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''Ab initio'' quantum chemistry methods are computational chemistry methods based on quantum chemistry. The term ''ab initio'' was first used in quantum chemistry by Robert Parr and coworkers, including David Craig in a semiempirical study on the excited states of benzene.〔(【引用サイトリンク】title=History of Quantum Chemistry )〕〔 〕 The background is described by Parr. In its modern meaning ('from first principles of quantum mechanics') the term was used by Chen (when quoting an unpublished 1955 MIT report by Allen and Nesbet), by Roothaan and, in the title of an article, by Allen and Karo, who also clearly define it. Almost always the basis set (which is usually built from the LCAO ansatz) used to solve the Schrödinger equation is not complete, and does not span the Hilbert space associated with ionization and scattering processes (see continuous spectrum for more details). In the Hartree–Fock method and the configuration interaction method, this approximation allows one to treat the Schrödinger equation as a "simple" eigenvalue equation of the electronic molecular Hamiltonian, with a discrete set of solutions. ==Accuracy and scaling== ''Ab initio'' electronic structure methods have the advantage that they can be made to converge to the exact solution, when all approximations are sufficiently small in magnitude and when the finite set of basis functions tends toward the limit of a complete set. In this case, configuration interaction, where all possible configurations are included (called "Full CI"), tends to the exact non-relativistic solution of the electronic Schrödinger equation (in the Born–Oppenheimer approximation). The convergence, however, is usually not monotonic, and sometimes the smallest calculation gives the best result for some properties. One needs to consider the computational cost of ''ab initio'' methods when determining whether they are appropriate for the problem at hand. When compared to much less accurate approaches, such as molecular mechanics, ''ab initio'' methods often take larger amounts of computer time, memory, and disk space, though, with modern advances in computer science and technology such considerations are becoming less of an issue. The HF method scales nominally as ''N4'' (''N'' being a relative measure of the system size, not the number of basis functions) – e.g., if you double the number of electrons and the number of basis functions (double the system size), the calculation will take 16 (24) times as long per iteration. However, in practice it can scale closer to ''N3'' as the program can identify zero and extremely small integrals and neglect them. Correlated calculations scale less favorably, though their accuracy is usually greater, which is the trade off one needs to consider: Second–order many–body perturbation theory (MBPT(2)), or when the HF reference is used, Møller–Plesset perturbation theory (MP2) scales as ''N4'' or ''N5'', depending on how it is implemented, MP3 scales as ''N6'' and coupled cluster with singles and doubles (CCSD) scales iteratively as ''N6'', MP4 scales as ''N7'' and CCSD(T) and CR-CC(2,3) scale iteratively as ''N6'', with one noniterative step which scales as ''N7''. Density functional theory (DFT) methods using functionals which include Hartree–Fock exchange scale in a similar manner to Hartree–Fock but with a larger proportionality term and are thus more expensive than an equivalent Hartree–Fock calculation. DFT methods that do not include Hartree–Fock exchange can scale better than Hartree–Fock. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Ab initio quantum chemistry methods」の詳細全文を読む スポンサード リンク
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