Challenges with relativistic calculations in solids and molecules.

For molecules and solids containing heavy elements, accurate electronic-structure calculations require accounting not only for electronic correlations but also for relativistic effects. In molecules, relativity can lead to severe changes in the ground-state description. In solids, the interplay between both correlation and relativity can change the stability of phases or it can lead to an emergence of completely new phases.

Relativistic Fully Self-Consistent for Molecules: Total Energies and Ionization Potentials.

The fully self-consistent (sc) method with an iterative solution of the Dyson equation provides a consistent approach for describing the ground and excited states without any dependence on the mean-field reference. In this work, we present a relativistic version of sc for molecules containing heavy elements using the exact two-component (X2C) Coulomb approximation. We benchmark SOC-81 data set containing closed shell heavy elements for the first ionization potential using the fully self-consistent as well as one-shot .

Comparing Self-Consistent and Vertex-Corrected (Γ) Accuracy for Molecular Ionization Potentials.

We test the performance of self-consistent and several representative implementations of vertex-corrected (Γ). These approaches are tested on benchmark data sets covering full valence spectra (first ionization potentials and some inner valence shell excitations). For small molecules, when comparing against state-of-the-art wave function techniques, our results show that full self-consistency in the scheme either systematically outperforms vertex-corrected or gives results of at least comparative quality.

Thermofield Theory for Finite-Temperature Electronic Structure.

Wave function methods have offered a robust, systematically improvable means to study ground-state properties in quantum many-body systems. Theories like coupled cluster and their derivatives provide highly accurate approximations to the energy landscape at a reasonable computational cost. Analogues of such methods to study thermal properties, though highly desirable, have been lacking because evaluating thermal properties involve a trace over the entire Hilbert space, which is a formidable task.

Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems.

We present a wave function representation for the canonical ensemble thermal density matrix by projecting the thermofield double state against the desired number of particles. The resulting canonical thermal state obeys an imaginary-time evolution equation. Starting with the mean-field approximation, where the canonical thermal state becomes an antisymmetrized geminal power (AGP) wave function, we explore two different schemes to add correlation: by number-projecting a correlated grand-canonical thermal state and by adding correlation to the number-projected mean-field state.

Thermofield Theory for Finite-Temperature Coupled Cluster.

We present a coupled cluster and linear response theory to compute properties of many-electron systems at nonzero temperatures. For this purpose, we make use of the thermofield dynamics, which allows for a compact wave function representation of the thermal density matrix, and extend our recently developed framework ( 2019 , 150 , 154109 , DOI: 10.1063/1.

Thermofield theory for finite-temperature quantum chemistry.

Thermofield dynamics has proven to be a very useful theory in high-energy physics, particularly since it permits the treatment of both time- and temperature-dependence on an equal footing. We here show that it also has an excellent potential for studying thermal properties of electronic systems in physics and chemistry. We describe a general framework for constructing finite temperature correlated wave function methods typical of ground state methods.