Two Single-Reference Approaches to Singlet Biradicaloid Problems: Complex, Restricted Orbitals and Approximate Spin-Projection Combined With Regularized Orbital-Optimized Møller-Plesset Perturbation Theory

Abstract

We present a comprehensive study of two single-reference approaches to singlet biradicaloids. These two approaches are based on the recently developed regularized orbital-optimized Møller-Plesset method ($\kappa$-OOMP2). The first approach is to combine the Yamaguchi's approximate projection (AP) scheme and $\kappa$-OOMP2 with unrestricted (U) orbitals ($\kappa$-UOOMP2). By capturing only essential symmetry breaking, $\kappa$-UOOMP2 can serve as a suitable basis for AP. The second approach is $\kappa$-OOMP2 with complex, restricted (cR) orbitals ($\kappa$-cROOMP2). Though its applicability is more limited due to the comparative rarity of cR solutions, $\kappa$-cROOMP2 offers a simple framework for describing singlet biradicaloids with complex polarization while removing artificial spatial symmetry breaking. We compare the scope of these two methods with numerical studies. We show that AP+$\kappa$-UOOMP2 and $\kappa$-cROOMP2 can perform similarly well in the TS12 set, a data set that includes 12 data points for triplet-singlet gaps of several atoms and diatomic molecules with a triplet ground state. This was also found to be true for the barrier height of a reaction involving attack on a cysteine ion by a singlet oxygen molecule. However, we also demonstrate that in highly symmetric systems like ${\text{C}}_{30}$ (${\text{D}}_{5h}$) $\kappa$-cROOMP2 is more suitable as it conserves spatial symmetry. Lastly, we present an organic biradicaloid that does not have a $\kappa$-cROOMP2 solution in which case only AP+$\kappa$-UOOMP2 is applicable. We recommend $\kappa$-cROOMP2 whenever complex polarization is essential and AP+$\kappa$-UOOMP2 for biradicaloids without essential complex polarization but with essential spin-polarization.

References in corpus (5)

• Heat-bath Configuration Interaction: An efficient selected CI algorithm inspired by heat-bath sampling
• Regularized Orbital-Optimized Second-Order Møller-Plesset Perturbation Theory: A Reliable Fifth-Order Scaling Electron Correlation Model with Orbital Energy Dependent Regularizers
• Distinguishing Artificial and Essential Symmetry Breaking in a Single Determinant: Approach and Application to the C${}_{60}$, C${}_{36}$, and C${}_{20}$ Fullerenes
• Polyradical character and spin frustration in fullerene molecules: An ab initio non-collinear Hartree--Fock study
• Open-Shell Coupled-Cluster Valence-Bond Theory Augmented with an Independent Amplitude Approximation for Three-Pair Correlations: Application to a Model Oxygen-Evolving Complex and Single Molecular Magnet

Cited by in corpus (18)

• Systematically Improvable Tensor Hypercontraction: Interpolative Separable Density-Fitting for Molecules Applied to Exact Exchange, Second- and Third-Order Møller-Plesset Perturbation Theory
• Excited States via Coupled Cluster Theory without Equation-of-Motion Methods: Seeking Higher Roots with Application to Doubly Excited States and Double Core Hole States
• Singlet-Triplet Energy Gaps of Organic Biradicals and Polyacenes with Auxiliary-Field Quantum Monte Carlo
• Third-Order Møller-Plesset Perturbation Theory Made Useful? Choice of Orbitals and Scaling Greatly Improves Accuracy for Thermochemistry, Kinetics and Intermolecular Interactions
• Utilizing Essential Symmetry Breaking in Auxiliary-Field Quantum Monte Carlo: Application to the Spin Gaps of the C${}_{36}$ Fullerene and an Iron Porphyrin Model Complex
• Polishing the Gold Standard: The Role of Orbital Choice in CCSD(T) Vibrational Frequency Prediction
• Kohn-Sham Density Functional Theory with Complex, Spin-Restricted Orbitals: Accessing a New Class of Densities without the Symmetry Dilemma
• Making Many-Body Interactions Nearly Pairwise Additive: The Polarized Many-Body Expansion Approach
• Unity of Kohn-Sham Density Functional Theory and Reduced Density Matrix Functional Theory
• A wave function perspective and efficient truncation of renormalised second-order perturbation theory
• Constrained-Path Auxiliary-Field Quantum Monte Carlo for Coupled Electrons and Phonons
• Towards a Resolution of the Static Correlation Problem in Density Functional Theory from Semidefinite Programming
• Approximate Functionals in Hypercomplex Kohn-Sham Theory
• Quantifying and reducing spin contamination in algebraic diagrammatic construction theory of charged excitations
• Regularized Perturbation Theory for Ab initio Solids
• Exploring Spin Symmetry-Breaking Effects for Static Field Ionization of Atoms: Is There an Analog to the Coulson-Fischer Point in Bond Dissociation?
• Two Determinant Distinguishable Cluster
• Efficient Random Phase Approximation for Diradicals