Hiroshima University, 1-3-1 Kagamiyama, Higashi-Hiroshima 73908526, Hiroshima, Japan
Interests: reactive intermediates chemistry; organic photoreactions

Special Issue Information

Dear Colleagues,

This Special Issue of Chemistry is dedicated to Dr. Masayoshi Nakano (1964–2021), who made significant contributions to the theoretical study of open-shell systems. He studied chemistry at the University of Osaka and later served as a professor there, dedicating his career to research and education in theoretical chemistry. His outstanding work on a development of the theoretical analysis for electronic structures in open-shell systems has greatly influenced our understanding of the behavior of π-electrons and the design of new functional materials in materials science. His theories continue to be widely applied in various fields of chemistry, impacting many scientists.

The aim of this Special Issue is to compile the latest research and applications related to open-shell systems, emphasizing the collaboration between experimental and theoretical approaches that Masayoshi Nakano deeply valued. The issue covers a wide range of topics, including the theoretical foundations of open-shell systems, methods for analyzing electronic structures, the development of novel π-conjugated open-shell molecules, the investigation of unique physical properties, and applications in materials science. We hope this Special Issue will serve as a valuable resource for researchers working on open-shell systems and help to honor his remarkable achievements.

Prof. Dr. Takashi Kubo
Prof. Dr. Yasutaka Kitagawa
Prof. Dr. Manabu Abe
Guest Editors

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Keywords

  • open-shell
  • radical, diradical, and multiradical
  • diradicaloid
  • magnetic and electroconductive properties
  • non-linear optics, singlet fissions, and optical properties
  • catalysis and reaction
  • theoretical model and calculation

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Published Papers (22 papers)

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12 pages, 3217 KiB  
Article
Paddlewheel-Type Diruthenium(II) Naphthyridine Complex with Electron-Withdrawing Trifluoroacetate Ligands
by Yusuke Kataoka, Nozomi Tada, Junya Omaki, Kanami Matsubara, Natsumi Yano and Makoto Handa
Chemistry 2025, 7(3), 72; https://doi.org/10.3390/chemistry7030072 (registering DOI) - 1 May 2025
Abstract
A ligand exchange reaction between [Ru2(npc)2(O2CMe)2] (1; npc = 1,8-naphthyridine-2-carboxylate) and trifluoroacetic acid yielded the diruthenium naphthyridine complex with two trifluoroacetate ligands, [Ru2(npc)2(O2CCF3)2] [...] Read more.
A ligand exchange reaction between [Ru2(npc)2(O2CMe)2] (1; npc = 1,8-naphthyridine-2-carboxylate) and trifluoroacetic acid yielded the diruthenium naphthyridine complex with two trifluoroacetate ligands, [Ru2(npc)2(O2CCF3)2] (2), which was structurally characterized by electrospray ionization mass spectrometry, elemental analysis, infrared spectrum, and synchrotron single-crystal X-ray diffraction. The crystal structure of 2 adopts a paddlewheel-type structure in which two npc and two O2CCF3 ligands are coordinated in a cis-2:2 arrangement around the Ru2 core. The temperature-dependent magnetic susceptibility measurements indicated that 2 has (i) an S = 1 spin state for the Ru24+ core and (ii) a large D value of 243 cm−1; characteristic of paddlewheel-type Ru2 complexes. The cyclic voltammetry measurements indicated that 2 exhibited one reversible oxidation wave (E1/2 = 0.72 V vs. SCE) and two reduction waves (E1/2 = −0.67 and −1.10 V vs. SCE); which were clearly positively shifted when compared with those of 1. Additionally, the absorption spectrum of 2 displayed intense absorption bands in the visible region; attributed to metal-to-ligand charge transfer from the Ru2 core to the npc ligands; which were blue-shifted by approximately 70–100 nm when compared with those of 1. These distinct shifts in redox potentials and absorption bands originated from the strong electron-withdrawing effect of the O2CCF3 ligands in 2. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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10 pages, 2365 KiB  
Article
Remarkably Efficient [4+4] Dimerization of [n]-Cyclacenes
by Ankit Somani, Divanshu Gupta and Holger F. Bettinger
Chemistry 2025, 7(2), 62; https://doi.org/10.3390/chemistry7020062 - 12 Apr 2025
Viewed by 210
Abstract
Cyclacenes with the general formula C4nH2n are cyclic analogs of acenes. Acenes are well-known for their high reactivity, which increases with the number of fused benzene rings. The cyclic strain, absence of a Clar sextet, and diradical or [...] Read more.
