Exponential ansatz, coupled-cluster singles

Chapter 13 discusses coupled-cluster theory. Important concepts such as connected and disconnected clusters, the exponential ansatz, and size-extensivity are discussed the Unked and unlinked equations of coupled-clustCT theory are compared and the optimization of the wave function is described. Brueckner theory and orbital-optimized coupled-cluster theory are also discussed, as are the coupled-cluster variational Lagrangian and the equation-of-motion coupled-cluster model. A large section is devoted to the coupled-cluster singles-and-doubles (CCSD) model, whose working equations are derived in detail. A discussion of a spin-restricted open-shell formalism concludes the chapter. 

So far, we have specified the wave operator H in the BW form (15). If we adopt an exponential ansatz for the wave operator Cl, we can speak about the single-root multireference Brillouin-Wigner coupled-cluster (MR BWCC) theory. The simplest way how to accomplish the idea of an exponential expansion is to exploit the so-called state universal or Hilbert space exponential ansatz of Jeziorski and Monkhorst [23]... 

The failing of MBPT is that it is basically an order-by-order perturbation approach. For difficult correlation problems it is frequently necessary to go to high orders. This will be the case particularly when the single determinant reference function offers a poor approximation for the state of interest, as illustrated by the foregoing examples at 2.0 R. A practical solution to this problem is coupled-cluster (CC) theory. In fact, CC theory simplifies the whole concept of extensive methods and the linked-diagram theorem into one very simple statement the exponential wavefunction ansatz. 

The use of coupled-cluster (CC) wave functions within EOM theory for excitation energies, IPs and EAs has been developed [34,35] upon slightly different lines than outlined in Section 17.2. The CC wave function ansatz for Q,N) is written as usual in terms of an exponential operator acting on a single-determinant (e.g. unrestricted HF) reference function lO >... 

The use of the exponential ansatz in formulating a quantum mechanical many-body theory was briefly described in Chapter 3, Section 3.3.2. This approach was first realized in nuclear physics by Coester and Ktimmel [81,82] and its introduction into quantum chemistry is usually attributed to Click. [76]. A recent overview of this method has been given by Paldus [73]. The single-reference coupled cluster approach has been described [83] as... 

In Section 4.2.3.1, we have defined the wave operator, 12, in the Brillouin-Wigner form (4.92). If we adopt an exponential ansatz for the wave operator, 12, we can develop the single-root (state-specific) multi-reference Brillouin-Wigner coupled-cluster (MR Bwcc) theory. This is the purpose of the present section. 

We turn now to the calculation of the effective Hamiltonian (4.98) for single-root multi-reference Brillouin-Wigner coupled cluster theory. Using the Hilbert space exponential ansatz of Jeziorski and Monkhorst, expression (4.103), the off-diagonal... 

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