Unitary coupled-cluster theory

Unitary coupled-cluster theory [33, 50]. Canonical diagonalization [22]. 

It is possible for groups of three or more lines to be identified as equivalent, though this can happen only in many-body perturbation theory, expectation value coupled cluster theory, or unitary coupled cluster theory. For such diagrams, a prefactor of where n is the number of electron lines, must be included. 

M. R. Hoffmann and J. Simons, Chem. Phys. Lett., 142, 451 (1987). Analytical Energy Gradients for a Unitary Coupled-Cluster Theory. 

Both the effective valence Hamiltonian method [31, 32] and unitary coupled cluster [33-35] employ a single two-body unitary transformation. In the effective valence Hamiltonian method [31, 32], the unitary transformation, selected by perturbation theory, is applied to the Hamiltonian to produce an effective... 

In addition to the encouraging numerical results, the canonical transformation theory has a number of appealing formal features. It is based on a unitary exponential and is therefore a Hermitian theory it is size-consistent and it has a cost comparable to that of single-reference coupled-cluster theory. Cumulants are used in two places in the theory to close the commutator expansion of the unitary exponential, and to decouple the complexity of the multireference wave-function from the treatment of dynamic correlation. 

X. Li and J. Paldus,/. Chem. Phys., 101, 8812 (1994). Automation of the Implementation of Spin-Adapted Open-Shell Coupled-Cluster Theories Relying on the Unitary Group Formalism. 

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

To summarize the theory dynamic correlations are described by the unitary operator exp A acting on a suitable reference funchon, where A consists of excitation operators of the form (4). We employ a cumulant decomposition to evaluate all expressions in the energy and amphtude equations. Since we are applying the cumulant decomposition after the first commutator (the term linear in the amplimdes), we call this theory linearized canonical transformation theory, by analogy with the coupled-cluster usage of the term. The key features of the hnearized CT theory are summarized and compared with other theories in Table II. 

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. 

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