Multireference methods

There are many more error correction methods, which are reviewed in detail by Duch and Diercksen. They also discuss the correction of other wave functions, such as multireference methods. In their tests with various numbers of Be atoms, the correction most closely reproducing the full Cl energy is... 

The isomer lowest in energy is predicted to be the 2,5-dihydro-1,2,4-triazine 198g. The most stable structures always show two C=N double bonds. Moreover, in polar solvents, 198h should also be a dominant species [00PCCP2187]. The valence and Rydberg excited states of 1,2,3-triazine have been studied by multireference methods (MRD-CI) and the results are compared with experimental spectra [98CP39]. 

In order to improve the quality of excited state description, correlation needs to be included. The methods having been developed can be categorized into two groups, the multireference methods, and the single-reference based methods. 

Multireference methods provide a straightforward way to treat excited states, since studying excited states requires the equivalent treatment of these states. Multireference methods are extensions of the single reference Hartree-Fock or configuration interaction (Cl) methods, where many configurations are used instead of a single configuration,... 

Most multireference methods described to date have been limited to second order in perturbation theory. As analytic gradients are not yet available, geometry optimization requires recourse to more tedious numerical approaches (see, for instance. Page and Olivucci 2003). While some third order results have begun to appear, much like the single-reference case, they do not seem to offer much improvement over second order. 

We may note a number of features of these results. First, nondynamical correlation is known to be much more important in the singlet state than in the triplet. Hence it is not surprising that the multireference methods perform better here than the single reference methods. Nevertheless, the errors in the single reference meth-... 

The directions presented and concluded here are the guide to our further investigations and applications in the frame of vibronic paradigm targeting the future approach of multireference methods, including the JT problems beside the PJT ones. 

K. Hirao, Recent Advances in Multireference Methods, (ed. K. Hirao), World Scientific, Singapore, 2001. 

The requirement needed to incorporate the solvent effects into a state-specific (multireference) method is fulfilled by using the effective Hamiltonian defined in Equation (1.159). The only specificity to take into account is that in order to calculate Va we have to know the density matrix of the electronic state of interest (see the contribution by Cammi for more details). Such nonlinear character of Va is generally solved through an iterative procedure [35] at each iteration the solvent-induced component of the effective Hamiltonian is computed by exploiting Equation (1.157) with the apparent charges determined from the standard ASC equation with the first order density matrix of the preceding step. At each iteration n the free energy of each state K is obtained as... 

A later study also focused on various means of computing the correlation contribution to the interaction energy in the HE dimer and reached very similar conclusions. All of the correlated methods (MP2, MP4, CCSD(T) and CISD) based on the Hartree-Fock reference configuration gave essentially the same binding energy. The results deteriorate when multireference methods are used. 

What remains to be done is a comparative study of the rearrangement of the non-complexed species using multireference methods. 

The MP4 and QCISD(T) methods give formation energies similar to the MP2 method. Multireference methods are not usually needed to describe hydrogen bonds (they are only needed when near degeneration situations are expected, as in the Bei dimer, where the s and p states of the Be atoms are nearly degenerate see, for instanee. Ref. 44). 

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