Low-valent Group 13 fragments can serve as neutral two-electron L-type metalloligands to transition-metal (TM) centers, enabling heterometallic M-TM platforms with bonding and reactivity patterns distinct from classical CO, phosphine, and carbene ligation. This chapter develops a unifying, descriptor-based view of aluminylene Al(I), gallylene Ga(I), and indylene In(I) donors, and contrasts them with the limited L-type behavior of Tl(I). We map synthetic gateways to isolable M(I) donors, analyze their sigma-donation/pi-acceptance profiles, and extract periodic design rules in which the sigma-donor strength decreases Al > Ga > In, whereas Tl(I) has not yet been convincingly shown to engage in neutral L-type Tl->TM coordination. Borderline cases that blur L-, X-, and Z-type classifications are also examined to clarify descriptors and guide consistent usage across the series. This contribution links ligand sterics/electronics, ambiphilicity at M(I), and the chosen TM fragment to guide the rational design of M-TM platforms that harness Group-13 M(I) donors for small-molecule activation and cooperative catalysis.
Visualization of weak interactions is now a very popular kind of analysis methods, which allows chemists to recognize existence, strength, and type of interactions in different regions of a chemical system easily and intuitively. Among these analysis methods, the independent gradient model (IGM) and its variant with better graphical effect, namely IGM based on Hirshfeld partition of molecular density (IGMH), are particularly useful. They can clearly reveal various interactions between specific fragments, and become widely popular in recent years. This chapter first briefly reviews the definition and characteristics of the two methods, and then introduces a new variant of IGM, called modified IGM (mIGM), which, like IGM, only requires atomic coordinate information to perform the analysis and thus the computational cost is fairly low, while its graphical quality in exhibiting weak interactions is almost as good as the markedly more expensive IGMH. This chapter then introduces the averaged mIGM (amIGM) method, which extends mIGM to visual analysis of the weak interactions involved in molecular dynamics trajectories. A series of examples fully demonstrate that amIGM can well display all kinds of weak interactions in dynamic environments, and its image quality and flexibility are all superior to the previously proposed averaged noncovalent interaction (aNCI) method with similar uses.
This chapter provides an overview of some hybrid forms of symmetry-adapted perturbation theory (SAPT), developed over the past decade and known collectively as "extended" (X)SAPT. Two primary innovations are a self-consistent charge embedding scheme to capture many-body polarization (the "XPol" procedure) and the use of low-cost dispersion models as replacements for SAPT's perturbative description of dispersion. The latter modification reduces the formal complexity to O(N^3) with system size. In conjunction with a many-body dispersion model (XSAPT+MBD) or empirical dispersion potentials fitted to ab initio data (XSAPT+aiD), the hybrid procedure achieves sub-kcal/mol accuracy with respect to high-level benchmarks. XSAPT is equipped with an energy decomposition that partitions the intermolecular interaction energy into components that include electrostatics, Pauli repulsion, dispersion, and induction, the latter of which can be further separated into polarization and charge transfer. As compared to energy decomposition analyses used in density functional theory, separation of the dispersion energy in XSAPT is less ambiguous and the energy partition agrees well with accurate third-order SAPT benchmarks. Theoretical foundations of XSAPT are reviewed, and we provide a thorough discussion of its performance in terms of both accuracy and cost. Exemplary applications are presented that illustrate how XSAPT can be used to uncover the fundamental molecular physics of intermolecular interactions.