Cyclacenes with the general formula C4nH2n are cyclic analogs of acenes. Acenes are well-known for their high reactivity, which increases with the number of fused benzene rings. The cyclic strain, absence of a Clar sextet, and diradical or polyradical nature are expected to render cyclacenes highly reactive under ambient conditions. Their primary decomposition pathway is anticipated to involve dimerization or polymerization. We explore the reaction pathway of the [π4s + π4s] dimerization of [n]-cyclacenes for 6 ≤ n ≤ 20 by density functional theory (DFT) using spin-unrestricted and thermally-assisted-occupation (TAO) formalisms. Computational analysis predicts a stepwise reaction mechanism that starts with the formation of a van der Waals complex and proceeds through a transition state to an intermediate with a single new C–C bond and two unsaturated valences. A subsequent second transition state results in the formation of the dimerization product. However, for smaller cyclacenes (n < 10), neither the van der Waals complex nor the first transition state is involved, and the intermediate is formed without a barrier. The largest [20]-cyclacene investigated exhibits the highest barriers for these processes. However, with a barrier as low as 3.9 kcal/mol at the UB3LYP-D3(BJ)/6-31G(d) level of theory, dimerization is anticipated to occur very rapidly. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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17 pages, 3000 KiB  
Article
Tetraanion of Tetracyclopentatetraphenylene Derivative: Global Versus Local Conjugation Modes
by Hirokazu Miyoshi, Ryosuke Sugiura, Ryohei Kishi, Atsuya Muranaka, Masanobu Uchiyama, Nagao Kobayashi, Yutaka Ie, Masayoshi Nakano and Yoshito Tobe
Chemistry 2025, 7(2), 51; https://doi.org/10.3390/chemistry7020051 - 31 Mar 2025
Viewed by 263
Abstract
Multiple reduced π-conjugated hydrocarbons exhibit π-electron conjugation modes different from neutral species due to the distinct number of electrons. Herein, we report the generation of a 32 π-electron tetraanion of a derivative of a doubly cyclic π-conjugated system with 28 π-electrons, tetracyclopentatetraphenylene (TCPTP), [...] Read more.
Multiple reduced π-conjugated hydrocarbons exhibit π-electron conjugation modes different from neutral species due to the distinct number of electrons. Herein, we report the generation of a 32 π-electron tetraanion of a derivative of a doubly cyclic π-conjugated system with 28 π-electrons, tetracyclopentatetraphenylene (TCPTP), through an exhaustive reduction with potassium. Although aggregation causes some complications, based on spectroscopic and theoretical investigations, it is revealed that negative charges are located at the outer and inner peripheries, suggesting that the tetraanion adopts a globally delocalized double annulenoid (annulene-within-an-annulene, AWA) mode, with 22 π-electron outer and 10 π-electron inner aromatic perimeters. On the other hand, excess charges of the outer perimeter are mainly located at the apical position of the pentagonal rings, indicating a significant contribution of the cyclopentadienide form. The theoretical analysis of magnetically induced ring current tropicities reveals counter-rotating ring currents at the outer and inner rings, supporting the predominant contribution of the cyclopentadienide form. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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16 pages, 2781 KiB  
Article
Tuning Low-Lying Excited States and Optical Properties in IndenoFluorene Diradicaloids and Longitudinally Extended Derivatives: A Computational Perspective
by Michele Orza, Andrea Zerbini and Fabrizia Negri
Chemistry 2025, 7(2), 47; https://doi.org/10.3390/chemistry7020047 - 19 Mar 2025
Viewed by 321
Abstract
In this work, we have considered the family of indenofluorene (IF) and its longitudinally elongated variants fluorenofluorene and diindenoanthracene and investigated their low-lying excited states and optical properties via quantum-chemical studies at the density functional theory (DFT) level. Singlet ground-state diradicals exhibit distinct [...] Read more.
In this work, we have considered the family of indenofluorene (IF) and its longitudinally elongated variants fluorenofluorene and diindenoanthracene and investigated their low-lying excited states and optical properties via quantum-chemical studies at the density functional theory (DFT) level. Singlet ground-state diradicals exhibit distinct optical properties due to the presence of a low-lying state dominated by a doubly excited configuration (DE state), often below the lowest allowed singly excited state (SE state). IFs and their elongated derivatives, with tunable diradical character and both symmetric and nonsymmetric structures, provide an ideal platform for exploring DE state energy modulation and spectroscopic behavior. The study shows that absorption spectra simulated using time-dependent (TD) calculations based on unrestricted broken-symmetry antiparallel-spin reference configuration (TDUDFT) closely match the available experimental data. Additionally, it reveals distinct spectral behavior for symmetric and nonsymmetric derivatives, highlighting the role of lowest-lying weakly allowed excited states potentially promoting non-radiative deactivation pathways. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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18 pages, 1432 KiB  
Article
Fragmentation-Based Linear-Scaling Method for Strongly Correlated Systems: Divide-and-Conquer Hartree–Fock–Bogoliubov Method, Its Energy Gradient, and Applications to Graphene Nano-Ribbon Systems
by Masato Kobayashi, Ryosuke Kodama, Tomoko Akama and Tetsuya Taketsugu
Chemistry 2025, 7(2), 46; https://doi.org/10.3390/chemistry7020046 - 18 Mar 2025
Viewed by 456
Abstract
This study introduces a fragmentation-based linear-scaling method for strongly correlated systems, specifically the divide-and-conquer Hartree–Fock–Bogoliubov (DC-HFB) approach. Two energy gradient formulations of the DC-HFB method are derived and implemented, enabling efficient optimization of molecular geometries in large systems. This method is applied to [...] Read more.
