Two aspects of electron correlation: multireference diagnostics and london dispersion interactions

Abstract

Electron correlation arises from the instantaneous interactions among electrons in atoms ormolecules. Its ubiquitous nature beyond any one-electron system and its essential role in characterizingelectronic structure render it of utmost importance in quantum chemistry and physics. In the contextof correlated wavefunction methods, this thesis explains two aspects of electron correlation: thedevelopment 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 somenovel natural orbital-based correlation indices in terms of various ansatzes, which areuniversally applicable across all electronic structure methods. We present analytical connectionsbetween two natural orbital-based correlation indices, ¿¿ND ¿¿¿¿¿ and ¿¿NDmax , and two establishedelectron correlation metrics: the leading term of a configuration interaction expansion, c0 andthe D2 diagnostic. MR diagnostics are helpful in assessing the reliability of a calculation ofsingle- reference methods. Although various MR diagnostics exist, many of them have beendesigned for specific methods. We explore relationships among various MR diagnostics andreduce them based on similarities. Thereby, a representative correlation measure is suggestedwith appropriate cutoff values for serving as effective MR diagnostics. Furthermore, extensivedatasets are used for a thorough analysis of the agreement extent between each two MRdiagnostics.In the field of London dispersion interactions, we first establish a theoreticalconnection between the long-range dynamic correlation energy retrieved by electron-electroninteraction energy and the dispersion energy based on the virial theorem. Then, we providenumerous numerical assessments over a collection of diatomic molecules at large separationand confirm that this relationship remains valid across various wavefunction methods.Among the pair density approaches, on one hand, we demonstrate the significance of usingonly few terms within the long-range components of correlated pair density to retrievedispersion energies in diatomic molecules. On the other hand, we also use the long-rangecomponent of the correlated pair density partition ¿¿¿¿¿II to capture dispersion interactions.The numerical results for diatomic molecules align with the former approach which usesapproximate pair density relying on few terms. Nonetheless, the pair density partitionapproach exhibits more robustness and can be extended to larger polyatomic molecules.In addition, we introduce a novel concept of dispersion hole for identifying andcalculating dispersion interactions, and it reveals a connection between the pair density anddispersion energy. In the end, we present a minimal dispersion model based on the molecularhydrogen which helps interpret previous numerical results. We explore the universal 1/R3decay in the long-range component of the Coulomb hole partition ¿¿¿II at large interatomicdistances, denoted as R. Moreover, we demonstrate that this decay is a necessary but notsufficient condition when connecting to the dispersion energy. These findings can help gainsome new insights into London dispersion from the pair density perspective.