Other beyond-Hartree-Fock methods

Several other methods for quantum chemical calculations that approach the correlation energy problem have been proposed, but their detailed examination would be out of place in this book [17]. They all require a substantial increase in computational effort with respect to HF and to MPn or DFT. Even these more refined methods stumble upon the fundamental physical obstacle represented by the fact that these intermolecular interaction energies are often very small (see Chapter 4). For inter-molecular selectivity, sometimes the decision has to be made at the level of less than 

5 kJ mol and this is an intrinsic barrier to the development of chemical theories of intermolecular bonding. 

---

The various methods used in quantum chemistry make it possible to compute equilibrium intermolecular distances, to describe intermolecular forces and chemical reactions too. The usual way to calculate these properties is based on the independent particle model this is the Hartree-Fock method. The expansion of one-electron wave-functions (molecular orbitals) in practice requires technical work on computers. It was believed for years and years that ab initio computations will become a routine task even for large molecules. In spite of the enormous increase and development in computer technique, however, this expectation has not been fulfilled. The treatment of large, extended molecular systems still needs special theoretical background. In other words, some approximations should be used in the methods which describe the properties of molecules of large size and/or interacting systems. The further approximations are to be chosen carefully this caution is especially important when going beyond the HF level. The inclusion of the electron correlation in the calculations in a convenient way is still one of the most significant tasks of quantum chemistry. 

Other methods which go beyond the Hartree-Fock level of approximation include Cluster Methods and Many-Body Perturbation Theory (Wilson 1984). These approaches involve the introduction of repulsion effects due to simultaneous interactions between three, four, and even more electrons in the expansion of the wavefunction. One important drawback of cluster methods and many-body perturbation theory is that they are not variational. That is to say, the calculated energies no longer represent upper bounds and it is possible to obtain predictions in excess of 100% of the experimental values. Nevertheless, their use is capable of reducing the error in the calculation of the energy of the helium atom to something of the order of lO %. 

---