OO-REMP: Approaching Chemical Accuracy with Second-Order Perturbation Theory

Orbital optimisation in xTC transcorrelated methods

We present a combination of the bi-orthogonal orbital optimisation framework with the recently introduced xTC version of transcorrelation. This allows us to implement non-iterative perturbation based methods on top of the transcorrelated Hamiltonian. Additionally, the orbital optimisation influences results of other truncated methods, such as the distinguishable cluster with singles and doubles. The accuracy of these methods in comparison to standard xTC methods is demonstrated, and the advantages and disadvantages of the orbital optimisation are discussed.

Reaching High Accuracy for Energetic Properties at Second-Order Perturbation Cost by Merging Self-Consistency and Spin-Opposite Scaling

Quantum chemical methods dealing with challenging systems while retaining low computational costs have attracted attention. In particular, many efforts have been devoted to developing new methods based on second-order perturbation that may be the simplest correlated method beyond Hartree-Fock. We have recently developed a self-consistent perturbation theory named one-body Møller-Plesset second-order perturbation theory (OBMP2) and shown that it can resolve issues caused by the noniterative nature of standard perturbation theory. In this work, we extend the method by introducing spin-opposite scaling to the double-excitation amplitudes, resulting in the O2BMP2 method. We assess the O2BMP2 performance on the triple-bond N2 dissociation, singlet-triplet gaps, and ionization potentials. O2BMP2 performs much better than standard MP2 and reaches the accuracy of coupled-cluster methods in all cases considered in this work.

Accurate Property Prediction by Second Order Perturbation Theory: The REMP and OO-REMP Hybrids

The prediction of molecular properties such as equilibrium structures or vibrationalwavenumbers is a routine task in computational chemistry. If very high accuracy is required, however, the use of computationally demanding ab initio wavefunction methods is mandatory. We present property calculations utilizing the REMP and OO-REMP hybrid perturbation theories showing that with the latter approach, very accurate results are obtained at second order in perturbation theory. Specifically, equilibrium structures and harmonic vibrational wavenumbers as well as dipole moments of closed and open shell molecules were calculated and compared to the best available experimental results or very accurate calculations.OO-REMP is capable of predicting bond lengths of small closed and open shell molecules with an accuracy of 0.2 pm and 0.5 pm, respectively, often within the range of experimental uncertainty. Equilibrium harmonic vibrational wavenumbers are predicted with an accuracy better than 20 cm−1 . Dipole moments of small closed and open shell molecules are reproduced with a relative error of less than 3 %. Across all investigated properties it turns out that a 20 %:80 % MP:RE mixing ratio consistently provides the best results. This is in line with our previous findings featuring closed and open shell reaction energies.

UREMP, RO-REMP, and OO-REMP: Hybrid perturbation theories for open-shell electronic structure calculations

An accurate description of the electron correlation energy in closed- and open-shell molecules is shown to be obtained by a second-order perturbation theory (PT) termed REMP. REMP is a hybrid of the Retaining the Excitation degree (RE) and the Møller–Plesset (MP) PTs. It performs particularly encouragingly in an orbital-optimized variant (OO-REMP) where the reference wavefunction is given by an unrestricted Slater determinant whose spin orbitals are varied such that the total energy becomes a minimum. While the approach generally behaves less satisfactorily with unrestricted Hartree–Fock references, reasonable performance is observed for restricted Hartree–Fock and restricted open-shell Hartree–Fock references. Inclusion of single excitations to OO-REMP is investigated and found—as in similar investigations—to be dissatisfying as it deteriorates performance. For the non-multireference subset of the accurate W4-11 benchmark set of Karton et al. [Chem. Phys. Lett. 510, 165–178 (2011)], OO-REMP predicts most atomization and reaction energies with chemical accuracy (1 kcal mol−1) if complete-basis-set extrapolation with augmented and core-polarized basis sets is used. For the W4-11 related test-sets, the error estimates obtained with the OO-REMP method approach those of coupled-cluster with singles, doubles and perturbative triples [CCSD(T)] within 20%–35%. The best performance of OO-REMP is found for a mixing ratio of 20%:80% MP:RE, which is essentially independent of whether radical stabilization energies, barrier heights, or reaction energies are investigated. Orbital optimization is shown to improve the REMP approach for both closed and open shell cases and outperforms coupled-cluster theory with singles and doubles (CCSD), spin-component scaled Møller-Plesset theory at second order (SCS-MP2), and density functionals, including double hybrids in all the cases considered.