First-Principles Study Of Molecular Symmetry And Chirality: Carbyne Knots And Amino Acids

Density functional theory (DFT) or the first-principles has become one of the most important methods in computational chemistry and biology for its moderate computational consume and high precision. The study of the molecular symmetry and chirality is one of the popular subjects in chemistry and biology. This dissertation is to study the symmetries and chiralities of the molecular knots and amino acids by using DFT method. Molecular knot is a novel kind of molecular figure with unique structure and property. In order to well understand the molecular knot theory, many efforts have been done on investigating the symmetries and chiralities of the molecular knots. Amino acids are the fundamental building blocks of protein. Analysis of the relations between molecular orbital and similarity or chirality of the 20 standard amino acids can help to study the generation and measurement of chirality, as well as the exploration of protein structure and folding. The main progress and results have been obtained as follows:Partâ… for carbyne knots (Chapter 2, 3 and 4):1. Theoretical study on the structures and helical chiraiities of C30 carbyne knots A theoretical study of the structures, spectrum and molecular orbital of the C₃₀ carbyne knot by using the DFT/B3LYP method is performed. Compared with the cyclo-C₃₀ carbyne, we study the "tied" process. Our results show that the C₃₀ carbyne knot, belonging to D₃ symmetry, is chiral, and its structure possesses three primary features: conjugated C≡C bonds, inherent helical structures and weak crossing bonds. Based on these structural characters and the helix theory, a new method named "helix-cutting- resembling" has been developed for understanding the chiralities of the mirror-imaged C₃₀ carbyne trefoil knots. The VCD spectra of the C₃₀ carbyne knot and its arc chains are also used to confirm our results. Our results show that the right-hand C₃₀ carbyne trefoil possesses right-handed chirality, and the left-hand one has left-handed chirality, these two knots present mirror-imaged symmetry. Moreover, their rotation strengths are predicted.2. Theoretical study on the chirality and helicity of carbyne knotA new method called "helix-cutting" has been developed to analyze the helical chiralities of the carbyne knots from 0₁ to 5₁. Our results show that the caybyne knots 0₁ and 4₁ belonging to D_30h and S₄ symmetry are achiral, whereas the caybyne knots 3₁ and 5₁ with D₃ and C₂ symmetry are chiral. In addition, the carbyne knots 3₁ and 5₁ possess left-handed chirality, whereas the 3₁^*and 5₁^* have right-handed chiralty. Moreover, a "helix-linker -assembling" model is also represent to design molecular knots with the helical chains and linkers.Our work on the carbyne knots in part 1, combining with the results reported by others would bring to roundly study the symmetry, chirality and design of molecular knot. All these may expand and enhance the molecular knot theory.Part 2 for amino acids (Chapter 5, 6 and 7):3. Molecular orbital study on the quantitative similarity and classification of amino acidsThe molecular orbitals of the amino acids show that the molecular orbital's energy level (MOEL) yielded a similar distribution. According to the MOEL similarity coefficient, 10 similarity pairs, cluster analysis and three similarity hierarchies of the 20 amino acids are investigated. On the basis of the similarity, an amino-acid substitution table is generated. Moreover, for amino acids, the more similar the molecular structure is, the more similar the degree of molecular chirality is.4. Density function theory study on the molecular orbital symmetry and chiralityInvestigation on the orbitals of the mirror-image molecules shows that the spatial arrangement of the molecular orbitais in the achiral molecule is symmetric, named symmetry (S'), anti-symmetry (A'), whereas it is asymmetric in chiral molecule, that is mirror-imaged symmetry (S_m) and mirror-imaged anti-symmetry (A_m). In addition, a chirality measure method based on the mirror-imaged anti-symmetry orbital (A_m) is presented and used to study the amino acids.Our work in this part is studied from a molecular orbital aspect. These studies of the amino acids are expected to provide a new method for inveatigating the generation and measurement of chirality, and study the protein structure and folding.