Misplaced Pages

Biradicaloids or diradicaloids are molecules with two radical electrons that have significant interaction with each other. The two unpaired electrons are coupled and can either form a singlet ground state (antiferromagnetic coupling) or a triplet ground state (ferromagnetic coupling) (Figure 1).

This is in contrast to "disbiradicals," where the two radical electrons have no significant interaction and act independently as isolated radical species. Diradicals are characterized by their diradical character, commonly quantified using an indicator ${\displaystyle \gamma }$. In the limit of fully degenerate frontier molecular orbitals, ${\displaystyle \gamma }$ approaches a value of 1, representing 100% diradical character. However, diradicaloids have a small gap between the highest occupied molecular orbital (HOMO) and the lowest occupied molecular orbital (LUMO) and thus can be described as having incomplete diradical character, generally corresponding to a value of ${\displaystyle \gamma }$ between 0.20 and 0.80. Diradicals have historically been characterized as transient species describing the transition state of a bond breaking and/or making process, but recently, the introduction of steric strain to prevent bond formation and substitution of carbon atoms with main-group elements have been found to significantly stabilize diradical species, leading to their isolation and structural characterization. However, these modifications decrease diradical character, leading these species to be more properly designated as diradicaloids. Diradicaloids have found applications in small molecule activation, molecular switching, nonlinear optics, and spintronics.

Theoretical description

Electronic structure

Due to the coupling interaction between the radical electrons in a diradical(oid) species, they cannot be simply described as the union of two independent radical centers. Both the open-shell singlet and triplet states must be considered to fully describe the electronic structure of diradical(oid) species.

The triplet state wavefunction ${\displaystyle \Psi _{T}}$ can be described as a single electronic configuration with a single Slater determinant. However, when the frontier molecular orbitals are degenerate or nearly degenerate, the lowest-energy singlet state wavefunction ${\displaystyle \Psi _{S}}$ must account for multiple electronic configurations (see electronic correlation). Thus, ${\displaystyle \Psi _{S}}$ is most accurately represented as a combination of Slater determinants. Here, the configuration interaction (CI) coefficients ${\displaystyle c_{1}}$ and ${\displaystyle c_{2}}$ define the contribution of each determinant to the total wavefunction, where ${\displaystyle \psi _{H}}$ refers to the HOMO and ${\displaystyle \psi _{L}}$ refers to the LUMO:

${\displaystyle \Psi _{T}=|...\psi _{H}\psi _{L}\rangle }$

${\displaystyle \Psi _{S}=c_{1}|...\psi _{H}^{2}\rangle -c_{2}|...\psi _{L}^{2}\rangle }$

When  ${\displaystyle c_{1}=c_{2}={\frac {1}{\sqrt {2}}}}$,  ${\displaystyle \psi _{H}}$ and ${\displaystyle \psi _{L}}$ are degenerate, and the singlet wavefunction ${\displaystyle \Psi _{S}}$ describes a perfect diradical. As the HOMO-LUMO gap increases, the wavefunction approaches that of a classical closed-shell species; ${\displaystyle c_{1}}$ approaches 1 and ${\displaystyle c_{2}}$ approaches 0 so that the lowest-energy singlet state is dominated by the doubly occupied HOMO.

To gain a more intuitive understanding of the diradical nature of the wavefunction, the triplet and singlet wavefunctions can be represented using a localized orbital basis, where ${\displaystyle \chi _{A}}$ and ${\displaystyle \chi _{B}}$ are the two localized orbitals (Figure 2). Assuming ${\displaystyle \chi _{A}}$ and ${\displaystyle \chi _{B}}$ are orthogonal, the overlap integral becomes 0. The HOMO ${\displaystyle \psi _{H}}$ can be decomposed into the in-phase overlap of ${\displaystyle \chi _{A}}$ and ${\displaystyle \chi _{B}}$, while the LUMO ${\displaystyle \psi _{L}}$ can be decomposed into the out-of-phase overlap of ${\displaystyle \chi _{A}}$ and ${\displaystyle \chi _{B}}$:

${\displaystyle \psi _{H}={\frac {1}{\sqrt {2}}}(\chi _{A}+\chi _{B})}$

${\displaystyle \psi _{L}={\frac {1}{\sqrt {2}}}(\chi _{A}-\chi _{B})}$

Consequently, the singlet wavefunction ${\displaystyle \Psi _{S}}$ can be expressed as the combination of a covalent contribution ${\displaystyle \Psi _{cov}}$ and an ionic contribution ${\displaystyle \Psi _{ion}}$. The covalent component represents the electron configuration in which both localized orbitals are singly occupied; this corresponds to diradical character. The ionic component represents the electron configuration in which one localized orbital is doubly occupied, leaving the other localized orbital empty; this corresponds to zwitterionic character:

${\displaystyle \Psi _{S}={\frac {c_{1}+c_{2}}{\sqrt {2}}}{\frac {1}{\sqrt {2}}}(|...\chi _{A}\chi _{B}\rangle -|...\chi _{B}\chi _{A}\rangle )+{\frac {c_{1}-c_{2}}{\sqrt {2}}}{\frac {1}{\sqrt {2}}}(|...\chi _{A}^{2}\rangle -|...\chi _{B}^{2}\rangle )}$

