Generalized coupled cluster theories

NEW ALTERNATIVES FOR ELECTRONIC STRUCTURE CALCULATIONS RENORMALIZED, EXTENDED, AND GENERALIZED COUPLED-CLUSTER THEORIES... 

New alternatives for electronic structure calculations Renormalized, extended, and generalized coupled-cluster theories 119... 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

Note that in contrast to a general similarity transformation (e.g., as found in the usual coupled-cluster theory) the canonical transformation produces a Hermitian effective Hamiltonian, which is computationally very convenient. When U is expressed in exponential form, the effective Hamiltonian can be constructed termwise via the formally infinite Baker-Campbell-Hausdorff (BCH) expansion,... 

First, we note that the determination of the exact many-particle operator U is equivalent to solving for the full interacting wavefunction ik. Consequently, some approximation must be made. The ansatz of Eq. (2) recalls perturbation theory, since (as contrasted with the most general variational approach) the target state is parameterized in terms of a reference iko- A perturbative construction of U is used in the effective valence shell Hamiltonian theory of Freed and the generalized Van Vleck theory of Kirtman. However, a more general way forward, which is not restricted to low order, is to determine U (and the associated amplitudes in A) directly. In our CT theory, we adopt the projection technique as used in coupled-cluster theory [17]. By projecting onto excited determinants, we obtain a set of nonlinear amplitude equations, namely,... 

Perturbative analyses have yielded many insights into single-reference coupled-cluster theory. Although we generally are using the canonical transformation... 

With increasing use of such models, methods are likely to become more concisely defined in the near future. At present, the models for which protocols and parameters have been most clearly defined and where a fair number of applications have appeared applying those models in a consistent fashion include the aheady noted AM1/TIP3P model (more generally AMl/OPLS when solvents other than water are employed in the MM region) and a similarly fashioned HF/3-21G/OPLS model (Freindorf and Gao 1996). Implementations carrying the QM level as far as coupled-cluster theory have been reported (Kongsted et al. 2003). 

In two recent publications we have tried to characterize the excited state properties of 1 and 3 in order to facilitate their detection by LIF-spectroscopy. Our main tool in this effort has been equation of motion coupled cluster theory (EOM-CC). The EOM-CCSD method, which is equivalent to linear response CCSD, has been shown to provide an accurate description of both valence and excited states even in systems where electron correlation effects play an important role [39]. Computed transition energies for excitations that are of mainly single substitution character are generally accurate to within 0.1 eV. We have found the EOM-CCSD method to perform particularly well in combination with the doubly-augmented cc-pVDZ (d-aug-cc-pVDZ) basis set. This basis seems to provide equally balanced descriptions of ground and excited states,... 

Evangelista, F. A. AUen, W. D. Schaefer m, H. F. Coupling term derivation and general implementation of state-specific multireference coupled cluster theories, J. Chem. Phys. 2007,127, 024102-024117. 

With any type of molecular modeling, there is generally a tradeoff between cost and reliability, and one typically shuns models that cost more without increasing reliability. In practice, this cost is usually expressed as computational effort, or computer time. In gas phase modeling, one typically finds molecular mechanics and semiempirical molecular orbital theory at the low-cost end and multireference configuration interaction or coupled-cluster theory at the other, with the choice dictated by the size of the system. System size also influences the choice of solvation model. We consider first the least expensive models, those that take no account of the quantum mechanical nature of the solute. 

Disconnected, in coupled cluster theory, 133 Exchange integral, 61, 67 General contraction of basis sets, 157 Hindered rotor, partition function for, 306... 

A. Baikova and R. J. Bartlett, On the singlet-triplet separation in methylene A critical comparison of single- versus two-determinant (generalized valence bond) coupled cluster theory, J. Chem. Phys. 102, 7116-7123 1995. 

We would like to stress that this chapter is a review of coupled cluster theory. It is not primarily intended to provide an analysis of the numerical performance of the coupled cluster model, and we direct readers in search of such information to several recent publications. " Instead, we offer a detailed explanation of the most important aspects of coupled cluster theory at a level appropriate for the general computational chemistry community. Although many of the topics described here have been discussed by other au-thors, ° this chapter is unique in that it attempts to provide a concise, practical introduction to the mathematical techniques of coupled cluster theory (both algebraic and diagrammatic), as well as a discussion of the efficient... 

Although a spin-orbital formulation is conceptually simple, desirable properties such as spin-adaptation may be lost when the electronic state of interest is open shell, for example. A rigorously spin-adapted theory must include spin-free definitions of the cluster operators, T, and an appropriate (perhaps multideterminant) reference wavefunction (Refs. 39, 41, 42, 156-158). Such general coupled cluster derivations are beyond the scope of this chapter, though some of the issues associated with difficult open-shell problems are discussed in the next section. 

M. Nooijen and R. J. Bartlett,/. Chem. Phys., 104,2652 (1996). General Spin Adaptation of Open-Shell Coupled Cluster Theory. 

We begin this paper by shortly recapitulating the concept of extremal pair functions (Sect. 2). Then we consider extremal pair functions in the context of Moller-Plesset perturbation theory (Sect. 3) and coupled-cluster theory (Sect. 4). We then come to the main topic of this paper, the use of extremal pairs in R12-methods. To this end we formulate a new access to R12-theory starting with two-electron systems (Sect. 5) and generalizing it to n-electron systems (Sect. 6). We show then how extremal pairs arise in a natural way in R12-methods (Sect. 7). We finish (Sect. 8) by giving numerical examples which demonstrate the gain in numerical stability by using extremal pairs in Recalculations. 

It is well known that electron correlation plays a key role in understanding the most interesting phenomena in molecules. It has been the focal point of atomic and molecular theory for many years [1] and various correlated methods have been developed [2]. Among them are many-body perturbation theory [3] (MBPT) and its infinite-order generalization, coupled cluster (CC) theory [4,5], which provides a systematic way to obtain the essential effects of correlation. Propagator [6-9] or Green s function methods (GFM) [10-14] provide another correlated tool to calculate the electron correlation corrections to ionization potentials (IPs), electron affinites (EAs), and electronic excitations. 

Because of the validity of eqs. (29) and (30), the completely contracted 9 s in any o can be brought adjacent to one another with a proper parity factor. We shall make use of this generalized version of our new Wick s theorem in our development of the Coupled Cluster theory in terms of tfa. The hamiltonian for the electronic system may be written as... 

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