Linear-Scaling Methods in Quantum Chemistry
نویسندگان
چکیده
With the introduction of the Schrödinger equation in 1926, it was in principle clear how to describe a molecular system and its properties exactly in a nonrelativistic sense. However, for most molecular systems of chemical interest, the analytic solution of the Schrödinger equation is not possible. Therefore, since 1926, a multitude of hierarchical approximations (some of which are displayed in Figure 1) have been devised that allow for a systematic approach to the exact solution of the Schrödinger equation. Although the Schrödinger equation as the fundamental equation in electronic structure theory is already quite old, the field of quantum chemistry is still fairly young and fast moving, and much can be expected in the future for developing and applying quantum chemical methods for the treatment of molecular systems. The importance of the systematic hierarchy for solving the Schrödinger equation cannot be overemphasized, because it allows one, in principle, to systematicallyapproach the exact result for a molecularpropertyof interest. The simplest approach in this hierarchy is the Hartree–Fock (HF) method, which describes electron–electron interactions within a mean-field approach. The electroncorrelation effects neglected in this approach can be described by the so-called
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