${\displaystyle \Psi _{S}=c_{cov}\Psi _{cov}+c_{ion}\Psi _{ion}}$ where ${\displaystyle c_{cov}={\frac {c_{1}+c_{2}}{\sqrt {2}}}}$ and ${\displaystyle c_{ion}={\frac {c_{1}-c_{2}}{\sqrt {2}}}}$

When ${\displaystyle c_{1}=c_{2}={\frac {1}{\sqrt {2}}}}$, ${\displaystyle c_{cov}=1}$ and ${\displaystyle c_{ion}=0}$; thus, this situation describes 100% diradical character. As the HOMO-LUMO gap increases, ${\displaystyle c_{1}}$ approaches 1 and ${\displaystyle c_{2}}$ approaches 0, which results in ${\displaystyle c_{cov}=c_{ion}}$; thus, this situation reduces to the complete delocalization of the electrons over the two-orbital system, which is equivalent to the electron configuration of the closed-shell species.

Indicators of diradical character

The CI coefficients ${\displaystyle c_{1}}$ and ${\displaystyle c_{2}}$ can be used to provide a quantification of diradical character. Some common indicators are listed below:

${\displaystyle \gamma ={\sqrt {2}}c_{2}=c_{cov}-c_{ion}}$

${\displaystyle d=2c_{1}c_{2}=c_{cov}^{2}-c_{ion}^{2}}$

${\displaystyle \beta =2c_{2}^{2}=(c_{cov}-c_{ion})^{2}}$

All of the above indicators (${\displaystyle \gamma ,d,\beta }$) effectively describe how much greater the relative weight of the covalent contribution is to the singlet wavefunction ${\displaystyle \Psi _{S}}$ compared to the ionic contribution. Thus, the greater the values of these indicators, the greater the diradical character. In the limit of 100% diradical character, these indicators approach a value of 1; in the limit of 100% classical closed-shell character, these indicators approach a value of 0.

Natural orbital (NO) occupation numbers are also another theoretical indicator of diradical character. The occupancy of the lowest unoccupied NO is equal to the ${\displaystyle \beta }$ indicator and ranges from 0 to 1; the closer the calculated occupancy is to 1, the greater the predicted diradical character. On the other hand, the occupancy of the highest occupied NO ranges from 1 to 2; the closer the calculated occupancy is to 1, the greater the predicted diradical character. These natural orbital occupancy numbers can be calculated using almost all computational methods and therefore can often be obtained with less computational cost than calculating ${\displaystyle \beta }$ using CI methods.

A small singlet-triplet energy gap can also indicate increased diradical character. Lastly, if the calculated A-B distance (where A and B are the two radical centers) is elongated compared to the sum of the covalent radii (the typical A-B distance of a closed-shell molecule) but is shorter than the sum of the van der Waals radii, this may also suggest the presence of a diradicaloid. Incorporating sterically bulky substituents and introducing ring strain in heterocycles can help to prevent bond formation and/or generate elongated bonds.

Synthesis

Cyclobutane-1,3-diyl analogues

Cyclobutane-1,3-diyl

Cyclobutane-1,3-diyl is the planar four-membered carbon ring species with radical character localized at the 1 and 3 positions. The singlet cyclobutane-1,3-diyl is predicted to be the transition state for the ring inversion of bicyclobutane, proceeding via homolytic cleavage of the transannular carbon-carbon bond (Figure 3).

A 1,3-dimethyl substituted derivative in the triplet state was detected by electron paramagnetic resonance spectroscopy; the diradical species was generated via irradiation of the precursor diazo compound below 25 K in a solid matrix (Figure 4). However, the all-carbon cyclobutane-1,3-diyl is very short-lived and quickly reacts to form the bicyclobutane isomer.

1,3-diphospha-cyclobutane-2,4-diyl

In 1995, Niecke and coworkers reported the first synthesis of a phosphorus analog of cyclobutane-1,3-diyl, ₂. This species consists of a -four-membered heterocycle with radical character centered on the two carbon atoms. The heterocycle was synthesized from the reaction of aryl(dichloromethylene)phosphene (aryl = Mes*, supermesityl) with n-butyllithium in a 2:1 ratio, followed by elimination of LiCl (Figure 5). X-ray diffraction revealed that that the unit exists in the planar four-membered ring form, rather than as the bicyclic isomer. MCSCF calculations predicted a singlet ground state. In addition, the calculated CI wavefunction has contributions from both the doubly occupied HOMO state and the doubly occupied LUMO state; this corresponded to occupation of the HOMO with 1.6 electrons, indicating considerable diradical character. The diphosphacyclobutane heterocycle is thermally stable, and transannular C-C bond formation is thermally forbidden according to the Woodward-Hoffmann rules. Heating at 100 °C in toluene led to the cleavage of the P-C bond, likely generating a ring-opened carbene intermediate that subsequently performed intramolecular C-H activation.

