In this research, orbital-optimized third-order Møller-Plesset perturbation theory (OMP3) and its spin-component and spin-opposite scaled variants (SCS-OMP3 and SOS-OMP3) are introduced. Using a Lagrangian-based approach, an efficient, quadratically convergent algorithm for variational optimization of the molecular orbitals (MOs) for third-order Møller-Plesset perturbation theory (MP3) is presented. Explicit equations for response density matrices, the MO gradient, and Hessian are reported in spin-orbital form. The OMP3, SCS-OMP3, and SOS-OMP3 approaches are compared with the second-order Møller-Plesset perturbation theory (MP2), MP3, coupled-cluster doubles (CCD), optimized-doubles (OD), and coupled-cluster singles and doubles (CCSD) methods. All these methods are applied to the

${\rm O}_{4} ^{+}$
O4+⁠, O3, and seven diatomic molecules. Results demonstrate that the OMP3 and its variants provide significantly better vibrational frequencies than MP3, CCSD, and OD for the molecules where the symmetry-breaking problems are observed. For
${\rm O}_{4} ^{+}$
O4+⁠, the OMP3 prediction, 1343 cm−1, for ω6 (b3u) mode, where symmetry-breaking appears, is even better than presumably more reliable methods such as Brueckner doubles (BD), 1194 cm−1, and OD, 1193 cm−1, methods (the experimental value is 1320 cm−1). For O3, the predictions of SCS-OMP3 (1143 cm−1) and SOS-OMP3 (1165 cm−1) are remarkably better than the more robust OD method (1282 cm−1); the experimental value is 1089 cm−1. For the seven diatomics, again the SCS-OMP3 and SOS-OMP3 methods provide the lowest average errors, |Δωe| = 44 and |Δωe| = 35 cm−1, respectively, while for OD, |Δωe| = 161 cm−1and CCSD |Δωe| = 106 cm−1. Hence, the OMP3 and especially its spin-scaled variants perform much better than the MP3, CCSD, and more robust OD approaches for considered test cases. Therefore, considering both the computational cost and the reliability, SCS-OMP3 and SOS-OMP3 appear to be the best methods for the symmetry-breaking cases, based on present application results. The OMP3 method offers certain advantages: it provides reliable vibrational frequencies in case of symmetry-breaking problems, especially with spin-scaling tricks, its analytic gradients are easier to compute since there is no need to solve the coupled-perturbed equations for the orbital response, and the computation of one-electron properties are easier because there is no response contribution to the particle density matrices. The OMP3 has further advantages over standard MP3, making it promising for excited state properties via linear response theory.

Topics
Moller-Plesset perturbation theory, Unrestricted Hartree-Fock, Coupled-cluster methods, Frozen-core approximation, Molecular properties, Molecular electronic properties, Diatomic molecule, Mathematical crystallography, Ozone, Density-matrix
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