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UGA-SSMRPT2 -- A Multireference Perturbation Theory Predicting Accurate Electronic Excitation Energies in Diverse Molecular Systems

Shamik Chanda, Pratyush Bhattacharjya, Avijit Sen, Sangita Sen

TL;DR

This work addresses the challenge of accurately predicting electronic excitations in systems with multireference character by introducing UGA-SSMRPT2, a spin-free, state-specific multireference perturbation theory derived from Mukherjee's Mk-MRCC via the Unitary Group Adapted framework. The theory employs a multi-partitioned one-body Fock-like Hamiltonian $H_0$ to build a second-order effective Hamiltonian, yielding both unrelaxed and relaxed energies while maintaining intruder-free, size-extensive behavior and avoiding empirical shifts. Benchmarking across 68 excitations spanning valence, Rydberg, charge-transfer, and singlet–triplet states shows a mean absolute deviation of $0.12$ eV and excellent correlation with EOM-CCSD and TBEs, often using compact active spaces such as CAS$(2,2)$–CAS$(4,8)$. These results demonstrate that UGA-SSMRPT2 provides a robust, scalable alternative to CASPT2/NEVPT2/MCQDPT2 for challenging excited-state problems, with broad applicability to organic photophysics and optoelectronics.

Abstract

UGA-SSMRPT2, the spin-free perturbative analogue of Mukerjee's State-Specific Multireference Coupled Cluster Theory (MkMRCC) is known to be successful for size-extensive and intruder-free construction of dissociation curves. This work demonstrates that UGA-SSMRPT2 is also an accurate and computationally inexpensive framework for computing excitation energies. The method achieves near-chemical accuracy for the vast majority of $π\to π^*$, $n \to π^*$, charge-transfer, valence-Rydberg and Rydberg excited states commonly used for benchmarking electronic structure theories for excited states. Our results demonstrate that UGA-SSMRPT2 excitation energies lie within 0.20 eV of EOM-CCSD and/or well-established theoretical best estimates often surpassing the popular MRPT2 approaches like NEVPT2, CASPT2, and MCQDPT while typically requiring smaller active spaces. Its state-specific formulation circumvents the well-known intruder-state problem and eliminates the need for empirical parameters such as IPEA shifts in CASPT2. This work proposes UGA-SSMRPT2 as a robust, and scalable approach for modeling challenging electronic excited states.

UGA-SSMRPT2 -- A Multireference Perturbation Theory Predicting Accurate Electronic Excitation Energies in Diverse Molecular Systems

TL;DR

This work addresses the challenge of accurately predicting electronic excitations in systems with multireference character by introducing UGA-SSMRPT2, a spin-free, state-specific multireference perturbation theory derived from Mukherjee's Mk-MRCC via the Unitary Group Adapted framework. The theory employs a multi-partitioned one-body Fock-like Hamiltonian to build a second-order effective Hamiltonian, yielding both unrelaxed and relaxed energies while maintaining intruder-free, size-extensive behavior and avoiding empirical shifts. Benchmarking across 68 excitations spanning valence, Rydberg, charge-transfer, and singlet–triplet states shows a mean absolute deviation of eV and excellent correlation with EOM-CCSD and TBEs, often using compact active spaces such as CAS–CAS. These results demonstrate that UGA-SSMRPT2 provides a robust, scalable alternative to CASPT2/NEVPT2/MCQDPT2 for challenging excited-state problems, with broad applicability to organic photophysics and optoelectronics.

Abstract

UGA-SSMRPT2, the spin-free perturbative analogue of Mukerjee's State-Specific Multireference Coupled Cluster Theory (MkMRCC) is known to be successful for size-extensive and intruder-free construction of dissociation curves. This work demonstrates that UGA-SSMRPT2 is also an accurate and computationally inexpensive framework for computing excitation energies. The method achieves near-chemical accuracy for the vast majority of , , charge-transfer, valence-Rydberg and Rydberg excited states commonly used for benchmarking electronic structure theories for excited states. Our results demonstrate that UGA-SSMRPT2 excitation energies lie within 0.20 eV of EOM-CCSD and/or well-established theoretical best estimates often surpassing the popular MRPT2 approaches like NEVPT2, CASPT2, and MCQDPT while typically requiring smaller active spaces. Its state-specific formulation circumvents the well-known intruder-state problem and eliminates the need for empirical parameters such as IPEA shifts in CASPT2. This work proposes UGA-SSMRPT2 as a robust, and scalable approach for modeling challenging electronic excited states.
Paper Structure (4 sections, 10 equations, 5 figures, 1 table)

This paper contains 4 sections, 10 equations, 5 figures, 1 table.

Table of Contents

  1. Introduction
  2. UGA-SSMRPT2 Theory
  3. Results and Discussions
  4. Summary and Future Outlook

Figures (5)

  • Figure 1: Test set of molecules in this study.
  • Figure 2: Correlation Plot for 68 excitations with all MRPTs vs EOM-CCSD with the error bar set at 0.25 eV
  • Figure 3: Signed Error histogram for 68 excitations with all MRPTs vs EOM-CCSD
  • Figure 4: Box-and-whisker plots of signed errors ($E_{\mathrm{method}} - E_{\mathrm{EOM\text{-}CCSD}}$) for various wavefunction methods. Boxes represent the interquartile range (IQR) and medians, whiskers extend to 1.5×IQR, and circles denote outliers.
  • Figure 5: Correlation plot of S$_1$-S$_0$ (eV) for sets A--F using various methods with respect to TBEs from Loos et. al.veril2021 where available and from Thiel et al.silva-junior2010b elsewhere.