Another synthetic route was developed by Yoshifuji and Ito to access a wider variety of substituents at phosphorus (Figure 7). 2 equivalents of Mes*-substituted phosphaalkyne can be reacted with the lithiated compound of the first substituent on phosphorus, forming the anionic four-membered ring. This intermediate can then be alkylated to attach the second phosphorus substituent. This two-step synthetic pathway allows for the synthesis of unsymmetrically substituted 1,3-diphospha-cyclobutane-2,4-diyls. The substituents on carbon are limited to Mes*, however, due to the limitation of the phosphaalkyne starting material. Most diradicaloids of this type can be handled in air and display high kinetic stability due to the steric protection provided by the Mes* substituents on the carbon radical centers.

1,3-diaza-2,4-dipnicta-cyclobutane-2,4-diyl

These diradical species consist of a heterocyclic core (Pn = pnictogen) where the radical sites are centered on the pnictogen atoms. The presence of a nitrogen atom in the heterocycle is thought to stabilize the planar form relative to the bicyclic isomer. This is believed to result from the inability of Pn-Pn bond formation in the bicyclobutane form to energetically compensate for the increase in Pn-N-Pn angle strain; consequently, the planar form, which allows for larger Pn-N-Pn angles, is more stable. The lack of electron delocalization found in calculations suggests that aromaticity from the presence of 6π electrons does not play a significant role in stabilization of the planar isomers.

In 2011, Schulz and coworkers synthesized the first example of a four-membered ring diradicaloid (here, Pn = phosphorus) with meta-terphenyl and hypersilyl substituents on the nitrogen atoms. The synthetic route begins with the chlorinated P₂N₂ heterocycle, which is then reduced to the diradicaloid with relatively mild titanium(II) or titanium(III) reducing agents (Figure 8). The bulky terphenyl and hypersilyl groups provide kinetic stabilization, preventing dimerization. The terphenyl-substituted diradicaloid is almost indefinitely stable under argon atmosphere at ambient temperatures as a solid and in solvent. The crystal structure reveals a planar four-membered ring and a long distance between the two phosphorus atoms (2.6186 Å compared to 2.22 Å, the sum of covalent radii), indicating no significant transannular interactions. Computations also support the diradical character of this species and predict a singlet ground state. The calculated CI wavefunction has contributions from both the doubly occupied HOMO state and the doubly occupied LUMO state; this corresponds to occupation of the HOMO with 1.7 electrons, indicating considerable diradical character.

Using a similar synthetic route, the arsenic analogue was also synthesized from the chlorinated precursor; reduction using magnesium metal generated the arsenic centered diradicaloid. The crystal structure confirmed a long As-As distance, and EPR spectroscopy indicated a singlet ground state. A mixed phosphorus-arsenic diradicaloid was also reported in 2015, the first with different radical centers. The crystal structure revealed a kite-shaped planar four membered ring with a transannular As-P distance of 2.790 Å, which is shorter than the sum of van der Waals radii (3.65 Å) but longer than the sum of covalent radii (2.32 Å).

Heavier derivatives (where Pn = antimony and bismuth) were observed in situ but could not be isolated due to rapid decomposition to the allyl analogues in the presence of magnesium; however, the corresponding diradicaloids could be trapped through cycloadditions with alkynes, thereby providing evidence for their existence. Calculations suggest that the antimony and bismuth-centered diradicaloids have higher diradical character than the lighter pnictogen analogues due to the singlet-triplet energy gap decreasing with heavier, larger pnictogens.

Other hetero-cyclobutane-1,3-diyls

In 2002, Bertrand and coworkers synthesized the first 1,3-diphospha-2,4-dibora-cyclobutane-2,4-diyl, in which the diradical character is localized on the boron atoms. In 2009, Schnöckel and coworkers reported the synthesis of a heavier aluminum-centered diradical analog. A silicon-centered diradical (1,3-diaza-2,4-disilacyclobutane-2,4-diyl) is also known, synthesized by Sekiguchi and coworkers in 2011. An analog in which the nitrogen atoms are replaced with carbon, as well as an all-silicon cyclobutane-1,3-diyl, have been synthesized. In 2004, Power and coworkers reported the synthesis of a germanium-centered diradical, the heavier analog of Sekiguchi's silicon diradical. The corresponding tin-centered diradicals have also been synthesized by Lappert and coworkers in 2004. In 2017, N-heterocyclic carbene-stabilized phosphorus-centered diradicals were reported; like the Niecke-type diradicaloid, the core heterocycle is a four-membered ring, but the radical centers are located on phosphorus rather than carbon. Lastly, one of the first hetero-cyclobutanediyl derivates synthesized is N₂S₂, disulfur dinitride, but its diradical character has been widely discussed in the literature and is still disputed today.

Cyclopentane-1,3-diyl analogues

Cyclopentane-1,3-diyl

Cyclopentane-1,3-diyl is the planar five-membered carbon ring species with radical character localized at the 1 and 3 positions. The triplet diradical was detected by EPR spectroscopy; the diradical species was generated via irradiation of the precursor diazo compound at 5.5 K in a solid matrix (Figure 11). Due to its very short lifetime, all-carbon cyclopentane-1,3-diyl cannot be isolated, but heating cyclopentane-1,3-diyl leads to the formation of a transannular C-C bond, producing the housane isomer. While the triplet state is predicted to be an energy minimum, the singlet state is predicted to be the transition state for housane inversion.