This study introduces a fragmentation-based linear-scaling method for strongly correlated systems, specifically the divide-and-conquer Hartree–Fock–Bogoliubov (DC-HFB) approach. Two energy gradient formulations of the DC-HFB method are derived and implemented, enabling efficient optimization of molecular geometries in large systems. This method is applied to graphene nanoribbons (GNRs) to explore their geometries and polyradical characters. Numerical results demonstrate that the present DC-HFB method has the potential to treat the static electron correlation and predict diradical character in GNRs, offering new avenues for studying large-scale strongly correlated systems. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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11 pages, 21344 KiB  
Article
Fully Conjugated Heteroatomic Non- and Quasi-Alternant Polyradicals
by Sergi Betkhoshvili, Jordi Poater, Ibério de P. R. Moreira and Josep Maria Bofill
Chemistry 2025, 7(2), 45; https://doi.org/10.3390/chemistry7020045 - 18 Mar 2025
Viewed by 422
Abstract
In this work, we present fully π-conjugated diradical(oid)s and tetraradical(oid)s with five-membered non-alternant cyclopentadienyl and quasi-alternant thiophene rings, the latter of which is used as a source of aromatic stabilization. By controlling the topology of the π-systems, we can restrict the [...] Read more.
In this work, we present fully π-conjugated diradical(oid)s and tetraradical(oid)s with five-membered non-alternant cyclopentadienyl and quasi-alternant thiophene rings, the latter of which is used as a source of aromatic stabilization. By controlling the topology of the π-systems, we can restrict the lower-bound number of unpaired electrons. Aromaticity and/or antiaromaticity in the different configurations of the compounds can be used to design conjugated compounds with high open-shell characters. We also designed the diradical(oid) based only on the five-membered rings, without any terminal radical groups. This work exemplifies the application of our theory of rational design of polyradicals to heteroatomic and non/quasi-alternant organic systems. The ability to create polyradicals with different classes of organic compounds establishes the possibility of creating multifunctional organic materials with tunable magnetic properties. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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12 pages, 1375 KiB  
Article
An Electronic Structural Analysis of O2-Binding Dicopper Complex: Insights from Spin Magnetism and Molecular Orbitals
by Ryusei Morimoto, Kanami Sugiyama, Masahiro Higashi and Hirofumi Sato
Chemistry 2025, 7(2), 44; https://doi.org/10.3390/chemistry7020044 - 18 Mar 2025
Viewed by 334
Abstract
We investigated the geometry and electronic structure of the oxygen-bridged dicopper complex [CuII2(NH3)4O2]2+ and discussed how different DFT methods and basis sets, including dispersion corrections and dielectric media, affect the predicted structure and [...] Read more.
We investigated the geometry and electronic structure of the oxygen-bridged dicopper complex [CuII2(NH3)4O2]2+ and discussed how different DFT methods and basis sets, including dispersion corrections and dielectric media, affect the predicted structure and spin state. Our results showed that pure functionals yielded the closed-shell singlet character, whereas hybrid functionals presented a partial diradical character that coincided with increased spin contamination. Incorporating a polarizable continuum model further enhanced the diradical character and more closely reproduced the measured Cu–Cu distance with a bent Cu2O2 core. Analysis of the molecular orbitals and computed absorption spectra revealed how orbitals produce the key transition from ligand-to-metal charge transfer. These findings underscore how environmental effects influence the description of Cu2O2 chemistry. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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10 pages, 2571 KiB  
Article
2,4,6-Trichlorophenyl-Substituted [3]Triangulene with Enhanced Stability
by Yiming Yang, Peipei Liu, Xiaoli Zhao and Xueliang Shi
Chemistry 2025, 7(2), 39; https://doi.org/10.3390/chemistry7020039 - 13 Mar 2025
Viewed by 656
Abstract
Triangulene, also known as Clar’s hydrocarbon, has been sought after by chemists for more than 70 years but with limited success. Herein, we report an oxidative dehydrogenation method to synthesize two kinetically blocked [3]triangulene derivatives TRI-1 (reported) and TRI-2 (newly synthesized), in which [...] Read more.
