Tensor hypercontraction for fully self-consistent imaginary-time GF2 and GWSOX methods: Theory, implementation, and role of the Green's function second-order exchange for intermolecular interactions.

We present an efficient MPI-parallel algorithm and its implementation for evaluating the self-consistent correlated second-order exchange term (SOX), which is employed as a correction to the fully self-consistent GW scheme called scGWSOX (GW plus the SOX term iterated to achieve full Green's function self-consistency). Due to the application of the tensor hypercontraction (THC) in our computational procedure, the scaling of the evaluation of scGWSOX is reduced from O(nτnAO5) to O(nτN2nAO2). This fully MPI-parallel and THC-adapted approach enabled us to conduct the largest fully self-consistent scGWSOX calculations with over 1100 atomic orbitals with only negligible errors attributed to THC fitting.

State-Interaction Approach for Evaluating -Tensors within EOM-CC and RAS-CI Frameworks: Theory and Benchmarks.

Among various techniques designed for studying open-shell species, electron paramagnetic resonance (EPR) spectroscopy plays an important role. The key quantity measured by EPR is the -tensor, describing the coupling between an external magnetic field and molecular electronic spin. One theoretical framework for quantum chemistry calculations of -tensors is based on response theory, which involves substantial developments that are specific to the underlying electronic structure models.

Natural orbitals and two-particle correlators as tools for the analysis of effective exchange couplings in solids.

Using generalizations of spin-averaged natural orbitals and two-particle charge correlators for solids, we investigate the electronic structure of antiferromagnetic transition-metal oxides with a fully self-consistent, imaginary-time GW method. Our findings disagree with the Goodenough-Kanamori (GK) rules that are commonly used for the qualitative interpretation of such solids. First, we found a strong dependence of the natural orbital occupancies on momenta, contradicting GK assumptions.

Evaluation of Neel Temperatures from Fully Self-Consistent Broken-Symmetry GW and High-Temperature Expansion: Application to Cubic Transition-Metal Oxides.

Using fully self-consistent thermal broken-symmetry GW, we construct effective magnetic Heisenberg Hamiltonians for a series of transition metal oxides (NiO, CoO, FeO, and MnO), capturing a rigorous but condensed description of the magnetic states. Then applying high-temperature expansion, we find the decomposition coefficients for spin susceptibility and specific heat. The radius of convergence of the found series determines the Neel temperature.

Spin-orbit couplings within spin-conserving and spin-flipping time-dependent density functional theory: Implementation and benchmark calculations.

We present a new implementation for computing spin-orbit couplings (SOCs) within a time-dependent density-functional theory (TD-DFT) framework in the standard spin-conserving formulation as well in the spin-flip variant (SF-TD-DFT). This approach employs the Breit-Pauli Hamiltonian and Wigner-Eckart's theorem applied to the reduced one-particle transition density matrices, together with the spin-orbit mean-field treatment of the two-electron contributions. We use a state-interaction procedure and compute the SOC matrix elements using zero-order non-relativistic states.

Broken-symmetry self-consistent GW approach: Degree of spin contamination and evaluation of effective exchange couplings in solid antiferromagnets.

We adopt a broken-symmetry strategy for evaluating effective magnetic constants J within the fully self-consistent GW method. To understand the degree of spin contamination present in broken-symmetry periodic solutions, we propose several extensive quantities demonstrating that the unrestricted self-consistent GW preserves the broken-symmetry character of the unrestricted Hartree-Fock solutions. The extracted J are close to the ones obtained from multireference wave-function calculations.

Iterative subspace algorithms for finite-temperature solution of Dyson equation.

One-particle Green's functions obtained from the self-consistent solution of the Dyson equation can be employed in the evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration techniques used in the traditional quantum chemistry self-consistent algorithms cannot be easily deployed for the Green's function methods because of a non-convex grand potential functional and a non-idempotent density matrix. Moreover, the optimization problem can become more challenging due to the inclusion of correlation effects, changing chemical potential, and fluctuations of the number of particles.

Software for the frontiers of quantum chemistry: An overview of developments in the Q-Chem 5 package.

This article summarizes technical advances contained in the fifth major release of the Q-Chem quantum chemistry program package, covering developments since 2015. A comprehensive library of exchange-correlation functionals, along with a suite of correlated many-body methods, continues to be a hallmark of the Q-Chem software. The many-body methods include novel variants of both coupled-cluster and configuration-interaction approaches along with methods based on the algebraic diagrammatic construction and variational reduced density-matrix methods.

Interpretation of multiple solutions in fully iterative GF2 and GW schemes using local analysis of two-particle density matrices.

Due to the presence of non-linear equations, iterative Green's function methods can result in multiple different solutions even for simple molecular systems. In contrast to the wave-function methods, a detailed and careful analysis of such molecular solutions was not performed before. In this work, we use two-particle density matrices to investigate local spin and charge correlators that quantify the charge resonance and covalent characters of these solutions.

Evaluation of two-particle properties within finite-temperature self-consistent one-particle Green's function methods: Theory and application to GW and GF2.

