Carbon centres in typical organic molecules have a coordination number that can reach a maximum of four, in which case the bonded atoms are situated at the vertices of a tetrahedron. Exceptions to those two structural rules have been posited and examined for decades, and planar tetracoordinate carbon (ptC) species are notable molecules that violate the second rule. There is continued interest in experimental and theoretical studies of ptCs, as well as emerging molecules that contain planar pentacoordinate carbon (ppC) and planar hexacoordinate carbon (phC) atoms, species that violate both structural rules. This Review describes recent progress in the theoretical prediction of viable entities that contain ppC centres. The first such molecule reported, the D_5h-symmetric ppC species CAl₅⁺, was followed by a series of predicted ppC species that could be obtained by substituting the Al centres for other heteroatoms. More complicated ppC systems have also been suggested, including metallocene-stabilized ppCs and quasi-ppCs embedded within cage structures or 2D materials. To date, computational studies have identified at least 65 local and 39 global minimum energy structures that contain ppCs or quasi-ppCs. The general design principles for ptC-centred candidate structures include delocalization of the central C 2p_z lone electron pair, ensuring an 18 valence electron count and allowing for strong electron delocalization. These principles have been extended to ppC systems with some success. It is hard to predict the extent to which the coordination number of planar C can be increased because it depends not only on the valence and size of C but also on the size of the atoms bonded to it and the mode of bonding. Although a few energetically low-lying planar hexacoordinate and heptacoordinate C species have been identified computationally, none have been observed experimentally.

典型有机分子中的碳中心的配位数最多可达到四个，在这种情况下，键合原子位于四面体的顶点。这两个结构规则的例外情况已经提出并进行了数十年的研究，而平面四配位碳（ptC）物种是违反第二条规则的引人注目的分子。ptC的实验和理论研究以及包含平面五配位碳（ppC）和平面六配位碳（phC）原子的新分子都引起了人们的持续关注，这些物种违反了这两种结构规则。这篇综述描述了包含ppC中心的可行实体的理论预测的最新进展。报道的第一个此类分子是D _{5 h}对称ppC物种CAl₅ ⁺，其后是一系列预测的ppC物种，可以通过用Al中心替代其他杂原子获得这些ppC物种。还提出了更复杂的ppC系统，包括金属茂稳定的ppC和嵌入笼结构或2D材料中的准ppC。迄今为止，计算研究已经确定了至少65个包含ppC或准ppC的局部最小能量结构和39个全局最小能量结构。以ptC为中心的候选结构的一般设计原则包括中心C 2 p _z的离域单电子对，确保18价电子计数并允许强电子离域。这些原则已成功扩展到ppC系统。很难预测平面C的配位数可以增加到什么程度，因为它不仅取决于C的化合价和尺寸，还取决于与其键合的原子的尺寸和键合方式。尽管已通过计算确定了一些能量低的平面六坐标和七坐标C物种，但实验上均未观察到。