| Traditional quantum chemistry methods are widely used to investigate the electronic structures and various properties of small-and medium-sized molecular systems. How-ever, the computational cost of these methods scales steeply with the system size, thus it is still difficult to apply them to large molecules. More effective algorithms for solv-ing the corresponding equations in these methods are desired. A popular way is to treat different regions of the target system with different theoretical levels. Specifically, a high-level method is used for a small but important part of the target system, while a low-level method is used for the rest part of the system. Such hybrid methods have been quite successful for some complex systems, in which the chemical transformation occurs in a local region (e.g. enzyme-catalyzed reactions). On the other hand, various linear scaling algorithms, mostly based on the near-sightedness of density matrices or the locality of electron correlation, have been developed. Such methods are expected to be applicable for any large systems, thus should be more promising for future use. Among various linear scaling algorithms, the generalized energy-based fragmentation (GEBF) approach developed by our group has been demonstrated to provide accurate results for many biological molecules and molecular clusters. The main part of this the-sis is about the further development of the GEBF approach for geometry optimizations, vibrational spectra, and thermochemistry calculations of large molecules. We have derived this method theoretically from the multipole expansion of the electrostatic po-tential, and given a reasonable explanation on the accuracy of the GEBF approach. The other part of this thesis is to investigate the conformation preferences of several short peptides in a self-assembled cage with the above-mentioned hybrid method, with the purpose of understanding the influence of the host-guest interaction to the conforma-tion preferences of short peptides. The main findings and innovations are summarized as follows:1. In chapter3, the GEBF approach is extended for geometry optimizations and vibrational spectra calculations of general large molecules or clusters. In this approach, the total energy and its derivatives, and some molecular properties, of a target system are obtained from conventional calculations on a series of subsystems derived from the target system. Each subsystem is electronically embedded in the background point charges generated by all other atoms outside the subsystem so that the long-range inter-actions and polarization effects between remote fragments are approximately taken into account. The approach computationally scales linearly with the system size and can be easily implemented for large-scale parallelization. By comparing the results from the conventional and GEBF calculations for several test molecules including a polypep-tide and a water cluster, we demonstrate that the GEBF approach is able to provide quite reliable predictions for molecular geometries, vibrational frequencies, and ther-mochemistry data and satisfactory descriptions for vibrational intensities, for general molecules with polar or charged groups.2. In chapter4, we have derived the GEBF energy equation at the Hartree-Fock level by keeping the leading term of the multipole expansion of the electrostatic poten-tial. Our numerical calculations for a model system show that the balanced treatment in approximating one-electron and two-electron integrals is mainly responsible for the high accuracy of the GEBF equation. The numerical results suggest that for small or medium-sized basis sets the distance threshold (3.5-4.0A) chosen in our previous works is reasonable, but for large basis sets a larger distance threshold should be used. This work also suggests that the GEBF approach may be further refined by introducing higher-order terms of the electrostatic potential. Such refinement is expected to im-prove the accuracy of the GEBF approach for ground-state energy and some property calculations.3. In chapter5, we have performed a computational investigation to understand the conformational preferences of four short peptides in a self-assembled cage based on a related experimental work. In this study, we have combined molecular dynamics simulations, Monte Carlo simulations, and quantum mechanical calculations to obtain energies and structures for several low-lying conformers of four peptides and the corre-sponding peptide-cage inclusion complexes. Our calculations at both B3LYP and MP2levels show that for each peptide the corresponding conformation within the host (as revealed by the crystal structure) does not represent the lowest-energy conformation of this peptide in vacuum. By comparing some low-lying conformers in vacuum and in the cavity (for the same peptide), we have found that the cage has significant in-fluence on the conformational propensities of peptides. First, one carbonyl oxygen of each peptide tends to bind to one Zn(II) atom of the cage, forming a Zn-O bond. The formation of this bond leads to significant charge transfer from the cage to the peptide. The electrostatic interaction between the cage and peptide is mainly responsible for the stabilization of the inclusion complexes. Second, this Zn-O bond causes the peptide to go through some local conformational changes. For larger peptides such as penta-, and hexapeptides, our calculations also show that some of their conformers must undergo significant structural changes, due to the confinement of the host. This computational study reveals the noticeable influence of the guest-host interaction on the conforma-tional preferences of short peptides, offering a detailed understanding on the "cavity-protecting" experiment under study. Based on this study, we suggest that an ideal host in "cavity-protecting" experiments should not contain coordination-unsaturated metal centers, and should have a large cavity so that short peptides (or other molecules) can be accommodated without undergoing significant conformational changes. |
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