We present a generalized energy-based fragmentation (GEBF) approach for approximately predicting the ground-state energies and molecular properties of large molecules, especially those charged and polar molecules. In this approach, the total energy (or properties) of a large molecule can be approximately obtained from energy (or properties) calculations on various small subsystems, each of which is constructed to contain a certain fragment and its local surroundings within a given distance. In the quantum chemistry calculation of a given subsystem, those distant atoms (outside this subsystem) are modeled as background point charges at the corresponding nuclear centers. This treatment allows long-range electrostatic interaction and polarization effects between distant fragments to be taken into account approximately, which are very important for polar and charged molecules. We also propose a new fragmentation scheme for constructing subsystems. Our test calculations at the Hartree-Fock and second-order Møller-Plesser perturbation theory levels demonstrate that the approach could yield satisfactory ground-state energies, the dipole moments, and static polarizabilities for polar and charged molecules such as water clusters and proteins.

A linear scaling local correlation approach is proposed for approximately solving the coupled cluster doubles (CCD) equations of large systems in a basis of orthogonal localized molecular orbitals (LMOs). By restricting double excitations from spatially close occupied LMOs into their associated virtual LMOs, the number of significant excitation amplitudes scales only linearly with molecular size in large molecules. Significant amplitudes are obtained to a very good approximation by solving the CCD equations of various subsystems, each of which is made up of a cluster associated with the orbital indices of a subset of significant amplitudes and the local environmental domain of the cluster. The combined effect of these two approximations leads to a linear scaling algorithm for large systems. By using typical thresholds, which are designed to target an energy accuracy, our numerical calculations for a wide range of molecules using the 6-31G or 6-31G* basis set demonstrate that the present local correlation approach recovers more than 98.5% of the conventional CCD correlation energy.

The chain length dependence of excitation energies of oilgomers of polyene, p-phenylene, pentafulvene, cyclopentadiene, pyrrole, furan, silole, phosphole, and thiophene was studied employing the time-dependent density functional theory with B3LYP functional. Band gaps and effective conjugation lengths of the corresponding polymers were obtained by extrapolating vertical excitation energies of trimers through pentamers to infinite chain length. Polypentafulvene, polycyclopentadiene, polysilole, and polyphosphole were predicted to have smaller band gaps than polythiophene, and polypentafulvene has the smallest band gap. Among the studied cyclopentadiene-based polymers, those with the third row heteroatoms were found to have narrower band gaps than their second row counterparts.

An efficient implementation of the "cluster-in-molecule" (CIM) approach is presented for performing local electron correlation calculations in a basis of orthogonal occupied and virtual localized molecular orbitals (LMOs). The main idea of this approach is that significant excitation amplitudes can be approximately obtained by solving the coupled cluster (or Moller-Plesset perturbation theory) equations of a series of "clusters," each of which contains a subset of occupied and virtual LMOs. In the present implementation, we have proposed a simple approach for constructing virtual LMOs of clusters, and new ways of constructing clusters and extracting the correlation contributions from calculations on clusters, which are more efficient than those suggested in the original work. More importantly, linear scaling of computational time of the CIM approach is achieved by evaluating the transformed two-electron integrals over LMOs using simple truncation techniques in limited operations (independent of the molecular size). With typical thresholds, for a variety of molecules our test calculations demonstrate that more than 99% of the conventional MP2 or coupled cluster with doubles correlation energies can be recovered in the present CIM approach.

An electrostatic field-adapted molecular fractionation with conjugated caps (EFA-MFCC) approach is implemented for treating macromolecules with several charge centers. The molecular fragmentation is performed in an "electrostatic field," which is described by putting point charges on charge centers, directly affecting the Hamiltonians of both fragments and conjugated caps. So the present method does not need truncation during the calculation of electrostatic interactions. Our test calculations on a series of charged model systems and biological macromolecules using the HF and B3LYP methods have demonstrated that this approach is capable of describing the electronic structure with accuracy comparable to other fragment-based methods. The EFA-MFCC approach is an alternative way for predicting the total energies of charged macromolecules with acyclic, loop, and intersectional loop structures and interaction energies between two molecules.