Hetero-cyclopentane-1,3-diyls

Five-membered diradicals with radical character localized on pnictogen atoms can be synthesized via the insertion of carbon monoxide and isonitriles into the corresponding pnictogen-centered cyclobutane-1,3-diyls. In 2015, Schulz and coworkers reported the first stable cyclopentane-1,3-diyl species generated from the ring expansion of terphenyl-substituted diphosphadiazanediyl using carbon monoxide (Figure 12). The computed structural data support an almost planar five-membered ring, and the HOMO/LUMO contributions to the CI wavefunction indicate an occupation of the HOMO with 1.44 electrons, suggesting diradical character. Experimentally, additions of phosphaalkyne and elemental sulfur across the phosphorus atom are consistent with diradicaloid reactivity.

Isonitriles can also insert into the same diphosphadiazanediyls to form the corresponding heterocyclic 5-membered diradicaloids (Figure 13a). The insertion reaction is sensitive to the steric bulk of the substituent on the isonitrile; for example, the terphenyl-substituted isonitrile was unable to undergo the insertion reaction, while the smaller 2,6-dimethylphenyl isonitrile was able to insert into the P-N bond.

Isonitrile insertion was also explored with mixed phosphorus-nitrogen and phosphorus-arsenic centered 4-membered ring diradicaloids. With the latter compound, the isonitrile selectively inserts into the arsenic-nitrogen bond over the phosphorus-nitrogen bond (Figure 13b). The resulting five-membered ring species was characterized via X-ray structural analysis, confirming the above connectivity (Figure 14). Calculations revealed a substantial diradical character (${\displaystyle \beta }$=0.24), which agrees with the experimentally observed activation of triple bonds.

Other main group diradicaloids

Diradicaloid 6-membered heterocycles have been reported. In 2020, a cyclic alkylaminocarbene-stabilized 9,10-diboraanthracene was synthesized. EPR spectroscopy and quantum calculations indicated a singlet diradical ground state, and the incorporation of boron atoms was demonstrated to lower the HOMO-LUMO band gap. In 2021, a cyclic germanium-centered diradicaloid with a framework was isolated. Calculations indicated a singlet diradical ground state, and the ability of the germanium species to split dihydrogen at room temperature further supported its diradical character.

A 1,2-diborete diradicaloid containing a highly strained framework was reported by Braunschweig and coworkers in 2022. In 2024, the first diborepin diradicals, in which the boron radical sites are disjointed, were synthesized by Gilliard and coworkers.

Reactivity

Diradicaloids, depending on the reaction conditions and extent of diradical character, can display both closed-shell and open-shell reactivity. Closed-shell reactivity (e.g., pericyclic reactions) is best understood using the delocalized molecular orbital picture, while open-shell reactivity (e.g., radical additions) is best understood using the localized atomic orbital picture.

Closed-shell reactivity

For example, the phosphorus-centered diradicaloid ₂ can undergo concerted pericyclic reactions with single bonds (H₂), double bonds (alkenes, aldehydes), and triple bonds (alkynes, nitriles) (Figure 15). Only the cis-addition products are observed, which is consistent with a concerted mechanism.

From a molecular orbital perspective, the formation of new bonds at phosphorus occurs through the interaction of the antibonding HOMO of the diradicaloid with the antibonding LUMO of the reacting partner or the interaction of the bonding LUMO of the diradicaloid with the bonding HOMO of the reacting partner, both of which are symmetry-allowed.

Interestingly, H₂ addition is reversible; below 50 °C, H₂ addition is observed, and above 60 °C, H₂ release occurs to regenerate the original diradicaloid species.

Diradicaloids can also react as nucleophiles or electrophiles from their zwitterionic resonance forms. For example, ₂ has been shown to react with both Lewis basic N-heterocyclic carbenes as well as Lewis acidic gold(I) chloride (Figure 17).

Open-shell reactivity

For example, the phosphorus-centered diradicaloid ₂ can undergo stepwise radical addition reactions with alkyl bromides (Figure 18). The trans-addition products were exclusively formed, which is consistent with a stepwise radical abstraction followed by radical recombination mechanism.

Applications

This section needs additional citations for verification. Please help improve this article by adding citations to reliable sources in this section. Unsourced material may be challenged and removed. Find sources: "Diradicaloid" – news · newspapers · books · scholar · JSTOR (December 2024) (Learn how and when to remove this message)

Hetero-cyclopentane-1,3-diyls have been shown to display molecular switching behavior; this property relies on the ability to use external stimuli to switch a molecule between two different stable states, thereby allowing for easy modulation of special reactivity and/or other properties. Diradicaloids can serve as molecular switches if certain external stimuli can reversibly toggle between the planar isomer, which displays diradical character and corresponding reactivity, and the bicyclic housane isomer, which is a closed shell species.

For example, the concept of switchable diradicals was demonstrated using the hetero-cyclopentane-1,3-diyl with phosphorus-phosphorus centered radicals (Figure 19). Upon exposure to red light, the planar five-membered ring diradical isomerizes to the bicyclic housane species. After irradiation, the thermally induced reverse reaction occurs, breaking the transannular bond to regenerate the planar diradicaloid species. Thus, the activation chemistry of the diradical can be switched "off" via irradiation and can be switched back "on" via stopping irradiation. This switching could be repeated several times without degradation of the diradicaloid.

