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.

Exploring Ligand-to-Metal Charge-Transfer States in the Photo-Ferrioxalate System Using Excited-State Specific Optimization.

The photo-ferrioxalate system (PFS), [Fe(III)(C2O4)]3-, more than an exact chemical actinometer, has been extensively applied in wastewater and environment treatment. Despite many experimental efforts to improve clarity, important aspects of the mechanism of ferrioxalate photolysis are still under debate. In this paper, we employ the recently developed WΓ-CASSCF to investigate the ligand-to-metal charge-transfer states that are key to ferrioxalate photolysis. This investigation provides a qualitative picture of these states and key potential energy surface features related to the photolysis. Our theoretical results are consistent with the prompt charge-transfer picture seen in recent experiments and clarify some features that are not visible in experiments. Two ligand-to-metal charge-transfer states contribute to the photolysis of ferrioxalate, and the avoided crossing barrier between them is low compared with the initial photoexcitation energy. Our data also clarify that one Fe-O bond cleaves first, followed by the C-C bond and the other Fe-O bond.

Correlated Reference-Assisted Variational Quantum Eigensolver.

We propose an active-space approximation to reduce the quantum resources required for variational quantum eigensolver (VQE). Starting from the double exponential unitary coupled-cluster ansatz and employing the downfolding technique, we arrive at an effective Hamiltonian for active space composed of the bare Hamiltonian and a correlated potential caused by the internal-external interaction. The correlated potential is obtained from the one-body second-order Møller-Plesset perturbation theory (OBMP2), which is derived using the canonical transformation and cumulant approximation. Considering different systems with singlet and doublet ground states, we examine the accuracy in predicting both energy and density matrix (by evaluating dipole moment). We show that our approach can dramatically outperform the active-space VQE with an uncorrelated Hartree-Fock reference.

Can second-order perturbation theory accurately predict electron density of open-shell molecules? The importance of self-consistency.

Electron density plays an essential role in predicting molecular properties. It is also a simple observable from which machine-learning models for molecular electronic structure can be derived. In this work, we present the performance of the one-body Møller-Plesset second-order perturbation (OBMP2) theory, which we have recently developed, in predicting electron density and related properties. In OBMP2, an effective one-body Hamiltonian including dynamic correlation at the MP2 level is derived using the canonical transformation followed by the cumulant approximation. We diagonalize the effective one-body Hamiltonian to yield eigenvalues and eigenvectors corresponding to molecular orbitals and orbital energies that are then used to update the MP2 double-excitation amplitudes. We examine the OBMP2 performance by considering three different groups of open-shell systems: atomic systems, main-group radicals, and halogen-bonding dimers. We find that OBMP2 outperforms standard MP2 and density functional theory in all cases considered here, and its accuracy is comparable to coupled-cluster singles and doubles (CCSD), a higher-level method. OBMP2 is thus believed to be an effective method for predicting the accurate electron density of open-shell molecules.

Improving Perturbation Theory for Open-Shell Molecules via Self-Consistency.

We present an extension of our one-body Møller-Plesset second-order perturbation (OBMP2) method for open-shell systems. We derived the OBMP2 Hamiltonian through the canonical transformation followed by the cumulant approximation to reduce many-body operators into one-body ones. The resulting Hamiltonian consists of an uncorrelated Fock (unperturbed Hamiltonian) and a one-body correlation potential (perturbed Hamiltonian) composed of only double excitations. Molecular orbitals and associated energy levels are then relaxed via self-consistency, similar to Hartree-Fock, in the presence of the correlation at the MP2 level. We demonstrate the OBMP2 performance by considering two examples well-known for requiring orbital optimization: bond breaking and isotropic hyperfine coupling constants. In contrast to noniterative MP2, we show that OBMP2 can yield a smooth transition through the unrestriction point and accurately predict isotropic hyperfine coupling constants.

Improving Excited-State Potential Energy Surfaces via Optimal Orbital Shapes.

We demonstrate that, rather than resorting to high-cost dynamic correlation methods, qualitative failures in excited-state potential energy surface predictions can often be remedied at no additional cost by ensuring that optimal molecular orbitals are used for each individual excited state. This approach also avoids the weighting choices required by state-averaging and dynamic weighting and obviates their need for expensive wave function response calculations when relaxing excited-state geometries. Although multistate approaches are of course preferred near conical intersections, other features of excited-state potential energy surfaces can benefit significantly from our single-state approach. In three different systems, including a double bond dissociation, a biologically relevant amino hydrogen dissociation, and an amino-to-ring intramolecular charge transfer, we show that state-specific orbitals offer qualitative improvements over the state-averaged status quo.

Tracking Excited States in Wave Function Optimization Using Density Matrices and Variational Principles.

We present a method for finding individual excited states' energy stationary points in complete active space self-consistent field theory that is compatible with standard optimization methods and highly effective at overcoming difficulties due to root flipping and near-degeneracies. Inspired by both the maximum overlap method and recent progress in excited-state variational principles, our approach combines these ideas in order to track individual excited states throughout the orbital optimization process. In a series of tests involving root flipping, near-degeneracies, charge transfers, and double excitations, we show that this approach is more effective for state-specific optimization than either the naive selection of roots on the basis of energy ordering or a more direct generalization of the maximum overlap method. We provide evidence that this state-specific approach improves the performance of complete active space perturbation theory for vertical excitation energies. Furthermore, we find that the state-specific optimization can help avoid state-averaging-induced discontinuities on potential energy surfaces. With a simple implementation, a low cost, and compatibility with large active space methods, the approach is designed to be useful in a wide range of excited-state investigations.

Self-Energy Embedding Theory (SEET) for Periodic Systems.

We present an implementation of the self-energy embedding theory (SEET) for periodic systems and provide a fully self-consistent embedding solution for a simple realistic periodic problem-one-dimensional (1D) crystalline hydrogen-that displays many of the features present in complex real materials. For this system, we observe a remarkable agreement between our finite-temperature periodic implementation results and well-established and accurate zero-temperature auxiliary quantum Monte Carlo data extrapolated to thermodynamic limit. We discuss differences and similarities with other Green's function embedding methods and provide the detailed algorithmic steps crucial for highly accurate and reproducible results.

Spin-Unrestricted Self-Energy Embedding Theory.

We present a new theoretical approach, unrestricted self-energy embedding theory (USEET), that is a Green's function embedding theory used to study problems in which an open, embedded system exchanges electrons with the environment. USEET has a high potential to be used in studies of strongly correlated systems with an odd number of electrons and open shell systems such as transition metal complexes important in inorganic chemistry. In this paper, we show that USEET results agree very well with common quantum chemistry methods while avoiding typical bottlenecks present in these methods.