Ab initio calculation
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. The background is described by Parr.Ab initio means "from first principles" or "from the beginning", implying that the only inputs into an ab initio calculation are physical constants.Ab initio quantum chemistry methods attempt to solve the electronic Schrödinger equation given the positions of the nuclei and the number of electrons in order to yield useful information such as electron densities, energies and other properties of the system. The ability to run these calculations has enabled theoretical chemists to solve a range of problems and their importance is highlighted by the awarding of the Nobel prize to John Pople and Walter Kohn.
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.
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