Ab initio quantum chemistry methods
Ab initio quantum chemistry methods are computational chemistry methods based on quantum chemistry.
The simplest type of ab initio electronic structure calculation is the Hartree-Fock (HF) scheme, in which the Coulombic electron-electron repulsion is not specifically taken into account. Only its average effect is included in the calculation. This is a variational procedure, therefore the obtained approximate energies, expressed in terms of the system's wave function, are always equal to or greater than the exact energy, and tend to a limiting value called the Hartree-Fock limit. Many types of calculations begin with a Hartree-Fock calculation and subsequently correct for electron-electron repulsion, referred to also as electronic correlation. Møller-Plesset perturbation theory (MPn) and coupled cluster theory (CC) are examples of these post-Hartree-Fock methods.
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.
The most popular classes of ab initio electronic structure methods:
Hartree-Fock methods
- Hartree-Fock (HF)
- Restricted Open-shell Hartree-Fock (ROHF)
- Unrestricted Hartree-Fock (UHF)
Post-Hartree-Fock methods
- Møller-Plesset perturbation theory (MPn)
- Multi-configurational self-consistent field (MCSCF)
- Configuration interaction (CI)
- Multi-reference configuration interaction (MRCI)
- Coupled cluster (CC)
- Quadratic configuration interaction (QCI)
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. The convergence, however, is usually not monotonic, and sometimes the smallest calculation gives the best result for some properties. The downside of ab initio methods is their computational cost. They often take enormous amounts of computer time, memory, and disk space. The HF method scales as N4 (N being the number of basis functions) – i.e. a calculation twice as big takes 16 times as long to complete – and correlated calculations often scale even less favorably (correlated DFT methods suffer the least from this problem).
The problem of computational expense can be alleviated through simplification schemes. In the density fitting scheme, the four-index integrals used to describe the interaction between electron pairs are reduced to simpler two- or three-index integrals, by treating the charge densities they contain in a simplified way. This reduces the scaling with respect to basis set size. Methods employing this scheme are denoted by the prefix "df", for example the density fitting MP2 is df-MP2 (lower-case is advisable to prevent confusion with DFT). In the local orbital approximation, the molecular orbitals, which are formally spread across the entire molecule, are restricted to localised domains. This eliminates the interactions between distant electron pairs and hence sharply reduces the scaling with molecular size, a major problem in the treatment of biologically-sized molecules. Methods employing this scheme are denoted by the prefix "L", e.g. LMP2. Both schemes can be employed together, as in the recently developed df-LMP2 method.
Valence bond methods
Valence bond (VB) methods are generally ab initio although some semi-empirical versions have been proposed. Current VB approaches are:-
- Generalized valence bond (GVB)
- Modern valence bond theory (MVBT)
Quantum Monte Carlo methods
A method that avoids making the variational overestimation of HF in the first place is Quantum Monte Carlo (QMC), in its variational, diffusion, and Green's function forms. These methods work with an explicitly correlated wave function and evaluate integrals numerically using a Monte Carlo integration. Such calculations can be very time-consuming, but they are probably the most accurate methods known today.