EOMXCC method

The purpose of this section is to introduce the basic equations of the new EOMXCC theory of electronically excited, ionized, and electron-attached states of molecular systems. As mentioned in the Introduction, the EOMXCC method is strongly linked to the so-called XCC theory, which applies to the ground-state problem. The specific variants of the EOMXCC formalism that apply to electron-attached states, ionized states, and electronically excited states are referred to as the EA-EOMXCC, IP-EOMXCC, and EE-EOMXCC methods, respectively. 

As in the ordinary EOMCC theory, in the EOMXCC method we solve the electronic Schrodinger equation (1) assuming that the excited states are represented by Eq. (7). We use the exponential representation of the ground-state wave function I S o), Eq. (8), but no longer assume that the cluster components Tn result from standard SRCC calculations (see below). The many-body expansions of the excitation operator Rk have the same form as in the ordinary EOMCC formalism. In particular, the three different forms of Rk discussed in the previous section [fi -E, R A, and REqs. (28), (30), and (26), respectively] are used to define the EE-EOMXCC, EA-EOMXCC, and IP-EOMXCC methods. As in the standard EOMCC method, by making suitable choices for the operators Qa, which define Rk, we can always extend the EOMXCC theory to other sectors of the Fock space. 

A comparison of the most basic elements of the EOMCC and EOMXCC theories is given in Table 1. This table also shows basic equations of the Cl approach indicating the fact that the EOMCC and EOMXCC methods can be regarded as methods which are built on top of Cl (by replacing the Hamiltonian by its similarity transformed analogs). 

Contrary to EOMCC and EOMXCC methods, no disconnected components of Reopen enter Eq. (233) [the disconnected part of ( Cl 7f open, i.e. 

The easiest way to derive the explicit equations of the EOMXCC method is by using the diagrammatic methods of MBPT. In this and in the next Appendix B, we focus on equations describing the EE-EOMXCCSD(PE3) scheme, which uses the Hamiltonian defined by Eqs. (178)-(180). We begin with the expressions for one-and two-body components Hi and H. ... 

EOMXCC A New Coupled-Cluster Method for Electronic Excited States... 

Examples of truncated EOMXCC schemes are the IP-EOMXCCSD, EE-EOMXCCSD, and EA-EOMXCCSD methods, in which Mr = 2 and Mr < 2. In the most complete (Mr = 2) variant of the IP-EOMXCCSD method, where R1 is given by Eq. (62), the formula for the corresponding operator ClR becomes... 

First of all, it should be emphasized that Eq. (201) has an interesting mathematical structure. It explicitly shows that the leading terms of the similarity transformed Hamiltonian of the EOMXCC theory are obtained by symmetrizing (Hermitizing) the H Hamiltonian of the standard EOMCC formalism. In particular, Eq. (202) represents the similarity transformed Hamiltonian of the EOMCCSD method, when projected on a manifold of singly and doubly excited configurations. In this case, the first three terms in Eq. (201) correspond to Hermitized EOMCCSD method. The departure from Hermiticity of H is described by Eq. (203), which contains second-and higher-order components of H. 

Notice that the similarity transformed Hamiltonian ff Eq. (222), has the same formal structure as the EOMXCC Hamiltonian Hn We may thus contemplate an approach (referred to as the EOMECC method), in which we transform the EOMCC eigenvalue problem, Eq. (33), using the operator es to obtain (cf. Ref. 77)... 

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