Multi-reference coupled-clusters

Specifically, if T] < 0.02, the CCSD(T) metliod is expected to give results close the full Cl limit for the given basis set. If is larger than 0.02, it indicates that the reference wave function has significant multi-determinant character, and multi-reference coupled cluster should preferentially be employed. Such methods are being developedbut have not yet seen any extensive use. 

W. D. Laidig and R. J. Bartlett, A multi-reference coupled-cluster method for molecular applications. Chem. Phys. Lett. 104, 424-430 (1984). 

The CASSCF method itself is not very useful for anything else than systems with few electrons unless an effective method to treat dynamical correlation effects could be developed. The Multi-Reference Cl (MRCI) method was available but was limited due to the steep increase of the size of the Cl expansion as a function of the number of correlated electrons, the basis set, and the number of active orbitals in the reference function. The direct MRCI formulation by P. Siegbahn helped but the limits still prevented applications to larger systems with many valence electrons [20], The method is still used with some success due to recent technological developments [21], Another drawback with the MRCI approach is the lack of size-extensivity, even if methods are available that can approximately correct the energies. Multi-reference coupled-cluster methods are studied but have not yet reached a state where real applications are possible. 

U.S. Mahapatra, B. Datta, D. Mukherjee, A state-specific multi-reference coupled cluster formalism with molecular applications. Mol. Phys. 94 (1998) 157. 

Debashis Mukherjee is a Professor of Physical Chemistry and the Director of the Indian Association for the Cultivation of Science, Calcutta, India. He has been one of the earliest developers of a class of multi-reference coupled cluster theories and also of the coupled cluster based linear response theory. Other contributions by him are in the resolution of the size-extensivity problem for multi-reference theories using an incomplete model space and in the size-extensive intermediate Hamiltonian formalism. His research interests focus on the development and applications of non-relativistic and relativistic theories of many-body molecular electronic structure and theoretical spectroscopy, quantum many-body dynamics and statistical held theory of many-body systems. He is a member of the International Academy of the Quantum Molecular Science, a Fellow of the Third World Academy of Science, the Indian National Science Academy and the Indian Academy of Sciences. He is the recipient of the Shantiswarup Bhatnagar Prize of the Council of Scientihc and Industrial Research of the Government of India. 

A posteriori corrections can be developed for calculations performed by using the Brillouin-Wigner perturbation expansion. These a posteriori corrections can be obtained for the Brillouin-Wigner perturbation theory itself and, more importantly, for methods, such as limited configuration interaction or multi-reference coupled cluster theory, which can be formulated within the framework of a Brillouin-Wigner perturbation expansion. 

Aspects of size extensivity in unitary group adapted multi-reference coupled cluster theories the role of cumulant decomposition of spin-free reduced density matrices... 

Abstract We present in this paper a comprehensive study of the various aspects of size extensivity of a set of unitary group adapted multi-reference coupled cluster (UGA-MRCC) theories recently developed by us. All these theories utilize a Jez-iorski-Monkhorst (JM) inspired spin-free cluster Ansatz of the forml P) = = exp(r ), where is... 

Abstract The purpose of this paper is to introduce a second-order perturbation theory derived from the mathematical framework of the quasiparticle-based multi-reference coupled-cluster approach (Rolik and Kallay in J Chem Phys 141 134112, 2014). The quasiparticles are introduced via a unitary transformation which allows us to represent a complete active space reference function and other elements of an orthonormal multi-reference basis in a determinant-like form. The quasiparticle creation and annihilation operators satisfy the fermion anti-commutation relations. As the consequence of the many-particle nature of the applied unitary transformation these quasiparticles are also many-particle objects, and the Hamilton operator in the quasiparticle basis contains higher than two-body terms. The definition of the new theory strictly follows the form of the single-reference many-body perturbation theory and retains several of its beneficial properties like the extensivity. The efficient implementation of the method is briefly discussed, and test results are also presented. 

The formulation of a multi-reference bwcc theory can now proceed in two distinct ways. In the first option, we can formulate a multi-root version of the multi-reference BWCC theory which yields all roots of the d-dimensional 9 space simultaneously. This is the approach employed in most multi-reference coupled cluster formulations which are based on the Rayleigh-Schrodinger expansion. In the second option, we can use the state-specific wave operator (4.59) and formulate a state-specific (or single root) version of multi-reference bwcc theory [10]. 

Although the past 20 years have witnessed a great progress in the Hilbert space multi-reference coupled cluster methods (see, for example, the work of Mukherjee and Pal [99],Paldus [101], Jeziorski and Paldus [102], Jankowski et al. [103],Paldus et al. [104], Paldus et al. [105], Meissner et al. [106], Kucharski and Bartlett [107], Balkovd et al. [108], Baikova and Bartlett [109], Balkovd et al. [110], Baikova et al. [Ill], Berkovic and Kaldor [112]) only a few applications of this approach have been reported, mostly oriented to the simple model systems exploiting a lowdimensional model space. Among the reasons for this paucity of applications are the choice of an appropriate model space, convergence difficulties arising from intruder state problems and from multiple solutions of non-linear coupled cluster equations. 

The application of the Brillouin-Wigner coupled cluster theory to the multireference function electron correlation problem yields two distinct approaches (i) the multi-root formalism which was discussed in Section 4.2.2 and (ii) the single-root formalism described in the previous subsections of this section. Section 4.2.3. The multiroot multi-reference Brillouin-Wigner coupled cluster formalism reveals insights into other formulations of the multi-reference coupled cluster problem which often suffer from the intruder state problem which, and in practice, may lead to spurious... 

Another category of approaches that avoids the symmetry breaking problem of the orbitals for the target state is based on using a related, well-behaved HF reference instead. Examples of such techniques include quasi-restricted Hartree-Fock coupled-cluster (QRHF CC) (11,19), symmetry adapted cluster configuration interaction (SAC-CI) (22,23), coupled-cluster linear response theory (CCLRT) (24-26) or equivalently equation-of-motion coupled-cluster (EOM-CC) (27-32), Fock space multi-reference coupled-cluster (FSMRCC) (33-37), and similarity transformed equation-of-motion coupled-cluster (STEOM-CC) (38-40). In the case of NO3 and N03, the restricted Hartree-Fock (RHF) orbitals of the closed-shell N03 anion system can be used as the reference. The anion orbitals are stable with respect to symmetry perturbations, and the system does not suffer from the artifactual symmetry breaking of the neutral and cation. 

State-specific Multi-reference Coupled-cluster Theory and its Approximate Versions... 

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