原子轨道线性组合

量子化学维基，人人都可编辑的量子化学百科全书。

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原子轨道线性组合，或者简写为LCAO,就是原子轨道的相互叠加。在量子力学里，原子的电子组态由波函数来描述。从数学上来看，这些波函数构成了函数基组。也就是说，对于给定的原子，它们是描述电子状态的基本函数。在化学反应过程中，轨道波函数会发生改变，例如，根据原子所参与形成的化学键的类型，电子云的形状会相应改变。原子轨道线性组合的分子轨道方法，或者叫LCAO-MO是量子化学中一种用来计算分子轨道的方法，它于1929年由Sir John Lennard-Jones引入，并且经由Ugo Fano进行了扩展。

由点群操作导出的不可约表示

轨道函数由基函数的线性组合来表示，而基函数是以分子中的原子核为中心的单电子函数。而典型的原子轨道函数一般采用类氢原子的波函数，因为它们的解析形式是已知的(例如：Slater型轨函)，但是除此之外，还可以有别的选择，例如作为基本基函数的Gaussian函数。通过极小化体系的总能，可以求得一组合适的线性组合系数。然而，随着计算化学的发展，LCAO方法已经不太真正用来优化得到实际的波函数了，但它仍可以用来对那些使用更现代的方法得到的计算结果做出预测或者有意义的讨论。However, since the development of computational chemistry, the LCAO method often refers not to an actual optimization of the wave function but to a hand-waving discussion which is very useful for predicting and rationalizing results obtained via more modern methods. In this case, the shape of the molecular orbitals and their respective energies are deduced approximately from comparing the energies of the atomic orbitals of the individual atoms (or molecular fragments) and applying some recipes known as level repulsion and alike. The graphs that are plotted to make this discussion clearer are called correlation diagrams. The required atomic orbital energies can come from calculations or directly from experiment via Koopmans' theorem.

This is done by using the symmetry of the molecules and orbitals involved in bonding. The first step in this process is assigning a point group to the molecule. A common example is water, which is of C_2v symmetry. Then a reducible representation of the bonding is determined. Each operation in the point group is performed upon the molecule. The number of bonds that are unmoved is the character of that operation. This reducible representation is decomposed into the sum of irreducible representations. These irreducible representations correspond to the symmetry of the orbitals involved.

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