Multireference theory

Merchan M, Serrano-Andres L, Fulscher MP, Roos BO. Multiconfigurational perturbation theory applied to excited states of organic compounds. In Hirao K, ed. Recent Advances in Multireference Theory. Yol. 4. Singapore World Scientific, 1999 161-195. 

H. Lischka, T. Muller, P. G. Szalay, I. Shavitt, R. M. Pitzer, and R. Shepard, COLUMBUS-A Program System for Advanced Multireference Theory Calculations, in Wiley Interdisciplinary Reviews Computational Molecular Science 1, (2011), pp. 191-199. 

Lischka H, Muller T, Szalay PG, Shavitt I, Pitzer RM, Shepard R (2011) COLUMBUS—a program system for advanced multireference theory calculations. In Wiley Interdisciplinary Reviews Computational Molecular Science, vol 1, p 191... 

A comparison of singlet and triplet states for one- and two-dimensional graphene nanoribbons using multireference theory... 

Also in the recently very active field of multireference coupled-cluster theory, first FI 2-extensions have been reported. Demel et al. reported such an development for the case of Mukherjee s state-specific multireference coupled-cluster ansatz (Mk-MRCC), while Liu et al. applied F12 theory to internally contracted multireference theory. 

In 1986, Schaefer et al. reported the first extensive ab initio calculations of S3 [61]. SCF and CISD calculations indicated that the global minimum is the ring D3h form. The more sophisticated CASSCF and MR-CISD calculations, on the other hand, favoured the open bent structure of 2 symmetry. The preference of the open form was subsequently confirmed by several other theoretical investigations [62-65]. The I>3h structure is calculated to be 31-44 kj mol less stable than the open C2V structure, depending on the method of calculation and the level of theory applied [56, 59-65]. The best estimate of the S-S bond length of the Czv form is 193.2 pm (CCSD(T)) [65] and the bond angle is 117°. Compared with the multireference calculations, DFT methods adequately describe the structure and PES of S3. 

Grimme S, Waletzke M (1999) A combination of KohnSham density functional theory and multireference configuration interaction methods. J Chem Phys 111 5645—5655... 

For a subset of 27 G2-2 molecules with fairly small experimental uncertainties, W1 theory had MAD of 0.7 kcal/mol, compared to the average experimental uncertainty of 0.4 kcal/mol. Some systems exhibit deviations from experiment in excess of 1 kcal/mol in the cases of BF3 andCF4, very slow basis set convergence is responsible, and W2 calculations in fact remove nearly all remaining disagreement with experiment for the latter system. (The best available value for BF3 is itself a theoretical one, so a comparison would involve circular reasoning.) Other molecules (N02 and C1NO) suffer from severe multireference effects. 

Since the time that Bowen s and co-workers article was published, the theory based on the BO approximation, except for one very recent multireference configuration interaction (MRCI) calculation by Chang et al. [127], has been unable to produce a value of the LiH adiabatic electron affinity that... 

By adopting the no-pair approximation, a natural and straightforward extension of the nonrelativistic open-shell CC theory emerges. The multireference valence-universal Fock-space coupled-cluster approach is employed [25], which defines and calculates an effective Hamiltonian in a low-dimensional model (or P) space, with eigenvalues approximating some desirable eigenvalues of the physical Hamiltonian. The effective Hamiltonian has the form [26]... 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

Equilibrium Bond Distance and the Harmonic Frequency for N2 from the 2-RDM Method with 2-Positivity (DQG) Conditions Compared with Their Values from Coupled-Cluster Singles-Doubles with Perturbative Triples (CCD(T)), Multireference Second-Order Perturbation Theory (MRPT), Multireference Configuration Interaction with Single-Double Excitations (MRCI), and Full Configuration Interaction (FCI)". 

T. Yanai and G. K. L. Chan, Canonical transformation theory for dynamic correlations in multireference problems, in Reduced-Density-Matrix Mechanics With Application to Many-Electron Atoms and Molecules, A Special Volume of Advances in Chemical Physics, Volume 134 (D.A. Mazziotti, ed.), Wiley, Hoboken, NJ, 2007. 

CANONICAL TRANSFORMATION THEORY FOR DYNAMIC CORRELATIONS IN MULTIREFERENCE PROBLEMS... 

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