Triangulene, also known as Clar’s hydrocarbon, has been sought after by chemists for more than 70 years but with limited success. Herein, we report an oxidative dehydrogenation method to synthesize two kinetically blocked [3]triangulene derivatives TRI-1 (reported) and TRI-2 (newly synthesized), in which the three most reactive sites are substituted by bulky mesityl groups and electron-withdrawing 2,4,6-trichlorophenyl groups, and meanwhile, three vertices of triangulene are substituted by tert-butyl groups. Interestingly, the dihydro-triangulene core possesses two isomers well characterized by UV-vis, NMR spectroscopy, and X-ray crystallographic analysis, which is interestingly substituent-dependent. The newly synthesized TRI-2 is isolated in crystalline form, and X-ray crystallographic analysis reveals that the aryl substituents are nearly perpendicular to the triangulene plane and thus cause little perturbation of the electronic properties of the triangulene. Notably, 2,4,6-trichlorophenyl-substituted TRI-2 exhibits enhanced stability compared to the reported mesityl-substituted TRI-1, e.g., TRI-2 is stable for months in a crystalline state under a nitrogen atmosphere, and TRI-2 in a solution state is also more persistent than TRI-1 (half-life for TRI-1 ≈ 18 h vs. TRI-2 ≈ 132 h). This achievement will facilitate the design and synthesis of stable triangulene dimers and oligomers with higher spin multiplicity. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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13 pages, 4415 KiB  
Article
A Stable π-Expanded o-Quinodimethane via the Photochemical Dearomative Cycloaddition of Corannulene with an Isolable Dialkylsilylene
by Shintaro Ishida, Maiko Mori, Shunya Honda and Takeaki Iwamoto
Chemistry 2025, 7(2), 37; https://doi.org/10.3390/chemistry7020037 - 11 Mar 2025
Viewed by 640
Abstract
A stable π-expanded o-quinodimethane derivative (2) was synthesized by photochemical dearomative cycloaddition of corannulene with an isolable dialkylsilylene (1) and isolated as a dark blue solid. Compound 2 adopts a very flat bowl shape in contrast to parent [...] Read more.
A stable π-expanded o-quinodimethane derivative (2) was synthesized by photochemical dearomative cycloaddition of corannulene with an isolable dialkylsilylene (1) and isolated as a dark blue solid. Compound 2 adopts a very flat bowl shape in contrast to parent corannulene. Structural and spectroscopic characteristics, redox properties, and computational study suggest that 2 has a small but significant diradical character (y0 = 0.11). One-electron reduction of 2 provides the corresponding radical anion as an isolable salt. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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10 pages, 3623 KiB  
Article
Solid–Liquid Phase Transition-Induced Magnetic Property Changes in Tetrakis(ethylthio)tetrathiafulvalene Radical Cation Salt
by Toshihiro Sakai, Soichiro Kawamorita, Takeshi Naota and Shuichi Suzuki
Chemistry 2025, 7(2), 32; https://doi.org/10.3390/chemistry7020032 - 1 Mar 2025
Viewed by 520
Abstract
We discovered that the radical cation salt [1•+][NTf2−], composed of tetrakis(ethylthio)tetrathiafulvalene radical cation and bis(N-trifluoromethanesulfonyl)imide ion, exhibits significant changes in its magnetic properties during a solid–liquid phase transition. Single-crystal structure analysis revealed that the radical [...] Read more.
We discovered that the radical cation salt [1•+][NTf2−], composed of tetrakis(ethylthio)tetrathiafulvalene radical cation and bis(N-trifluoromethanesulfonyl)imide ion, exhibits significant changes in its magnetic properties during a solid–liquid phase transition. Single-crystal structure analysis revealed that the radical cation salt [1•+][NTf2−] forms an associated structure called a π-dimer in the crystalline phase. The extremely weak ESR signal in the crystalline state indicates strong antiferromagnetic interactions between unpaired electrons within the π-dimer. Upon heating, the crystalline phase transitions into a liquid state without decomposition at 144 °C (417 K). The ESR signals in the liquid state are significantly stronger than those in the solid state, suggesting the formation of a paramagnetic state with weak interactions between radical cations. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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16 pages, 3603 KiB  
Article
Synthesis of Terbenzo- and Tetrabenzoolympicenyl Radicals and Their Cations
by Zewen Guo, Xiaoqi Tian and Zhe Sun
Chemistry 2025, 7(2), 28; https://doi.org/10.3390/chemistry7020028 - 24 Feb 2025
Viewed by 388
Abstract
The synthesis of two polycyclic aromatic hydrocarbon (PAH) monoradicals, terbenzoolympicenyl radical (BOR1) and tetrabenzoolympicenyl radical (BOR2), is reported. One-electron oxidation of both BOR1 and BOR2 yielded stable cationic species BOR1+ and BOR2+, whose structures were unambiguously characterized using [...] Read more.
