Correlation-Driven Singlet--Triplet Inversion and Optical Spectra of N-Substituted Phenalenyls: Insights from PPP-FCI and TDDFT
Abstract
Several researchers have reported an atypical inversion of the lowest singlet (S1) and triplet (T1) excited states in nitrogen-substituted planar hydrocarbons. Contrary to Hund's rule of maximum multiplicity, poly-aza derivatives of phenalenyl, such as cyclazine and heptazine, have long been known to possess a negative singlet-triplet gap, ΔEST=E(S1)−E(T1). Using the well-known Pariser-Parr-Pople (PPP) model, a semi-empirical, wave-function-based Hamiltonian for correlated π-electrons, we investigate the singlet-triplet gap in ten N-substituted phenalenyl motifs. Two schemes of long-range Coulomb interactions are considered, and key parameters, including the on-site orbital energy, Hubbard U, and hopping integrals, are systematically tuned to benchmark the model for reliably estimating negative singlet-triplet gaps. Full configuration-interaction (FCI) method is employed to incorporate electron-correlation effects. Ground-state and T1 absorption spectra are subsequently calculated using the optimized PPP parameters that best reproduce the available experimental data. For validation, first-principles TDDFT calculations using various exchange--correlation functionals are also performed. Conventional adiabatic TDDFT fails to reproduce the inverted (S1−T1) ordering, indicating that the inclusion of the correlation driven multiconfigurational effects are essential for describing it. We find that the singlet TDDFT ground-state absorption spectra reproduce several qualitative features of the PPP-FCI spectra, although the TDDFT excitation energies are systematically higher. Detailed analysis of the ground-state and T1 absorption spectra reveals significant configuration mixing, providing a comprehensive characterization of the optical response of the N-substituted phenalenyl derivatives studied.
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BibTeX
@misc{rakshit2026correlationdriven,
title = {{Correlation-Driven Singlet--Triplet Inversion and Optical Spectra of N-Substituted Phenalenyls: Insights from PPP-FCI and TDDFT}},
author = {Medha Rakshit and Alok Shukla},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.31738},
eprint = {2609.31738},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.31738},
}
RIS
TY - UNPB
TI - Correlation-Driven Singlet--Triplet Inversion and Optical Spectra of N-Substituted Phenalenyls: Insights from PPP-FCI and TDDFT
AU - Medha Rakshit
AU - Alok Shukla
PY - 2026
DA - 2026/09/22
PB - arXiv
DO - 10.48550/arxiv.2609.31738
UR - https://arxiv.org/abs/2609.31738
AB - Several researchers have reported an atypical inversion of the lowest singlet (S_1) and triplet (T_1) excited states in nitrogen-substituted planar hydrocarbons. Contrary to Hund's rule of maximum multiplicity, poly-aza derivatives of phenalenyl, such as cyclazine and heptazine, have long been known to possess a negative singlet-triplet gap, ΔE_ST=E(S_1)−E(T_1). Using the well-known Pariser-Parr-Pople (PPP) model, a semi-empirical, wave-function-based Hamiltonian for correlated π-electrons, we investigate the singlet-triplet gap in ten N-substituted phenalenyl motifs. Two schemes of long-range Coulomb interactions are considered, and key parameters, including the on-site orbital energy, Hubbard U, and hopping integrals, are systematically tuned to benchmark the model for reliably estimating negative singlet-triplet gaps. Full configuration-interaction (FCI) method is employed to incorporate electron-correlation effects. Ground-state and T_1 absorption spectra are subsequently calculated using the optimized PPP parameters that best reproduce the available experimental data. For validation, first-principles TDDFT calculations using various exchange--correlation functionals are also performed. Conventional adiabatic TDDFT fails to reproduce the inverted (S_1−T_1) ordering, indicating that the inclusion of the correlation driven multiconfigurational effects are essential for describing it. We find that the singlet TDDFT ground-state absorption spectra reproduce several qualitative features of the PPP-FCI spectra, although the TDDFT excitation energies are systematically higher. Detailed analysis of the ground-state and T_1 absorption spectra reveals significant configuration mixing, providing a comprehensive characterization of the optical response of the N-substituted phenalenyl derivatives studied.
ER -