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Insights into Symmetry and Substitution Patterns Governing Singlet-Triplet Energy Gap in the Chemical Space of Azaphenalenes

Atreyee Majumdar, Raghunathan Ramakrishnan

TL;DR

This study systematically maps the space of 104 azaphenalene structures to identify substitutions and symmetry-lowering distortions that enable inverted singlet–triplet gaps ($S_1$-$T_1$). Using a geometry-extrapolated CCSD(T) framework coupled with Laplace-transform CC2 for excited states, the authors generate near-CCSD(T)/cc-pVTZ-quality geometries and accurate $S_1$ and $T_1$ energies across 117 configurations. They show that pseudo-Jahn–Teller distortions commonly erase the inversion, with cyclazine remaining inverted even after distortion, and identify 30 INVEST APs (notably including 7AP) as viable cores for fifth-generation OLED emitters. The work establishes design principles linking substitution motifs and symmetry to STG behavior and provides a curated dataset for future high-level screening and experimental validation of DFIST materials.

Abstract

Molecules that violate Hund's rule by exhibiting an inverted singlet-triplet gap (STG), where the first excited singlet (S$_1$) lies below the triplet (T$_1$), are rare but hold great promise as efficient fifth-generation light emitters. Azaphenalenes (APs) represent one of the few known molecular classes capable of such inversion of the S$_1$/T$_1$ energy ordering, yet a systematic exploration of all unique APs is lacking. Here, we investigate 104 distinct APs and classify them based on their adherence to or deviation from Hund's rule using S$_1$-T$_1$ gaps computed with the second-order coupled-cluster method employing the Laplace transform (L-CC2). To capture substitution-dependent pseudo-Jahn-Teller distortions that are inadequately described by MP2 and DFT methods, we employ focal-point extrapolation scheme to obtain near-CCSD(T)/cc-pVTZ-quality geometries. We find three APs to undergo $D_{\rm 3h} \rightarrow C_{\rm 3h}$ and ten to show $C_{\rm 2v}\rightarrow C_{\rm s}$ symmetry lowering, leading to a total of 117 configurations of 104 unique APs. Our study identifies top candidates with inverted STGs, revealing how substitution and symmetry-lowering modulate these gaps to uncover new stable AP cores that provide promising targets for designing molecular light-emitters.

Insights into Symmetry and Substitution Patterns Governing Singlet-Triplet Energy Gap in the Chemical Space of Azaphenalenes

TL;DR

This study systematically maps the space of 104 azaphenalene structures to identify substitutions and symmetry-lowering distortions that enable inverted singlet–triplet gaps (-). Using a geometry-extrapolated CCSD(T) framework coupled with Laplace-transform CC2 for excited states, the authors generate near-CCSD(T)/cc-pVTZ-quality geometries and accurate and energies across 117 configurations. They show that pseudo-Jahn–Teller distortions commonly erase the inversion, with cyclazine remaining inverted even after distortion, and identify 30 INVEST APs (notably including 7AP) as viable cores for fifth-generation OLED emitters. The work establishes design principles linking substitution motifs and symmetry to STG behavior and provides a curated dataset for future high-level screening and experimental validation of DFIST materials.

Abstract

Molecules that violate Hund's rule by exhibiting an inverted singlet-triplet gap (STG), where the first excited singlet (S) lies below the triplet (T), are rare but hold great promise as efficient fifth-generation light emitters. Azaphenalenes (APs) represent one of the few known molecular classes capable of such inversion of the S/T energy ordering, yet a systematic exploration of all unique APs is lacking. Here, we investigate 104 distinct APs and classify them based on their adherence to or deviation from Hund's rule using S-T gaps computed with the second-order coupled-cluster method employing the Laplace transform (L-CC2). To capture substitution-dependent pseudo-Jahn-Teller distortions that are inadequately described by MP2 and DFT methods, we employ focal-point extrapolation scheme to obtain near-CCSD(T)/cc-pVTZ-quality geometries. We find three APs to undergo and ten to show symmetry lowering, leading to a total of 117 configurations of 104 unique APs. Our study identifies top candidates with inverted STGs, revealing how substitution and symmetry-lowering modulate these gaps to uncover new stable AP cores that provide promising targets for designing molecular light-emitters.

