CCSD energy equation

As an example, consider the CCSD energy equation derived earlier in Eq. [134] using Wick s theorem. Each term of the general expression... 

The CCSD energy is given by the general CC equation (4.53), and amplitude equations are derived by multiplying (4.50) with a singly excited determinant and integrating (analogously to eq. (4.54)). 

Here, Ti and T2 are the singly and doubly excited clusters obtained by solving the CCSD equations, is the CCSD energy, and... 

Let us now examine the contents of the QMMCC theory, in a somewhat greater detail, by discussing the QMMCC equations for the special case, where the QMMCC corrections are added to the CCSD energy (7 = Ti + T2) and Z is... 

The hydrogen dissociation energy ) [Equation (15)] amounts to 3.1 kcal mor [TZ(3dl/,lp) CCSD(T) + ZPVE + BSSE], which is much less than for GeH (10 kcal mor ). 

This equation is not restricted to the CCSD approximation, however. Since higher excitation cluster operators such as T3 and T4 cannot produce fully contracted terms with the Hamiltonian, their contribution to the coupled cluster energy expression is zero. Therefore, Eq. [134] also holds for more complicated methods such as CCSDT and CCSDTQ. Higher excitation cluster operators can contribute to the energy indirectly, however, through the equations used to determine the amplitudes, and t-h, which are needed in the energy equation above. 

Scuseria, Janssen, and Schaefer, for example, developed a set of intermediates based on their reformulation of the CCSD amplitude and energy equations in a unitary group formalism designed to offer special efficiency when the refer-... 

Once the system of CCSD equations, Eqs. (5) and (6), is solved for the cluster amplitudes and the CCSD energy is calculated using the expression... 

In this work, in addition to the CCSD approximation, we examine two different ways of correcting the CCSD energy for the effects of the connected triply excited clusters, namely, the CCSD(T) method and its completely renormalized CR-CC(2,3) extension. Since the CCSD(T) approach can be obtained as a natural approximation to CR-CC(2,3) [24, 25], we begin our brief description of both methods with the key equations of CR-CC(2,3). 

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