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Rodney J. Bartlett, Tom Hughes, Norbert Flocke
There are many manifestations of fragmentation for large molecules that can lead to calculations that scale linearly. All are ultimately based upon a many-body expansion of the wavefunction and associated density matrices where Ψ(ABC...)= φ(A)φ(B)φ(C),,,, and E(ABC...)=e(A)+e(B)+...e(AB)+...+e(ABC)+..., and Γ(ABC...)=γ(A)+γ(B)+...+γ(AB)+...+γ(ABC)+... . For semi-conductors or insulators, the many-body expansion is well defined. A realization of the separable wavefunction is obviously given by size-extensive methods like coupled-cluster theory, as Ψ(ABC...)= exp(TA +TB +...)|A'B'...ñ, where the separable unit, A, might be encompassed, but distinguished from its vacuum state, A'. Our work is based upon the observation that ¡transferable units¢ for the various functional groups can explain much of chemistry. In some cases those are chemical bonds, in others peptide groups, or phenol rings, etc. Hence, we hypothesize that the final CC wavefunction and associated properties can be separated into wavefunctions/properties for such functional groups. Clearly, to do this successfully requires that the above many-body expansion minimize (or incorporate perhaps via a dispersion correction, eg) the consequences of the 'AB', 'ABC', etc terms. If that is achieved, then for extensive properties we can simply add together the energies, the separable density matrices, and even the 'response' units that are pertinent to intensive properties like excitation energies and related properties. Just as a chemist might readily put together a structure of a protein by combining chemical bonds and angles known from long experience, to obtain a first approximation to the structure of the molecule; we propose to be able to construct a 'library' of functional units that allows for a first approximation to the 'electronic structure' of a complicated molecule, with a mechanism to improve upon that description to identify the critical elements that distinguish the real situation from its initial approximation, We argue the latter is the subject of chemistry. In practice, we attempt to identify the electronic characteristics of the functional group (QM1) by performing CC calculations in natural localized occupied and unoccupied MO's, which we find to be a very convenient set for this purpose in a buffer unit, QM2 (QM2ÌQM1), and using the 'scale' introduced by the localized orbitals, extract from the CC result in QM2, the amplitudes for the QM1 group. This is repeated for all pertinent groups in the system, typically identified by chemical experience. However, as we replace the groups in the molecule by their newly obtained densities, density matrices, etc, there is, in principle, a self-consistency check that allows us to assess that the choice of groups we made adequately effects the functional group fragmentation, or we can repeat the procedure until the choice is deemed self-consistent. Because of the expected transferability, once the units are defined, they can be used in any size molecule to provide an approximation to its electronic structure, which can then be refined to observe the presumably modest changes that would occur in the real system. In this talk we will focus on the transferability of correlation energies, and static and dynamic polarizabilities. In the latter case, we can explicitly observe the degree of localization of excited and ionized states by using the NLSCC form of the equation-of-motion (EOM-CC) method. |
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