References

1. Salem, Lionel; Rowland, Colin (1972). "The Electronic Properties of Diradicals". Angewandte Chemie International Edition in English. 11 (2): 92–111. doi:10.1002/anie.197200921. ISSN 1521-3773.
2. Chemistry (IUPAC), The International Union of Pure and Applied. "IUPAC - diradicals (D01765)". goldbook.iupac.org. doi:10.1351/goldbook.d01765. Retrieved 2024-12-12.
3. ^ Schulz, Axel (2018-09-25). "Group 15 biradicals: synthesis and reactivity of cyclobutane-1,3-diyl and cyclopentane-1,3-diyl analogues". Dalton Transactions. 47 (37): 12827–12837. doi:10.1039/C8DT03038C. ISSN 1477-9234. PMID 30183025.
4. Chemistry (IUPAC), The International Union of Pure and Applied. "IUPAC - biradical (B00671)". goldbook.iupac.org. doi:10.1351/goldbook.b00671. Retrieved 2024-12-12.
5. ^ Bresien, Jonas; Eickhoff, Liesa; Schulz, Axel; Zander, Edgar (2023-01-01), Reedijk, Jan; Poeppelmeier, Kenneth R. (eds.), "1.04 - Biradicals in main group chemistry: Synthesis, electronic structure, and application in small-molecule activation", Comprehensive Inorganic Chemistry III (Third Edition), Oxford: Elsevier, pp. 165–233, doi:10.1016/b978-0-12-823144-9.00029-7, ISBN 978-0-12-823153-1, retrieved 2024-12-12
6. ^ Hinz, Alexander; Bresien, Jonas; Breher, Frank; Schulz, Axel (2023-08-23). "Heteroatom-Based Diradical(oid)s". Chemical Reviews. 123 (16): 10468–10526. doi:10.1021/acs.chemrev.3c00255. ISSN 0009-2665. PMID 37556842.
7. ^ Stuyver, Thijs; Chen, Bo; Zeng, Tao; Geerlings, Paul; De Proft, Frank; Hoffmann, Roald (2019-11-13). "Do Diradicals Behave Like Radicals?". Chemical Reviews. 119 (21): 11291–11351. doi:10.1021/acs.chemrev.9b00260. ISSN 0009-2665. PMID 31593450.
8. Hinz, Alexander; Kuzora, Rene; Rosenthal, Uwe; Schulz, Axel; Villinger, Alexander (2014). "Activation of Small Molecules by Phosphorus Biradicaloids". Chemistry – A European Journal. 20 (45): 14659–14673. doi:10.1002/chem.201403964. ISSN 1521-3765. PMID 25266101.
9. Kishi, Ryohei; Murata, Yusuke; Saito, Michika; Morita, Keisuke; Abe, Manabu; Nakano, Masayoshi (2014-11-13). "Theoretical Study on Diradical Characters and Nonlinear Optical Properties of 1,3-Diradical Compounds". The Journal of Physical Chemistry A. 118 (45): 10837–10848. Bibcode:2014JPCA..11810837K. doi:10.1021/jp508657s. ISSN 1089-5639. PMID 25325668.
10. Hu, Xiaoguang; Wang, Wenxiang; Wang, Dongsheng; Zheng, Yonghao (2018-11-01). "The electronic applications of stable diradicaloids: present and future". Journal of Materials Chemistry C. 6 (42): 11232–11242. doi:10.1039/C8TC04484H. ISSN 2050-7534.
11. ^ Bresien, Jonas; Kröger-Badge, Thomas; Lochbrunner, Stefan; Michalik, Dirk; Müller, Henrik; Schulz, Axel; Zander, Edgar (2019-03-20). "A chemical reaction controlled by light-activated molecular switches based on hetero-cyclopentanediyls". Chemical Science. 10 (12): 3486–3493. doi:10.1039/C8SC04893B. ISSN 2041-6539. PMC 6430090. PMID 30996939.
12. Gopalakrishna, Tullimilli Y.; Zeng, Wangdong; Lu, Xuefeng; Wu, Jishan (2018-02-27). "From open-shell singlet diradicaloids to polyradicaloids". Chemical Communications. 54 (18): 2186–2199. doi:10.1039/C7CC09949E. ISSN 1364-548X. PMID 29423462.
13. Goddard, William A. III; Dunning, Thom H. Jr.; Hunt, William J.; Hay, P. Jeffrey (1973-11-01). "Generalized valence bond description of bonding in low-lying states of molecules". Accounts of Chemical Research. 6 (11): 368–376. doi:10.1021/ar50071a002. ISSN 0001-4842.
14. Hayes, Edward F.; Siu, Albert K. Q. (1971-04-01). "Electronic structure of the open forms of three-membered rings". Journal of the American Chemical Society. 93 (8): 2090–2091. Bibcode:1971JAChS..93.2090H. doi:10.1021/ja00737a064. ISSN 0002-7863.