The synthesis of two polycyclic aromatic hydrocarbon (PAH) monoradicals, terbenzoolympicenyl radical (BOR1) and tetrabenzoolympicenyl radical (BOR2), is reported. One-electron oxidation of both BOR1 and BOR2 yielded stable cationic species BOR1+ and BOR2+, whose structures were unambiguously characterized using 2D nuclear magnetic resonance (NMR) spectroscopy. The physical properties of BOR1 and BOR2 were investigated by means of electron paramagnetic resonance (EPR), UV-vis-NIR, cyclic voltammetry (CV), and density functional theory (DFT) calculations. BOR1+ and BOR2+ exhibited intense near-infrared (NIR) absorption, which may be of potential use in the biological fields. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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9 pages, 2847 KiB  
Communication
Crystalline Diradical Dianions and Radical Anions of Indenofluorenediones
by Xue Dong, Tao Wang, Yu Zhao, Quanchun Sun, Shuxuan Tang, Yue Zhao and Xinping Wang
Chemistry 2025, 7(1), 27; https://doi.org/10.3390/chemistry7010027 - 19 Feb 2025
Viewed by 381
Abstract
Fluorenone derivatives represent promising candidates for electron-transport materials in organic electronic devices. Given that anionic species serve as electron-transfer carriers in electron-transport materials, it is highly desirable to isolate and characterize the radical anions and dianions of indenofluorened derivatives (IFO). In this work, [...] Read more.
Fluorenone derivatives represent promising candidates for electron-transport materials in organic electronic devices. Given that anionic species serve as electron-transfer carriers in electron-transport materials, it is highly desirable to isolate and characterize the radical anions and dianions of indenofluorened derivatives (IFO). In this work, the reduction of three indenofluorenedione derivatives (IFO, 1, 2 and 3) with potassium resulted in three radical anion salts (1K[(crypt-222)], 2K[(crypt-222)] and 3K) and one dianion salt (2[K(crypt-222)]2). Single-crystal X-ray diffraction and electron paramagnetic resonance (EPR) spectroscopy reveal that 1K[(crypt-222)] and 2K[(crypt-222)] have a full delocalization of the unpaired electron which is supported by calculated spin density distributions. We demonstrate that the polarization of electron spin in 3K is induced by potassium ion coordination through single-crystal X-ray structure analysis and DFT calculations, suggesting the electrostatic effect by potassium ion has a significant influence on the spin density modulation. Superconducting quantum interference device (SQUID) measurements and DFT calculations show that 2[K(crypt-222)]2 has an open-shell singlet base with a large singlet-triplet energy gap (ΔEos-t = −7.40 kcal mol−1) so that the excited triplet state is not accessible at room temperature. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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13 pages, 14910 KiB  
Article
Too Persistent to Resist: Aromaticity in 16e Osmapentalene Radicals Survives Regardless of Redox
by Shijie Pan, Jun Yan, Weitang Li, Zhigang Shuai and Jun Zhu
Chemistry 2025, 7(1), 22; https://doi.org/10.3390/chemistry7010022 - 8 Feb 2025
Viewed by 1052
Abstract
As one of the most important concepts in organic chemistry, aromaticity has attracted considerable attention from both theoretical and experimental chemists. Limited by the traditional rules (Hückel’s rules and Baird’s rules), species can only achieve aromaticity in a single state (S0 or [...] Read more.
As one of the most important concepts in organic chemistry, aromaticity has attracted considerable attention from both theoretical and experimental chemists. Limited by the traditional rules (Hückel’s rules and Baird’s rules), species can only achieve aromaticity in a single state (S0 or T1) in most cases. In 2018, our group first reported 16 electron osmapentalene that showed aromaticity in both the S0 and T1 states, which is defined as adaptive aromaticity. In recent years, although adaptive aromatic compounds have been expanded, the adaptive aromatics containing metal-centered radical has not been reported. Here, we carry out density functional theory calculations to explore the aromaticity of the corresponding radicals based on osmapentalyne and osmapentalenes in their S0 states. It is found that the corresponding radicals of adaptive aromatic osmapentalene exhibit aromaticity regardless of the radicals formed by oxidation or reduction, supported by a series of aromaticity indices including ΔBL, NICS, AICD, EDDB, and ELF. In contrast, for the nonaromatic or antiaromatic compound in the T1 state, only its cationic radical shows aromaticity. Furthermore, the spin density localization on the metal center is the key factor for the radicals to achieve aromaticity. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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10 pages, 2021 KiB  
Communication
Stable Fluorenyl Radicals Showing Tunable Doublet Emission
by Xudong Hou, Tingting Xu, Jun Zhu, Shaofei Wu and Jishan Wu
Chemistry 2025, 7(1), 21; https://doi.org/10.3390/chemistry7010021 - 7 Feb 2025
Viewed by 828
Abstract
Neutral organic radicals with intrinsic spin-allowed doublet emission have emerged as a promising class of luminescent materials, garnering significant research interest. However, the development of stable luminescent radicals with tunable emission remains challenging. Herein, we present the synthesis of a series of 9-(2,4,6-trichlorophenyl)-substituted [...] Read more.
