SRCC theory

It can be easily verified that the stationarity of AfJ(E,T) with respect to E yields Eq. (226). In the exact (full CC) limit, the system of equations defined by Eq. (226) becomes equivalent to standard CC equations for T, Eq. (35), and AE(E,T) becomes identical to AE c [75]. It can be further demonstrated that the stationarity of AE(E, T) with respect to T yields (again, in the full CC limit) the lambda equation of the analytic gradient SRCC theory,... 

Cluster expansion representation of a wave-function built from a single determinant reference function [1] has been eminently successful in treating electron correlation effects with high accuracy for closed shell atoms and molecules. The cluster expansion approach provides size-extensive energies and is thus the method of choice for large systems. The two principal modes of cluster expansion developments in Quantum Chemistry have been the use of single reference many-body perturbation theory (SR-MBPT) [2] and the non-perturbative single reference Coupled Cluster (SRCC) theory [3,4]. While the former is computationally economical for the first few orders of the perturbation expansion... 

It has recently been demonstrated that the applicability of the ground-state SRCC approaches, including the popular noniterative approximations, such as CCSD(T), can be extended to bond breaking and quasidegenerate states, if we switch to a new type of the SRCC theory, termed the method of moments of CC equations (MMCC) (7,16-18). It has further been demon-... 

In the SRCC theory, we represent the ground-state wave function of an iV-electron system, described by the Hamiltonian H, in the following way ... 

Solid solution theory The chemical theories of primary importance to understanding factors controlling carbonate mineral compositions in natural systems are associated with solid solutions. Carbonate minerals of less than pure composition can be viewed as mixtures of component minerals (e.g., SrCC>3 and CaSC>4 in CaCC>3). If the mixtures are of a simple mechanical type then the free energy of formation of the resulting solid will be directly proportional to the composition of the aggregate. Thus, for a two component, a and b, mixture ... 

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. 

It is now well established by numerous and extensive applications that the single reference (SR) based many-body methods, viz. many-body perturbation theory (PT) [1], coupled cluster (CC) theory [2], coupled electron-pair approximations (CEPA) [3], etc. provide rather accurate descriptions of the energy in and around the equilibrium geometry of the closed-shell states. In particular, the single reference coupled cluster (SRCC)... 

We recall the approximation that leads to the single-reference CEPA (SR-CEPA) [42]. CEPA(O) emerges when the SRCC equations are totally linearized, and the virtual space is restricted to functions reached via the hamiltonian. In the same spirit, we can generate the analogous SS-MRCEPA(O), if we hnearize our SS-MRCC equations and retain only the one- and the two-body cluster operators in T. In the SR-CEPA(2), the diagonal exclusion principle violating (EPV) terms are additionally retained, and we propose a similar scheme, SS-MRCEPA(2), where analogous terms in H are retained in the SS-MRCC theory. 

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