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The natural auxiliary function (NAF) approach is an approximation to decrease the size of the auxiliary basis set required for quantum chemical calculations utilizing the density fitting technique. It has been proven efficient to speed up various correlation models, such as second-order Møller–Plesset (MP2) theory and coupled-cluster methods. Here, for the first time, we discuss the theory of analytic derivatives for correlation methods employing the NAF approximation on the example of MP2. A detailed algorithm for the gradient calculation with the NAF approximation is proposed in the framework of the method of Lagrange multipliers. To assess the effect of the NAF approximation on gradients and optimized geometric parameters, a series of benchmark calculations on small and medium-sized systems was performed. Our results demonstrate that, for MP2, sufficiently accurate gradients and geometries can be achieved with a moderate time reduction of 15–20% for both small and medium-sized molecules.

Four possible structural isomers at the Si3H4 potential surface, a trisilene, a trisilaallene, and two structurally different silylenes, have been studied by quantum chemical methods. With the investigation of the Si−Si−Si bond angle the different structures could be distinguished and characterized. α > 100° represents silaallenes with Si&dbd;Si double bonds and C2 symmetry. In the 80° < α < 100° region the Si&dbd;Si bond order is about 1.5 and the molecule is planar or almost planar and can be characterized with an in-plane lone electron pair and a delocalized π-system. A cyclic silylene with single Si−Si bonds and C2 symmetry can be found in the α < 80° region. With systematic variation of the substituents using π-donor or -acceptor groups both silylenes can be stabilized. Some possible stabilized structures of each type are suggested.