Neutral organic radicals with intrinsic spin-allowed doublet emission have emerged as a promising class of luminescent materials, garnering significant research interest. However, the development of stable luminescent radicals with tunable emission remains challenging. Herein, we present the synthesis of a series of 9-(2,4,6-trichlorophenyl)-substituted fluorenyl radicals functionalized with various substituents at the 3,6-positions. These radicals exhibit enhanced stability through efficient spin delocalization and kinetic protection. Notably, they display red-shifted photoluminescence compared to traditional polychlorotriphenylmethyl radicals, with maximum emission wavelengths ranging from 679 nm to 744 nm. The mechanisms underlying the doublet emission, as well as their electrochemical properties, have been thoroughly investigated. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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13 pages, 4484 KiB  
Article
Synthesis and Characterization of Quinoxaline-Fused Cyclopenta[cd]azulene
by Tomohiro Oda, Yuina Onishi, Akihito Konishi and Makoto Yasuda
Chemistry 2025, 7(1), 15; https://doi.org/10.3390/chemistry7010015 - 23 Jan 2025
Viewed by 1500
Abstract
Azulene-based polycyclic hydrocarbons have garnered much attention as potential materials for organic optoelectronic devices and as molecular models for graphene nanosheets with structural defects. Although various methods for ring fusions to an azulene core have been established for ring fusions to an azulene [...] Read more.
Azulene-based polycyclic hydrocarbons have garnered much attention as potential materials for organic optoelectronic devices and as molecular models for graphene nanosheets with structural defects. Although various methods for ring fusions to an azulene core have been established for ring fusions to an azulene core, efficient synthetic methodologies for ortho- and peri-fusion to an azulene core are still lacking, which hinders the investigation of the effect of the ortho- and peri-fusion on the electronic properties of the embedded azulene core. Herein, we describe the synthesis and characterization of quinoxaline-fused cyclopenta[cd]azulene 4 as a new ortho- and peri-fused azulene derivative. The target molecule 4 was successfully synthesized in four steps from 4-methylazulene. The ring annulation decreased the lowest excitation energy compared with that of azulene and its structural isomer 5 and led to multiple reversible reduction processes. Characterization of the molecular geometry and optoelectronic properties of 4 revealed that the embedded azulene core preserves its original aromaticity, while the fused quinoxaline acts as a nucleophilic and basic site. These features suggest that 4 could serve as a metal ligand, a near-infrared absorber, and a component in organic functional devices. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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21 pages, 6552 KiB  
Article
Systematic Investigation on Surface Diradicals Using Theoretical Models: 2M/MgO and 2M/BaO (M = Cu, Ag, and Au)
by Kohei Tada, Koki Masuda, Ryohei Kishi and Yasutaka Kitagawa
Chemistry 2024, 6(6), 1572-1592; https://doi.org/10.3390/chemistry6060095 - 5 Dec 2024
Viewed by 869
Abstract
Diradical character is one of the characteristic quantities of functional open-shell molecules. Prof. Nakano devotedly studied the relationship between diradical character and material properties of open-shell molecules; now, we can use the diradical character as a powerful tool for molecular material designs. It [...] Read more.
Diradical character is one of the characteristic quantities of functional open-shell molecules. Prof. Nakano devotedly studied the relationship between diradical character and material properties of open-shell molecules; now, we can use the diradical character as a powerful tool for molecular material designs. It is still unclear how the open-shell molecules are affected by the interaction with the surface although the molecules have been immobilised for device applications. In the present study, the adsorptions of model diradical molecules with s-electrons on the MgO (001) and BaO (001) surfaces are investigated using approximate spin projected density functional theory with plane-wave basis (AP-DFT/plane-wave) to provide a systematic discussion of surface–diradical interactions. The accuracy of AP-DFT/plane-wave was verified by comparisons with the calculated results by NEVPT2. The computational error introduced by DFT calculations on the diradical state (spin contamination error) is reduced by the surface–diradical interaction. In addition, it is shown that (1) the diradical character is amplified by the orbital polarisation effects of oxide ions, and (2) the character decreases when the magnetic orbitals become electron-rich due to electron donation from the surfaces. The two effects are competing; the former is pronounced in Au systems, whereas the latter is pronounced in Ag systems. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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12 pages, 1933 KiB  
Article
Theoretical Study on One- and Two-Photon Absorption Properties of π-Stacked Multimer Models of Phenalenyl Radicals
by Masako Yokoyama, Ryohei Kishi and Yasutaka Kitagawa
Chemistry 2024, 6(6), 1427-1438; https://doi.org/10.3390/chemistry6060085 - 14 Nov 2024
Viewed by 1176
Abstract
Effects of the number of monomers (N) on the two-photon absorption (TPA) properties of π-stacked multimer models consisting of phenalenyl radicals were investigated theoretically. We conducted spectral simulations for the π-stacked N-mer models (N = 2, 4, and 6) [...] Read more.
