PhD Thesis defense: Two aspects of electron correlation: Multireference diagnostics and London dispersion interactions

PhD Program

Xiang Xu
Ekitaldi Aretoa of the Kimika Fakultatea
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PhD Thesis defense: Two aspects of electron correlation: Multireference diagnostics and London dispersion interactions

Supervisors: Eduard Matito (DIPC) and Eloy Ramos-Cordoba.

Electron correlation arises from the instantaneous interactions among electrons in atoms or molecules. Its ubiquitous nature beyond any one-electron system and its essential role in characterizing electronic structure render it of utmost importance in quantum chemistry and physics. In the context of correlated wavefunction methods, this thesis explains two aspects of electron correlation: the development and statistical analysis of various correlation measures including Multireference (MR) diagnostics, and the study of London dispersion interactions from the pair density perspective.

In the aspect of correlation measures and MR diagnostics, we first introduce some novel natural orbital-based correlation indices in terms of various ansatzes, which are universally applicable across all electronic structure methods. We present analytical connections between two natural orbital-based correlation indices and two established electron correlation metrics: the leading term of a configuration interaction expansion, c0 and the D2 diagnostic. MR diagnostics are helpful in assessing the reliability of a calculation of single- reference methods. Although various MR diagnostics exist, many of them have been designed for specific methods. We explore relationships among various MR diagnostics and reduce them based on similarities. Thereby, a representative correlation measure is suggested with appropriate cutoff values for serving as effective MR diagnostics. Furthermore, extensive datasets are used for a thorough analysis of the agreement extent between each two MR diagnostics.

In the field of London dispersion interactions, we first establish a theoretical connection between the long-range dynamic correlation energy retrieved by electron-electron interaction energy and the dispersion energy based on the virial theorem. Then, we provide numerous numerical assessments over a collection of diatomic molecules at large separation and confirm that this relationship remains valid across various wavefunction methods. Among the pair density approaches, on one hand, we demonstrate the significance of using only few terms within the long-range components of correlated pair density to retrieve dispersion energies in diatomic molecules. On the other hand, we also use the long-range component of the correlated pair density partition cII to capture dispersion interactions. The numerical results for diatomic molecules align with the former approach which uses approximate pair density relying on few terms. Nonetheless, the pair density partition approach exhibits more robustness and can be extended to larger polyatomic molecules.
In addition, we introduce a novel concept of dispersion hole for identifying and calculating dispersion interactions, and it reveals a connection between the pair density and dispersion energy. In the end, we present a minimal dispersion model based on the molecular hydrogen which helps interpret previous numerical results. We explore the universal 1/R3 decay in the long-range component of the Coulomb hole partition cII at large interatomic distances, denoted as R. Moreover, we demonstrate that this decay is a necessary but not sufficient condition when connecting to the dispersion energy. These findings can help gain some new insights into London dispersion from the pair density perspective.