One-particle Green's function methods can model molecular and solid spectra at zero or non-zero temperatures. One-particle Green's functions directly provide electronic energies and one-particle properties, such as dipole moment. However, the evaluation of two-particle properties, such as ⟨S⟩ and ⟨N⟩, can be challenging because they require a solution of the computationally expensive Bethe-Salpeter equation to find two-particle Green's functions.

Effective Hamiltonians derived from equation-of-motion coupled-cluster wave functions: Theory and application to the Hubbard and Heisenberg Hamiltonians.

Effective Hamiltonians, which are commonly used for fitting experimental observables, provide a coarse-grained representation of exact many-electron states obtained in quantum chemistry calculations; however, the mapping between the two is not trivial. In this contribution, we apply Bloch's formalism to equation-of-motion coupled-cluster wave functions to rigorously derive effective Hamiltonians in Bloch's and des Cloizeaux's forms. We report the key equations and illustrate the theory by application to systems with two or three unpaired electrons, which give rise to electronic states of covalent and ionic characters.

Calculation of spin-orbit couplings using RASCI spinless one-particle density matrices: Theory and applications.

This work presents the formalism and implementation for calculations of spin-orbit couplings (SOCs) using the Breit-Pauli Hamiltonian and non-relativistic wave functions described by the restricted active space configuration interaction (RASCI) method with general excitation operators of spin-conserving spin-flipping, ionizing, and electron-attaching types. The implementation is based on the application of the Wigner-Eckart theorem within the spin space, which enables the calculation of the entire SOC matrix based on the explicit calculation of just one transition between the two spin multiplets. Numeric results for a diverse set of atoms and molecules highlight the importance of a balanced treatment of correlation and adequate basis sets and illustrate the overall robust performance of RASCI SOCs.

Equation-of-Motion Coupled-Cluster Theory to Model L-Edge X-ray Absorption and Photoelectron Spectra.

We present an extension of the equation-of-motion coupled-cluster singles and doubles (EOM-CCSD) theory for computing X-ray L-edge spectra, both in the absorption (XAS) and in the photoelectron (XPS) regimes. The approach is based on the perturbative evaluation of spin-orbit couplings using the Breit-Pauli Hamiltonian and nonrelativistic wave functions described by the fc-CVS-EOM-CCSD ansatz (EOM-CCSD within the frozen-core core-valence separated (fc-CVS) scheme). The formalism is based on spinless one-particle density matrices.

The elusive dynamics of aqueous permanganate photochemistry.

Despite decades of investigation, mechanistic details of aqueous permanganate photo-decomposition remain unclear. Here we follow photoinduced dynamics of aqueous permanganate with femtosecond spectroscopy. Photoexcitation of KMnO(aq) in the visible unleashes a sub-picosecond cascade of non-radiative transitions, leading to a distinct species which relaxes to S with a lifetime of 16 ps.

Extension of frozen natural orbital approximation to open-shell references: Theory, implementation, and application to single-molecule magnets.

Natural orbitals are often used to achieve a more compact representation of correlated wave-functions. Using natural orbitals computed as eigenstates of the virtual-virtual block of the state density matrix instead of the canonical Hartree-Fock orbitals results in smaller errors when the same fraction of virtual space is frozen. This strategy, termed frozen natural orbital (FNO) approach, is effective in reducing the cost of regular coupled-cluster (CC) calculations and some multistate methods, such as EOM-IP-CC (equation-of-motion CC for ionization potentials).

Quantitative El-Sayed Rules for Many-Body Wave Functions from Spinless Transition Density Matrices.

One-particle transition density matrices and natural transition orbitals enable quantitative description of electronic transitions and interstate properties involving correlated many-body wave functions within the molecular orbital framework. Here we extend the formalism to the analysis of tensor properties, such as spin-orbit couplings (SOCs), which involve states of different spin projection. By using spinless density matrices and Wigner-Eckart's theorem, the approach allows one to treat the transitions between states with arbitrary spin projections in a uniform way.

General framework for calculating spin-orbit couplings using spinless one-particle density matrices: Theory and application to the equation-of-motion coupled-cluster wave functions.

Standard implementations of nonrelativistic excited-state calculations compute only one component of spin multiplets (i.e., M = 0 triplets); however, matrix elements for all components are necessary for deriving spin-dependent experimental observables.

Spin-Forbidden Channels in Reactions of Unsaturated Hydrocarbons with O(P).

The electronic structure of four prototypical Cvetanović diradicals, species derived by addition of O(P) to unsaturated compounds, is investigated by high-level electronic structure calculations and kinetics modeling. The main focus of this study is on the electronic factors controlling the rate of intersystem crossing (ISC): minimal energy crossing points (MECPs) and spin-orbit couplings (SOCs). The calculations illuminate significant differences in the electronic structure of ethene- and ethyne-derived compounds and explain the effect of methylation.

Double Precision Is Not Needed for Many-Body Calculations: Emergent Conventional Wisdom.

Using single-precision floating-point representation reduces the size of data and computation time by a factor of 2 relative to double precision conventionally used in electronic structure programs. For large-scale calculations, such as those encountered in many-body theories, reduced memory footprint alleviates memory and input/output bottlenecks. Reduced size of data can lead to additional gains due to improved parallel performance on CPUs and various accelerators.