Benchmark of dynamic electron correlation models for seniority-zero wavefunctions and their application to thermochemistry

Wavefunctions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included \textit{a posteriori}. In this article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allow us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multi-reference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an \textit{a posteriori} linearized coupled cluster correction on top of AP1roG against CR-CCSD(T) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the N$_2$, C$_2$, and BN dimers against MRCI-SD and MRCI-SD+Q reference data. Our numerical results indicate that the best performance is obtained from a linearized coupled cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG allow us to reliably model molecular systems dominated by static/nondynamic as well as dynamic electron correlation.Comment: 15 pages, 2 figure

Linearized Coupled Cluster Correction on the Antisymmetric Product of 1 reference orbital Geminals

We present a Linearized Coupled Cluster (LCC) correction based on an Antisymmetric Product of 1 reference orbital Geminals (AP1roG) reference state. In our LCC ansatz, the cluster operator is restricted to double and to single and double excitations as in standard single-reference CC theory. The performance of the AP1roG-LCC models is tested for the dissociation of diatomic molecules (C$_2$ and F$_2$), spectroscopic constants of the uranyl cation (UO$_2^{2+}$), and the symmetric dissociation of the H$_{50}$ hydrogen chain. Our study indicates that an LCC correction based on an AP1roG reference function is more robust and reliable than corrections based on perturbation theory, yielding spectroscopic constants that are in very good agreement with theoretical reference data.Comment: 9 pages, 4 figure

Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states

Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.Comment: 15 pages, 8 figure

Optimized Unrestricted Kohn-Sham Potentials from Ab Initio Spin Densities

The reconstruction of the exchange-correlation potential from accurate ab initio electron densities can provide insights into the limitations of the currently available approximate functionals and provide guidance for devising improved approximations for density-functional theory (DFT). For open-shell systems, the spin density is introduced as an additional fundamental variable in Spin-DFT. Here, we consider the reconstruction of the corresponding unrestricted Kohn-Sham potentials from accurate ab initio spin densities. In particular, we investigate whether it is possible to reconstruct the spin exchange-correlation potential, which determines the spin density in spin-unrestricted Kohn-Sham-DFT, despite the numerical difficulties inherent to the optimization of potentials with finite orbital basis sets. We find that the recently developed scheme for unambiguously singling out an optimal optimized potential [J. Chem. Phys. 135, 244102 (2011)] can provide such spin potentials accurately. This is demonstrated for two test cases, the lithium atom and the dioxygen molecule, and target (spin) densities from Full-CI and CASSCF calculations, respectively

A configuration interaction correction on top of pair coupled cluster doubles

Numerous numerical studies have shown that geminal-based methods are a promising direction to model strongly correlated systems with low computational costs. Several strategies have been introduced to capture the missing dynamical correlation effects, which typically exploit \textit{a posteriori} corrections to account for correlation effects associated with broken-pair states or inter-geminal correlations. In this article, we scrutinize the accuracy of the pair coupled cluster doubles (pCCD) method extended by configuration interaction (CI) theory. Specifically, we benchmark various CI models, including, at most double excitations against selected CC corrections as well as conventional single-reference CC methods. A simple Davidson correction is also tested. The accuracy of the proposed pCCD-CI approaches is assessed for challenging small model systems such as the \ce{N2} and \ce{F2} dimers and various di- and triatomic actinide-containing compounds. In general, the proposed CI methods considerably improve spectroscopic constants compared to the conventional CCSD approach, provided a Davidson correction is included in the theoretical model. At the same time, their accuracy lies between the linearized frozen pCCD and frozen pCCD variants.Comment: 4 figure

Benchmarking ionization potentials from pCCD tailored coupled cluster models

The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological devices. We recently showed that limiting the CC ansatz to the seniority-zero sector proves insufficient in predicting reliable and accurate ionization potentials within an IP equation-of-motion coupled-cluster formalism. Specifically, the absence of dynamic correlation in the seniority-zero pair coupled cluster doubles (pCCD) model led to unacceptably significant errors of approximately 1.5 eV. In this work, we aim to explore the impact of dynamical correlation and the choice of the molecular orbital basis (canonical vs. localized) in CC-type methods targeting 201 ionized states in 41 molecules. We focus on pCCD-based approaches as well as the conventional IP-EOM-CCD and IP-EOM-CCSD. Their performance is compared to the CCSDT equivalent and experimental reference data. Our statistical analysis reveals that all investigated frozen-pair coupled cluster methods exhibit similar performance, with differences in errors typically within chemical accuracy (1 kcal/mol or 0.05 eV). Notably, the effect of the molecular orbital basis, such as canonical Hartree-Fock or natural pCCD-optimized orbitals, on the IPs is marginal if dynamical correlation is accounted for. Our study suggests that triple excitations are crucial in achieving chemical accuracy in IPs when modeling electron detachment processes with pCCD-based methods.Comment: 8 pages, 3 figure