Multi-reference wavefunction

The array of methods in gamess for treating spin-orbit coupling effects has recently been the subject of two reviews [46,47]. These methods include the full Breit-Pauli spin-orbit operator and approximations to it, primarily developed by Koseki and Fedorov. All of the methods require a multi-reference wavefunction as a starting point. This can be MCSCF, first or second order Cl, or MRPT2. The simplest method is a... 

Part of a wavefunction corresponding to a particular state of a multi-reference wavefunction. 

Several theoretical chemists have made groundbreaking contributions to our understanding of the fundamental quantum mechanics that underlies the chemical bond. The landmark series of papers by Ruedenberg and co-workers on the nature of the chemical bond will be discussed in some detail below, as will the extension of the localized orbital concept to more complex, multi-reference wavefunctions. In a parallel series... 

CC2, CCS, etc.) can be devised offering a good balance between cost and accuracy. Other simple (second-order) perturbative approaches that are comparable to CC2 can be found in the ADC(2) [19] or CIS(D) [20] methods. As is the case for TDDFT, these linear response or propagator formulations are not only interesting from a formal perspective (by allowing one to obtain information from the excited states based on ground-state quantities) but also because of their black box nature, that is, one does not need to construct a complicated, multi-reference wavefunction via the definition of orbital active spaces. However, as we shall see, the restriction to closed-shell references somewhat limits their applicability to the actinides. 

Bundgen P, Grein F and Thakkar A J 1995 Dipole and quadrupole moments of small molecules. An ab initio study using perturbatively corrected, multi-reference, configuration interaction wavefunctions J. Mol. Struct. (Theochem) 334 7... 

However, if this is not the case, the perturbations are large and perturbation theory is no longer appropriate. In other words, perturbation methods based on single-determinant wavefunctions cannot be used to recover non-dynamic correlation effects in cases where more than one configuration is needed to obtain a reasonable approximation to the true many-electron wavefunction. This represents a serious impediment to the calculation of well-correlated wavefunctions for excited states which is only possible by means of cumbersome and computationally expensive multi-reference Cl methods. 

The total energies and wavefunctions of the Hamiltonian (1) have been calculated as the eigenvalues and eigenvectors of a Cl matrix. Full Cl has been used for all calculations of quasi-one-dimensional quantum dots and for quasi-two-dimensional quantum dots with N = 2, while multi-reference Cl has been used for quasi-two-dimensional quantum dots with N = 3 and 4. The results are presented in atomic units. They can be scaled by the effective Bohr radius of 9.79 nm and the effective Hartree energy of 11.9 meV for GaAs semiconductor quantum dots [25,26]. 

Most studies limit the Cl space to single and double substitutions from a single reference (CISD). Occasionally, when one reference does not provide a sufficient zeroth-order wavefunction, the multi-reference CISD method will be employed. The applications of such methods are too numerous to discuss here their general performance has already been described in section 2. We consider studies which go beyond CISD for one or a few references such highly correlated wavefunctions are useful when very accurate results are desired or when several electron configurations are needed for a qualitatively correct reference wavefunction (such as when multiple bonds are broken). We will limit our attention to methods which select the Cl space in an a priori fashion based on the distribution of electrons among various orbital subspaces. 

All of the methods discussed above are based on a multi-reference (MR) approach to obtaining wavefunctions and properties. Such MR approaches are often necessary, because many chemical problems involve species with considerable configurational mixing due the existence of near degeneracies (diradical character). However, the amount of diradical character in a chemical system can span a very broad range, from essentially zero (e.g. HOMO occupancy 2, LUMO occupancy 0) to fully diradical (HOMO occupancy 1, LUMO occupancy 1). As one approaches fully diradical character, all single reference methods break down, but they do not break down at the same rate as one approaches this limit. In particular, there is considerable evidence that coupled cluster (CC) methods, particularly those like CCSD(T) that incorporate a triples correction, can overcome the deficiency of a single reference wavefunction for problems with non-trivial diradical character. This has been demonstrated, for example, by... 

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