Effects of the number of monomers (N) on the two-photon absorption (TPA) properties of π-stacked multimer models consisting of phenalenyl radicals were investigated theoretically. We conducted spectral simulations for the π-stacked N-mer models (N = 2, 4, and 6) with different stacking distances (d1) and their alternation patterns (d2/d1). Excitation energies and transition dipole moments were calculated at the extended multi-configurational quasi-degenerate second-order perturbation theory (XMC-QDPT2) level based on the complete active space self-consistent field (CASSCF) wavefunctions with the active space orbitals constructed from the singly occupied molecular orbitals (SOMOs) of monomers. The TPA cross-section value per dimer unit at the first peak, originating from the electronic transition along the stacking direction, was predicted to increase significantly as the d2/d1 approaches one, as the d1 decreases, and as the N increases from 2 to 6. These tendencies are similar to the calculation results for the static hyperpolarizabilities. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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12 pages, 3150 KiB  
Article
Diazenium Betaines Derived from the Stable Free Radical DPPH with Diradicaloid Behavior
by Adela F. Dobre, Augustin M. Mădălan, Anamaria Hanganu and Petre Ionita
Chemistry 2024, 6(5), 899-910; https://doi.org/10.3390/chemistry6050052 - 3 Sep 2024
Viewed by 1207
Abstract
Starting from the well known stable free radical DPPH (or its reduced counterpart, 2,2-diphenyl-1-picryl-hydrazine) and several amino derivatives, novel zwitterionic compounds (diazenium betaines) were obtained and characterized by different means, like NMR, IR, MS, and UV–Vis. These betaines are highly intense blue-colored compounds [...] Read more.
Starting from the well known stable free radical DPPH (or its reduced counterpart, 2,2-diphenyl-1-picryl-hydrazine) and several amino derivatives, novel zwitterionic compounds (diazenium betaines) were obtained and characterized by different means, like NMR, IR, MS, and UV–Vis. These betaines are highly intense blue-colored compounds that can be easily reduced by ascorbic acid (vitamin C) or sodium ascorbate to their corresponding para-phenyl substituted derivatives of DPPH, which have a yellow color. Most of such redox processes were found to be reversible. However, the oxidation of 2-p-aminophenyl-2-phenyl-1-picryl-hydrazine led to an azo-derivative of DPPH diradical, and its structure was unveiled by X-ray monocrystal diffraction. Possible diradicaloid behavior is also discussed. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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14 pages, 5433 KiB  
Article
The Magnetic Properties of Fluorenyl and tert-Butyl-nitroxyl Acene-Based Derivatives: A Quantum Chemical Insight
by Alyona A. Starikova, Maxim G. Chegerev, Andrey G. Starikov and Vladimir I. Minkin
Chemistry 2024, 6(5), 816-829; https://doi.org/10.3390/chemistry6050049 - 23 Aug 2024
Cited by 2 | Viewed by 1395
Abstract
Acenes, as a class of polycyclic aromatic hydrocarbons, attract considerable attention due to their remarkable nonlinear optical and magnetic properties. The aim of this work was the elucidation of the capability of radical-substituted acene derivatives to undergo spin-state-switching rearrangements. For this purpose, a [...] Read more.
Acenes, as a class of polycyclic aromatic hydrocarbons, attract considerable attention due to their remarkable nonlinear optical and magnetic properties. The aim of this work was the elucidation of the capability of radical-substituted acene derivatives to undergo spin-state-switching rearrangements. For this purpose, a series of acene-based (anthracene, pentacene, heptacene) molecules bearing fluorenyl and tert-butyl-nitroxyl radicals were investigated through comprehensive quantum chemical modeling of their electronic structures, isomerization and magnetic properties. A possible mechanism of the transformation of the closed-shell folded isomer into the biradical twisted structure of the bis-fluorenyl anthracene has been ascertained by applying the procedure of searching for the Minimum Energy Crossing Point. The conditions favoring the occurrence of spin-state-switching in such classes of polycyclic aromatic hydrocarbon derivatives have been formulated. By varying the size of an acene core and the type of radical substituent, the compounds capable of changing their magnetic properties have been revealed. Considering the unique features of radical-bearing acene-based derivatives, the proposed molecules can be used as functional materials in photonics and electronics. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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Review

Jump to: Research

42 pages, 14272 KiB  
Review
Experimental Methods and Nonlinear Optical Properties of Open-Shell Molecular Species
by Kenji Kamada
Chemistry 2025, 7(3), 67; https://doi.org/10.3390/chemistry7030067 (registering DOI) - 22 Apr 2025
Viewed by 151
Abstract
Degenerate third-order nonlinear optical (NLO) responses of organic molecules have a wide range of applications in science and engineering because they relate to the intensity-dependent refractive index (IDRI) and nonlinear absorption (NLA), such as two-photon absorption (TPA). Among the many molecular systems, open-shell [...] Read more.
