Orbital domains

Of all local CC methods to date, the approaches that have received the most attention are those of Hampel and Werner [55] and Schiitz and Werner [56-60]. These authors reported the fully operational, low-order [55] or linear scaling implementations of the local CCSD [56, 60], CCSD(T) [57, 58], and CCSDT-1 [59] methods. Their implementations of local CC methods exploit the local correlation formalism of Pulay [82] and Pulay and Saeb0 [83-87], in which one solves the CC equations in a basis of orthonormal occupied LMOs obtained with one of the conventional MO localization schemes [88-90] and non-orthogonal unoccupied orbitals constructed from the projected AOs (PAOs), while dividing the large system of interest into orbital domains to which excitations defining the CC ansatz are restricted. 

As pointed out in the Introduction, the CIM ansatz of Refs. [38-40], which we have further developed and extended to the CCSD, CR-CC(2,3), and CCSD(T) methods in this and related work [102], originates from the observation that the total correlation energy of a large system can be determined by summing up the contributions from the occupied orthonormal LMOs and their associated occupied and unoccupied orbital domains as long as each of those domains provides an accurate description of the contributions to the correlation energy associated with each occupied LMO. Indeed, in the previous section we have already demonstrated that the CCSD correlation energy Eq. (9), and the triples corrections to the... 

In order to complete our description of the theoretical and computational details behind the CIM-CCSD, CIM-CR-CC(2,3), and CIM-CCSD(T) approaches, we must provide information about the actual design of the occupied and unoccupied LMOs defining the CIM subsystems (P). This is done in the next subsection. Obviously, if we do not introduce any approximations and there is only one subsystem or orbital domain that corresponds to all orbitals of the system, Eqs. (23)-(38) become equivalent to the exact expressions, Eqs. (9) and (11) for the CCSD correlation energy and Eqs. (13) and (14) for the triples correction to CCSD. In this case, the CIM and canonical CC calculations yield identical results, i.e., and = 3 (2.3) -phe key idea of the CIM-CC... 

Determination of Local Orbital Domains for the CIM-CCSD, CIM-CR-CC(2,3), and CIM-CCSD(T) Calculations... 

The CIM framework, originally introduced in Refs. [38-40], and further developed in Ref. [102] and this work, meets the above requirements. The key algorithmic steps that lead to the design of the orbital domains defining the individual CIM subsystems, relevant to the development and efficient computer implementation of the CIM-CCSD, CIM-CR-CC(2,3), and CIM-CCSD(T) methods discussed in this work, are as follows ... 

Many chemists describe the arrangement of electrons around an atom in a molecule using different terminology than what we are using. The electron pairs around the central atom in a molecule are said to be in a set of orbitals (domains) that are hybridized (constructed) from the usual set of atomic orbitals (5, p, d) for the atom. The construction of hybrid atomic orbitals is beyond the scope of this ChemActivity, but one salient point can be made ... 

The observation of this 7hg- 4hu band in CgO " means that now the 7hg- 4hu, 4hu->5tiu and 5tiu->2tig transitions have all been observed experimentally, in C60 . C60 and C60 respectively. This enables us to map the frontier orbital domain of C o using entirely experimental results, as illustrated in Scheme 3. 

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