## Introduction

Dicoordinated d^{10}-transition-metal complexes ML_{2} occur in numerous catalytic reaction mechanisms.1 These complexes, in general, have a linear geometry2, 3, 4, 5 with a ligand–metal–ligand (LML′) angle (or bite angle) of 180°, although exceptions6, 7 have been observed. This geometrical preference can be easily understood for a closed-shell d^{10} configuration. In most cases, the dominant bonding orbital interaction is σ donation from the ligand’s lone-pair orbitals into the empty metal (*n*+1)s atomic orbital (AO), which has a ligand–metal bond overlap that is independent of the LML′ angle (see Figure 1).8 At the same time, the steric repulsion associated with a L⋅⋅⋅L′ overlap between the lone pairs (and other closed shells) of the two ligands yields a force that maximizes their mutual distance and thus yields the well-known linear LML′ arrangement.

The same conclusion is obtained if one uses valence shell electron pair repulsion (VSEPR) theory adapted for treating transition-metal complexes,9, 10 or more sophisticated methods based on molecular orbital (MO) theory. Proceeding from the latter, one can deduce the preference for linear over bent ML_{2} complexes from the number of electrons in the valence orbitals and the dependence of the orbital energies on the geometrical parameter of interest (here, the LML angle) in Walsh diagrams.8 These diagrams show again that dicoordinate d^{10}-transition-metal complexes, for example, Ag(NH_{3})_{2}^{+}, adopt a linear geometry due to the significant destabilization of the metal d_{xz} AO by the ligand’s lone-pair orbitals in combination with steric repulsion between the latter upon bending (see below). Nearly all instances with substantial deviations of the LML bite angle from linearity are complexes in which this distortion is imposed by the structural constraints in bidentate ligands in which a bridge or scaffold forces the two coordinating centers L towards each other.1b–d

In this work, we show that d^{10}-ML_{2} complexes are not necessarily linear and may even have a pronounced intrinsic preference to adopt a nonlinear equilibrium geometry. To this end, we have investigated the molecular geometries and electronic structure of a series of d^{10}-ML_{2} complexes (M=Co^{−}, Rh^{−}, Ir^{−}, Ni, Pd, Pt, Cu^{+}, Ag^{+}, Au^{+}; L=NH_{3}, PH_{3}, CO) using relativistic density functional theory (DFT). Simple d^{10}-ML_{2} complexes are found with substantial deviations from linearity, featuring bite angles as small as 131° or even less. All that is necessary for bent d^{10}-ML_{2} complexes to occur is sufficiently strong π backdonation. This emerges from our detailed metal–ligand bonding analyses in the conceptual framework of quantitative MO theory contained in Kohn–Sham DFT. The analyses explain the phenomenon and provide a tool for rationally tuning the bite angle. Based on our analyses, we can augment the text-book Walsh diagram for bending ML_{2} complexes involving only σ donation with an extended Walsh diagram that also includes π backbonding.