By Mitchell A. C. G.

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This approximation is so efficient that it hardly affects the chemical properties of electronic ground states. Therefore, this approximation is used by default in quantum chemical calculations. With this adiabatic approximation, since the nuclear–nuclear interactions Vnn can be neglected, Eq. 11) which appears similar to the Hamiltonian of the helium atom. However, the equation is more difficult to solve than it appears, because the hydrogen molecule has two atomic nuclei. Actually, the position vectors of the electrons must be considered for each atomic nucleus, although these are represented as rn in Eq.

Philos. Soc. : Ann. Phys. : Phys. Rev. : Le Meilleur des Mondes Possibles (Japanese). : Trans. Faraday Soc. : Rev. Mod. Phys. : J. Chem. Phys. : Z. Phys. : Rev. Mod. Phys. : Z. Phys. : Rev. Mod. Phys. : Wave Mechanics: Advanced General Theory. : J. Chem. Phys. : Quantum Physics 2nd edn. : Proc. R. Soc. Lond. : Math. Proc. Camb. Philos. Soc. : Solid State Phys. : Z. Phys. : Z. Phys. : Z. Phys. : Chem. Phys. Lett. : J. Chem. Phys. : Phys. Rev. : Z. Phys. : Z. Phys. : J. Chem. Phys. : The Philosophy of Quantum Mechanics: The Interpretations of Quantum Mechanics in Historical Perspective.

After the development of this method, quantum chemistry began to make progress that tracked the growth of computer power. Based on the LCAO–MO approximation given in Sect. 58) pD1 where nAO is the number of atomic orbitals. The expansion coefficient Cpi is called the molecular orbital (MO) coefficient. Although f p g is essentially the set of atomic orbitals, it is more efficient and general to use basis functions modeling atomic orbitals (For basis sets, see Sect. 6). 5 Roothaan Method 49 of statistical systems.