Paper Structure

This paper contains 20 sections, 10 equations, 6 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Systems and Methods
  3. Enumeration of azaphenalene chemical space
  4. Survey of APs
  5. Basis set extrapolation scheme for geometries
  6. CCSD(T) Diagnostics to probe symmetry lowering
  7. Computational details
  8. Results and Discussions
  9. Accuracies of geometries
  10. Pseudo-Jahn--Teller (PJT) distortion and the impact on singlet-triplet gap of azaphenalenes
  11. Effect of symmetry and substitution pattern on singlet-triplet gaps
  12. Hund's rule violating azaphenalenes
  13. Conclusions
  14. Supplementary Information
  15. Data Availability
  16. ...and 5 more sections

Figures (6)

  • Figure 1: Representation of 104 azaphenalenes. The name of each molecule follows the convention prefixcycl[3.3.3]azine or prefixcyclazine, where prefix is stated below the structure. The first molecule (top, left) is cycl[3.3.3]azine or cyclazine without a prefix. Molecules with negative S$_1$-T$_1$ energy gaps predicted with L-CC2/aug-cc-pVDZ in the range $<-0.2$ eV, $\left(-0.2 , -0.15\right]$ eV, $\left(-0.15 , -0.1\right]$ eV, and $(-0.1, 0.0]$ eV are shown in red, orange, green, and blue boxes.
  • Figure 2: HOMO and LUMO density distributions along the periphery of cyclazine, illustrating the classification of substitution sites as electron-rich (HOMO-dominated) or electron-deficient (LUMO-dominated). The complete set of APs, derived from these substitution patterns are categorized according to the maximum symmetry point group allowed by their composition; arrows indicate cases of symmetry lowering. Cyclazine, a special case undergoing $D_{\rm 3h}$$\rightarrow$$C_{\rm 3h}$ distortion, is not included in any of these classes, as it contains no N atoms along the periphery.
  • Figure 3: Histograms of errors in bond lengths and bond angles of the Z-matrix parameters for geometries optimized using $\textbf{X}^{\rm CCSD(T),\,\Delta_{DT}}_{\rm VTZ}$ relative to the reference $\textbf{X}^{\rm CCSD(T)}_{\rm VTZ}$ for the benchmark systems listed in Table \ref{['tab:geom_benchmark']}.
  • Figure 4: For 2,5,8-triazacyclazine (4AP) in the $C_{\rm 3h}$ geometry, C–C and C–N bond lengths are shown for structures optimized using various methods with the cc-pVTZ basis set. All bond distances are given in Å. The MP2 results highlight its inability to capture the pseudo-Jahn--Teller distortion from $D_{\rm 3h}$ to $C_{\rm 3h}$ .
  • Figure 5: L-CC2/aug-cc-pVDZ singlet-triplet gaps of cyclazine (1AP) and its fifteen topologically charge-stabilized polyaza systems with N substituting the electron-rich carbon centers. 1,3,4,6-tetraazacyclazine (5AP) is the only unsubstituted azaphenalene for which the singlet-triplet has been experimentally measured (0-0 value is $-$0.047 eV)wilson2024spectroscopic. Heptazine (7AP) corresponds to 1,3,4,6,7,9-hexaazacyclazine. Names of molecules with singlet-triplet gaps in the range $<-0.2$ eV, $\left(-0.2 , -0.15\right]$ eV, $\left(-0.15 , -0.1\right]$ eV, and $> -0.1$ eV are shown in red, orange, green, and blue.
  • ...and 1 more figures