Deexcitation operators

This dependence on ordering occurs because, unlike the set of operators and in the 3-positivity conditions, the operators do not include the set of single-particle excitation and deexcitation operators, that is,... 

Where H is the similarity-transformed Hamiltonian, eq (14), with respect to two independent cluster operators T and Z or, more precisely, with respect to the excitation operator T and the deexcitation operator Z The advantage of eq (36) over the expectation value of the Hamiltonian with the CC wave function, which can also improve the results for multiple bond breaking (28, 127), is the fact that EcC(z,j is a finite series in T and Z. Unfortunately, the power series expansions of (Z,7), eq (36), in terms of T and Z contain higher powers of... 

Formally, each operator Lk is a deexcitation operator, whose many-body expansion is... 

Equations (54) and (55) show that operators Lk cannot be regarded as ordinary deexcitation operators. Indeed, we cannot use Lk in the same way as we use Rk to define the excited ket states [see Eq. (7)]. The excited... 

The left-hand deexcitation operator Cl is defined in a similar way as the left-hand operator Ck of the EOMXCC theory [cf. Eq. (102)],... 

The Kramers-restricted form of the Hamiltonian that was used in Cl theory is not suitable for Coupled Cluster theory because it mixes excitation and deexcitation operators. One possibility is to define another set of excitation operators that keep the Kramers pairing and use these in the exponential parametrization of the wavefunction. This would automatically give Kramers-restricted CC equations upon rederivation of the energy and amplitude equations. A more pedestrian but simpler alternative is to start from the spin-orbital formulation and inspect the relations that follow from the Kramers relation of the two-electron integrals. This method does also readily give the relations between the Kramers symmetry-related amplitudes. We will briefly discuss the basic steps in this approach, a detailed description of a possible algorithm is given in reference [47],... 

There is a price that is incurred by the use of the double commutator. Deexcitation operators of the form... 

In a simple and very commonly used approximation to the PP, the reference state 0> is chosen to be a single-configuration (but not necessarily single determinant) HF wavefunction. The operator manifold T then is taken as the set of particle-hole excitation and deexcitation operators used for optimizing the reference state ... 

Just as e is an excitation operator working on the function to the right, e" is a deexcitation operator working on the function to the left. Multiplying with O from the left and integrating leads directly to the energy equation. 

The deexcitation operator e working on (0 now generates the reference wave function in addition to the singly excited state. 

This may be further transformed by an inner projection onto a complete set of excitation and deexcitation operators, h. This is equivalent to inserting a resolution... 

Deexcitation operator Dissociation energy Density matrix... 

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