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Energy decomposition analysis (EDA) has become an important tool to relate electronic structure calculations to physically meaningful contributions. The second generation of the absolutely localized molecular orbitals (ALMO)-EDA accounts for polarization with a well- defined basis set limit using truncated virtual orbitals, namely fragment electric-field response functions (FERF). In this work, we introduce a hessian-free uncoupled FERF (uFERF) al- ternative that has very similar accuracy and is 8-10 times faster to evaluate. Furthermore, we investigate the use of monopole uFERFs (response to scaled nuclear charges) for inter-molecular interactions and establish their role in strong ion-neutral interactions. 

In this article, we introduce the occupied-virtual orbitals for chemical valence (OVOCV). The OVOCVs can replace or complement the closely related idea of the natural orbitals for chemical valence (NOCV). The input is a difference density matrix connecting any initial single determinant to any final determinant, at a given molecular geometry, and a given one-particle basis. This arises in problems such as orbital rearrangement or charge-transfer in energy decomposition analysis. The OVOCVs block-diagonalize the density difference operator into 2 × 2 blocks which are spanned by one level that is filled in the initial state (the occupied OVOCV) and one which is empty (the virtual OVOCV). By contrast, the NOCVs fully diagonalize the density difference matrix, and therefore are orbitals with mixed occupied-virtual character. Use of the OVOCVs makes it much easier to identify the donor and acceptor orbitals. We also introduce two different types of energy decomposition analysis (EDA) methods with the OVOCVs, and most importantly, a charge decomposition analysis (CDA) method that fixes the unreasonably large charge transfer amount obtained directly from NOCV analysis. 

The chemical bond is the cornerstone of chemistry, providing a conceptual framework to understand and predict the behavior of molecules in complex systems. However, the fundamental origin of chemical bonding remains controversial, and has been responsible for fierce debate over the past century. Here we present a unified theory of bonding, using a separation of electron delocalization effects from orbital relaxation to identify three mechanisms -- node-induced confinement (typically associated with Pauli repulsion, though more general), orbital contraction and polarization -- that each modulate kinetic energy during bond formation. Through analysis of a series of archetypal bonds, we show that an exquisite balance of energy-lowering delocalizing and localizing effects are dictated simply by atomic electron configurations, nodal structure and electronegativities. The utility of this unified bonding theory is demonstrated by its application to explain observed trends in bond strengths throughout the periodic table, including main group and transition metal elements. 

Energy decomposition analysis (EDA) is a useful method to unravel an intermolecular interaction energy into chemically meaningful components such as geometric distortion, frozen interactions, polarization, and charge transfer. A further decomposition of the polarization (POL) and charge transfer (CT) energy into fragment-wise contributions would be useful to understand the significance of each fragment during these two processes. To complement the existing exact pairwise decomposition of the CT term, this work describes formulation and implementation of a non-perturbative polarization analysis that decomposes the POL energy into an exactly fragment-wise additive sum based on the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA). These fragment-wise contributions can be further decomposed into chemically intuitive molecular orbital pairs using complementary occupied-virtual pairs (COVP) analysis. A very useful phase convention is established for each COVP such that constructive interference of occupied and virtual corresponds to electron flow into that region, whilst destructive interference corresponds to electron outflow. A range of model problems are used to demonstrate that the polarization process is typically a collective behavior of the electrons that is quite different from the charge transfer process. This provides another reason in addition to their different distance-dependence on fragment separation for separating these two processes in EDA.