15. Herebian, Diran; Wieghardt, Karl E.; Neese, Frank (2003-09-01). "Analysis and Interpretation of Metal-Radical Coupling in a Series of Square Planar Nickel Complexes: Correlated Ab Initio and Density Functional Investigation of [Ni(LISQ)2] (LISQ=3,5-di-tert-butyl-o-diiminobenzosemiquinonate(1-))". Journal of the American Chemical Society. 125 (36): 10997–11005. Bibcode:2003JAChS.12510997H. doi:10.1021/ja030124m. ISSN 0002-7863. PMID 12952481.
16. Bachler, Vinzenz; Olbrich, Gottfried; Neese, Frank; Wieghardt, Karl (2002-08-01). "Theoretical Evidence for the Singlet Diradical Character of Square Planar Nickel Complexes Containing Two o-Semiquinonato Type Ligands". Inorganic Chemistry. 41 (16): 4179–4193. doi:10.1021/ic0113101. ISSN 0020-1669. PMID 12160406.
17. Jung, Yousung; Head-Gordon, Martin (2003). "How Diradicaloid Is a Stable Diradical?". ChemPhysChem. 4 (5): 522–525. doi:10.1002/cphc.200200668. ISSN 1439-7641. PMID 12785272.
18. Doehnert, Detlef; Koutecky, Jaroslav (1980-03-01). "Occupation numbers of natural orbitals as a criterion for biradical character. Different kinds of biradicals". Journal of the American Chemical Society. 102 (6): 1789–1796. Bibcode:1980JAChS.102.1789D. doi:10.1021/ja00526a005. ISSN 0002-7863.
19. Carl Lineberger, W.; Thatcher Borden, Weston (2011). "The synergy between qualitative theory, quantitative calculations, and direct experiments in understanding, calculating, and measuring the energy differences between the lowest singlet and triplet states of organic diradicals". Physical Chemistry Chemical Physics. 13 (25): 11792–12513. Bibcode:2011PCCP...1311792C. doi:10.1039/c0cp02786c. ISSN 1463-9076. PMID 21614391.
20. Nguyen, Kiet A.; Gordon, Mark S.; Boatz, Jerry A. (1994-10-01). "The Inversion of Bicyclobutane and Bicyclodiazoxane". Journal of the American Chemical Society. 116 (20): 9241–9249. Bibcode:1994JAChS.116.9241N. doi:10.1021/ja00099a047. ISSN 0002-7863.
21. Jain, Rakesh; Snyder, Gary J.; Dougherty, Dennis A. (1984-11-01). "Direct, ESR observation of the localized biradical 1,3-dimethyl-1,3-cyclobutadiyl". Journal of the American Chemical Society. 106 (23): 7294–7295. Bibcode:1984JAChS.106.7294J. doi:10.1021/ja00335a098. ISSN 0002-7863.
22. Jain, Rakesh.; Sponsler, Michael B.; Coms, Frank D.; Dougherty, Dennis A. (1988-03-01). "Cyclobutanediyls: a new class of localized biradicals. Synthesis and EPR spectroscopy". Journal of the American Chemical Society. 110 (5): 1356–1366. Bibcode:1988JAChS.110.1356J. doi:10.1021/ja00213a006. ISSN 0002-7863.
23. Niecke, Edgar; Fuchs, Andre'; Baumeister, Fred; Nieger, Martin; Schoeller, Wolfgang W. (1995). "A P2C2 Four-Membered Ring with Unusual Bonding—Synthesis, Structure, and Ring Opening of a 1,3-Diphosphacyclobutane-2,4-diyl". Angewandte Chemie International Edition in English. 34 (5): 555–557. doi:10.1002/anie.199505551. ISSN 1521-3773.
24. Sugiyama, Hiroki; Ito, Shigekazu; Yoshifuji, Masaaki (2003). "Synthesis of a 1,3-Diphosphacyclobutane-2,4-diyl from Mes*CP". Angewandte Chemie International Edition. 42 (32): 3802–3804. doi:10.1002/anie.200351727. ISSN 1521-3773. PMID 12923849.
25. Grande-Aztatzi, Rafael; Mercero, Jose M.; Ugalde, Jesus M. (2016-04-28). "The stability of biradicaloid versus closed-shell [E(μ-XR)]2 (E = P, As; X = N, P, As) rings. Does aromaticity play a role?". Physical Chemistry Chemical Physics. 18 (17): 11879–11884. Bibcode:2016PCCP...1811879G. doi:10.1039/C5CP07263H. ISSN 1463-9084. PMID 26911902.
26. Beweries, Torsten; Kuzora, Rene; Rosenthal, Uwe; Schulz, Axel; Villinger, Alexander (2011). "[P(μ-NTer)]2: A Biradicaloid That Is Stable at High Temperature". Angewandte Chemie International Edition. 50 (38): 8974–8978. doi:10.1002/anie.201103742. ISSN 1521-3773. PMID 21858902.
27. Demeshko, Serhiy; Godemann, Christian; Kuzora, René; Schulz, Axel; Villinger, Alexander (2013). "An Arsenic–Nitrogen Biradicaloid: Synthesis, Properties, and Reactivity". Angewandte Chemie International Edition. 52 (7): 2105–2108. doi:10.1002/anie.201208360. ISSN 1521-3773. PMID 23319315.
28. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2015). "A Mixed Arsenic–Phosphorus Centered Biradicaloid". Angewandte Chemie International Edition. 54 (2): 668–672. doi:10.1002/anie.201408639. ISSN 1521-3773. PMID 25404061.
29. Bresien, J.; Hinz, A.; Schulz, A.; Villinger, A. (2018-03-26). "Trapping of transient, heavy pnictogen-centred biradicals". Dalton Transactions. 47 (13): 4433–4436. doi:10.1039/C8DT00487K. ISSN 1477-9234. PMID 29492506.
30. Scheschkewitz, David; Amii, Hideki; Gornitzka, Heinz; Schoeller, Wolfgang W.; Bourissou, Didier; Bertrand, Guy (2002-03-08). "Singlet Diradicals: from Transition States to Crystalline Compounds". Science. 295 (5561): 1880–1881. Bibcode:2002Sci...295.1880S. doi:10.1126/science.1068167. PMID 11884750.
31. Henke, Patrick; Pankewitz, Tobias; Klopper, Wim; Breher, Frank; Schnöckel, Hansgeorg (2009). "Snapshots of the AlAl σ-Bond Formation Starting from AlR2 Units: Experimental and Computational Observations". Angewandte Chemie International Edition. 48 (43): 8141–8145. doi:10.1002/anie.200901754. ISSN 1521-3773. PMID 19708044.
32. Takeuchi, Katsuhiko; Ichinohe, Masaaki; Sekiguchi, Akira (2011-08-17). "Access to a Stable Si2N2 Four-Membered Ring with Non-Kekulé Singlet Biradical Character from a Disilyne". Journal of the American Chemical Society. 133 (32): 12478–12481. Bibcode:2011JAChS.13312478T. doi:10.1021/ja2059846. ISSN 0002-7863. PMID 21776998.
33. Zhang, Shu-Hua; Xi, Hong-Wei; Lim, Kok Hwa; Meng, Qingyong; Huang, Ming-Bao; So, Cheuk-Wai (2012). "Synthesis and Characterization of a Singlet Delocalized 2,4-Diimino-1,3-disilacyclobutanediyl and a Silylenylsilaimine". Chemistry – A European Journal. 18 (14): 4258–4263. doi:10.1002/chem.201103351. ISSN 1521-3765. PMID 22378245.
34. Yildiz, Cem B.; Leszczyńska, Kinga I.; González-Gallardo, Sandra; Zimmer, Michael; Azizoglu, Akin; Biskup, Till; Kay, Christopher W. M.; Huch, Volker; Rzepa, Henry S.; Scheschkewitz, David (2020). "Equilibrium Formation of Stable All-Silicon Versions of 1,3-Cyclobutanediyl". Angewandte Chemie International Edition. 59 (35): 15087–15092. doi:10.1002/anie.202006283. ISSN 1521-3773. PMC 7496386. PMID 32407571.
35. Richards, A. F.; Brynda, M.; Power, P. P. (2004-08-01). "Synthesis and Characterization of Ge2{Sn(X)Ar#}3 and Ga2{Ge(X)Ar#}3 (Ar# = C6H3-2,6-Mes2), X = (Cl/I): Rare Examples of Mixed Heavier Group 14/14, 13/14 Element Clusters". Organometallics. 23 (17): 4009–4011. doi:10.1021/om0497137. ISSN 0276-7333.
36. Cox, Hazel; Hitchcock, Peter B.; Lappert, Michael F.; Pierssens, Luc J.-M. (2004). "A 1,3-Diaza-2,4-distannacyclobutanediide: Synthesis, Structure, and Bonding". Angewandte Chemie. 116 (34): 4600–4604. Bibcode:2004AngCh.116.4600C. doi:10.1002/ange.200460039. ISSN 1521-3757.
37. Li, Zhongshu; Chen, Xiaodan; Andrada, Diego M.; Frenking, Gernot; Benkö, Zoltán; Li, Yaqi; Harmer, Jeffrey R.; Su, Cheng-Yong; Grützmacher, Hansjörg (2017). "(L)2C2P2: Dicarbondiphosphide Stabilized by N-Heterocyclic Carbenes or Cyclic Diamido Carbenes". Angewandte Chemie International Edition. 56 (21): 5744–5749. doi:10.1002/anie.201612247. ISSN 1521-3773. PMID 28436079.
38. Harcourt, Richard D.; Klapötke, Thomas M.; Schulz, Axel; Wolynec, Peter (1998-03-01). "On the Singlet Diradical Character of S2N2". The Journal of Physical Chemistry A. 102 (10): 1850–1853. Bibcode:1998JPCA..102.1850H. doi:10.1021/jp9733835. ISSN 1089-5639.
39. Buchwalter, S. L.; Closs, G. L. (1975-06-01). "Electron spin resonance study of matrix isolated 1,3-cyclopentadiyl, a localized 1,3-carbon biradical". Journal of the American Chemical Society. 97 (13): 3857–3858. Bibcode:1975JAChS..97.3857B. doi:10.1021/ja00846a073. ISSN 0002-7863.
40. Conrad, Morgan P.; Pitzer, Russell M.; Schaefer, Henry F. III (1979-04-01). "Geometrical structure and energetics of Closs's diradical: 1,3-cyclopentadiyl". Journal of the American Chemical Society. 101 (8): 2245–2246. Bibcode:1979JAChS.101.2245C. doi:10.1021/ja00502a073. ISSN 0002-7863.