Degenerate third-order nonlinear optical (NLO) responses of organic molecules have a wide range of applications in science and engineering because they relate to the intensity-dependent refractive index (IDRI) and nonlinear absorption (NLA), such as two-photon absorption (TPA). Among the many molecular systems, open-shell molecular species such as intermediate singlet diradicaloids have attracted considerable attention because of their enhanced response, predicted theoretically by Nakano et al. Experimental studies for proofing and evaluating the enhanced nonlinearities play an important role in the development of the field. This tutorial review provides the solid fundamentals of the NLO processes of open-shell molecular species even to those who are not familiar with the experimental works. Its scope ranges from the basics of NLO responses, definitions, and interrelations of the key parameters of the responses, such as hyperpolarizability and TPA cross-section, to the experimental techniques used to evaluate them. Including the recent achievements, the evolution of experimental works on the TPA properties of singlet diradicaloids is also reviewed according to families of molecular structures. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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16 pages, 6576 KiB  
Review
m-Quinodimethane-Based Fused-Ring Diradicals with Singlet and Triplet Ground States
by Akihiro Shimizu
Chemistry 2025, 7(2), 40; https://doi.org/10.3390/chemistry7020040 - 13 Mar 2025
Viewed by 398
Abstract
Diradicals have attracted the attention of chemists due to their unique electronic structures and properties originating from unpaired electrons. One of the fundamental motifs of diradicals is quinodimethane; p- and o-quinodimethanes are singlet Kekulé hydrocarbons, while m-quinodimethane is a triplet [...] Read more.
Diradicals have attracted the attention of chemists due to their unique electronic structures and properties originating from unpaired electrons. One of the fundamental motifs of diradicals is quinodimethane; p- and o-quinodimethanes are singlet Kekulé hydrocarbons, while m-quinodimethane is a triplet non-Kekulé hydrocarbon. Most of the hydrocarbon diradicals studied to date have been limited to p- and o-quinodimethane-based non-fused-ring and fused-ring open-shell singlet diradicals and m-quinodimethane-based non-fused-ring triplet diradicals. In this account, studies on m-quinodimethane-based fused-ring diradicals, including an open-shell singlet Kekulé hydrocarbon, an open-shell singlet zwitterion, non-Kekulé hydrocarbon-based triplet diradical and diradical cation, and a triplet Kekulé hydrocarbon, are summarized. They are designed, successfully synthesized, and isolated as crystals, and their fundamental electronic structures and properties have been elucidated by optical, electrochemical, and magnetic measurements, together with DFT calculations. A series of studies showed that controlling the interaction between the two unpaired electrons of m-quinodimethane through an appropriate molecular design would produce polycyclic diradicals with various open-shell singlet diradical characters and the energy differences between singlet and triplet states. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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69 pages, 11327 KiB  
Review
Quantum Mechanical Approaches to Strongly Correlated Electron Systems: Structure, Bonding, and Properties of Diradicals, Triradicals, and Polyradicals
by Satoru Yamada, Isamu Shigemoto, Takashi Kawakami, Hiroshi Isobe, Mitsuo Shoji, Koichi Miyagawa and Kizashi Yamaguchi
Chemistry 2025, 7(2), 38; https://doi.org/10.3390/chemistry7020038 - 12 Mar 2025
Viewed by 766
Abstract
The structure, bonding, and properties of diradicals, triradicals, and polyradicals have been investigated using broken symmetry (BS) molecular orbital (MO) and BS density functional theory (DFT) methods, which are regarded as the first steps in the mean-field approach toward strongly correlated electron systems [...] Read more.
The structure, bonding, and properties of diradicals, triradicals, and polyradicals have been investigated using broken symmetry (BS) molecular orbital (MO) and BS density functional theory (DFT) methods, which are regarded as the first steps in the mean-field approach toward strongly correlated electron systems (SCES). The natural orbital (NO) analyses of the BS MO and BS DFT solutions were performed to elucidate the natural orbitals of their occupation numbers, which are used for derivations of the diradical character (y) and several chemical indices for the open-shell molecules under investigation. These chemical indices are also obtained using SCES, the next theoretical step, which uses symmetry-recovered resonating BS (RBS) and multi-determinant methods such as multi-reference (MR) configuration interaction (CI) and MR-coupled cluster (CC) methods that employ the NOs generated in the first step. The nonlinear optical response properties of organic open-shell species were theoretically investigated with several procedures, such as MR CI (CC), the numerical Liouville, and Monte Carlo wavefunction methods, as the third step to SCES. The second-order hyperpolarizability (γ) of diradicals such as a phenalenyl radical dimer were mainly investigated in relation to the generation of quantum squeezed lights, which are used for the construction of the quantum entangled states for quantum optical devices such as quantum sensing and quantum computation. Basic quantum mechanical concepts, such as the Pegg–Barnett quantum phase operator, were also revisited in relation to the design and chemical synthesis of stable diradicals and polyradicals such as optical quantum molecular materials and future molecular qubits materials. Full article
(This article belongs to the Special Issue Open-Shell Systems—a Memorial Issue Dedicated to Professor Masayoshi Nakano)
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