41. Sherrill, C. David; Seidl, Edward T.; Schaefer, Henry F. III (1992-04-01). "Closs's diradical: some surprises on the potential energy hypersurface". The Journal of Physical Chemistry. 96 (9): 3712–3716. doi:10.1021/j100188a029. ISSN 0022-3654.
42. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2015). "Stable Heterocyclopentane-1,3-diyls". Angewandte Chemie International Edition. 54 (9): 2776–2779. doi:10.1002/anie.201410276. ISSN 1521-3773. PMID 25604347.
43. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2015-08-12). "Tunable Cyclopentane-1,3-diyls Generated by Insertion of Isonitriles into Diphosphadiazanediyls". Journal of the American Chemical Society. 137 (31): 9953–9962. Bibcode:2015JAChS.137.9953H. doi:10.1021/jacs.5b05596. ISSN 0002-7863. PMID 26204242.
44. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2015-12-17). "Zwitterionic and biradicaloid heteroatomic cyclopentane derivatives containing different group 15 elements". Chemical Science. 7 (1): 745–751. doi:10.1039/C5SC03515E. ISSN 2041-6539. PMC 5953028. PMID 29896358.
45. Saalfrank, Christian; Fantuzzi, Felipe; Kupfer, Thomas; Ritschel, Benedikt; Hammond, Kai; Krummenacher, Ivo; Bertermann, Rüdiger; Wirthensohn, Raphael; Finze, Maik; Schmid, Paul; Engel, Volker; Engels, Bernd; Braunschweig, Holger (2020). "cAAC-Stabilized 9,10-diboraanthracenes—Acenes with Open-Shell Singlet Biradical Ground States". Angewandte Chemie International Edition. 59 (43): 19338–19343. doi:10.1002/anie.202008206. ISSN 1521-3773. PMC 7589216. PMID 32662218.
46. Sharma, Mahendra K.; Ebeler, Falk; Glodde, Timo; Neumann, Beate; Stammler, Hans-Georg; Ghadwal, Rajendra S. (2021-01-13). "Isolation of a Ge(I) Diradicaloid and Dihydrogen Splitting". Journal of the American Chemical Society. 143 (1): 121–125. Bibcode:2021JAChS.143..121S. doi:10.1021/jacs.0c11828. ISSN 0002-7863. PMID 33373236.
47. Gärtner, Annalena; Meier, Lukas; Arrowsmith, Merle; Dietz, Maximilian; Krummenacher, Ivo; Bertermann, Rüdiger; Fantuzzi, Felipe; Braunschweig, Holger (2022-11-23). "Highly Strained Arene-Fused 1,2-Diborete Biradicaloid". Journal of the American Chemical Society. 144 (46): 21363–21370. Bibcode:2022JAChS.14421363G. doi:10.1021/jacs.2c09971. ISSN 0002-7863. PMID 36350352.
48. Hollister, Kimberly K.; Molino, Andrew; Jones, Nula; Le, VuongVy V.; Dickie, Diane A.; Cafiso, David S.; Wilson, David J. D.; Gilliard, Robert J. Jr. (2024-03-13). "Unlocking Biradical Character in Diborepins". Journal of the American Chemical Society. 146 (10): 6506–6515. Bibcode:2024JAChS.146.6506H. doi:10.1021/jacs.3c08297. ISSN 0002-7863. PMID 38420913.
49. Rosenboom, Jan; Villinger, Alexander; Schulz, Axel; Bresien, Jonas (2022-09-13). "Concerted addition of aldehydes to the singlet biradical [P(μ-NTer)]2". Dalton Transactions. 51 (35): 13479–13487. doi:10.1039/D2DT02229J. ISSN 1477-9234. PMID 35997123.
50. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2016). "Metal-Free Activation of Hydrogen, Carbon Dioxide, and Ammonia by the Open-Shell Singlet Biradicaloid [P(μ-NTer)]2". Angewandte Chemie International Edition. 55 (40): 12214–12218. doi:10.1002/anie.201606892. ISSN 1521-3773. PMID 27585355.
51. Hinz, Alexander; Schulz, Axel; Villinger, Alexander (2016-04-28). "On the behaviour of biradicaloid [P(μ-NTer)]2 towards Lewis acids and bases". Chemical Communications. 52 (37): 6328–6331. doi:10.1039/C6CC01935H. ISSN 1364-548X. PMID 27086655.
52. Rosenboom, Jan; Chojetzki, Lukas; Suhrbier, Tim; Rabeah, Jabor; Villinger, Alexander; Wustrack, Ronald; Bresien, Jonas; Schulz, Axel (2022). "Radical Reactivity of the Biradical [⋅P(μ-NTer)2P⋅] and Isolation of a Persistent Phosphorus-Cantered Monoradical [⋅P(μ-NTer)2P-Et]". Chemistry – A European Journal. 28 (36): e202200624. doi:10.1002/chem.202200624. ISSN 1521-3765. PMC 9322606. PMID 35445770.

• Molecular machines
• Radicals