One-dimensional System Dmrg Method And Shrink The Theory Of Glycerol And Its Water Complex Vcd

The density-matrix renormalization group (DMRG) were established on the basis of the Wilson's numerical renormalization group method, the key point of which was that the decimation procedure of the Hilbert space is to take the lowest-lying eigenstates of the compound block. However, the truncation procedure to system states of DMRG preserves a maximum of system-environment entanglement basing on the eigenvalues of the reduced density-matrix. Since the density-matrix renormalization group was origined by S. White in 1992, it is a numerical algorithm for the efficient truncation of the Hilbert space of low-dimensional strongly correlated quantum systems based on a rather general decimation prescription. DMRG can be used to calculate more large many-body problem than exact diagonalization (ED), and DMRG has no negative-sign problem that plagues the quantum Monte Carlo (QMC) method. It was the negative-sign problem that limited QMC been used for frustrated spin or fermionic system.DMRG has achieved unprecedented precision in the description of one-dimensional quantum systems. It has therefore quickly become the method of choice for numerical studies of such systems. Its applications to the calculation of static, dynamic (with the help of Green function method), and thermodynamic quantities (combined with the transfer matrix renormalization group, TMRG) in these systems are developed. A field in which DMRG will make increasingly important contributions in the next few years is quantum chemistry. While the first quantum-chemical DMRG calculations on cyclic polyene and polyacetylene were still very much in the spirit of extended Hubbard models, more recent work has moved on to calculations in generic bases with arbitrary interactions. The major drawback of DMRG is that it displays its full force mainly for one-dimensional systems; nevertheless, interesting forays into higher dimensions have been made.It is now the very important field in chemitry, considering the absolute 3D-structures of a molecular. Especially, the structures of the biologic molecule are very vital, since they are relavtive to the living progress. Many biologic molecule are chiral. Two enantiomers of chiral molecule have different effects:(1) one has living effect, the other has not;(2) both enantiomers have the same or similar effects;(3) two enantiomers have the contrary effects;(4) one has living effect, the other has poisonous effect;(5) both enantiomers have living effects, however, one of them is perfected;(6) one has living effect, the other has antagonistic effect.So, it is necessary to determine the absolute structure of chiral molecule. There are about five such methods: (1) The vibrational circular dichroism (VCD) and rotational spectroscopies; (2) X radial method; (3)Fredge method; (4) experiential method; (5) chemical method. The first method is broadly used because of its excellences.The vibrational circular dichroism spectroscopies plays an important role in determining the molecular configurations. The VCD spectrum provides unique fingerprint information for a chiral molecule, which has at least one chiral center and so exhibits chirality and optical activity.There is a growing interest in the study on epoxides because they are versatile intermediates in organic synthesis. Particularly, glycidol and its derivatives have a compact skeleton of glycerol and wide potential for synthesis. They are considered to be versatile chiral synthesis units. Both enantiomers of glycidol have become widely used as starting materials for the synthesis of many interesting compounds, such as anticancer drugs, protein synthesis inhibitors, as well as a 2-oxazolidinone derivative used against depression. Glycidol has also been demonstrated to be carcinogenic and mutagenic in many mutagenicity test systems, because the alkylating glycidol could introduce dihydroxypropyl groups onto nitrogens in protein and thus damage protein. Both from theoretical and experimental point of view, glycidol is a suitable model for investigation of epoxides and alcohols.This article is started with a discussion of the basis theory of quantum mechnics and the key algorithmic ideas needed to deal with the most conventional DMRG problem, the study the properties of a onedimensional quantum Hamiltonian. In section III, it is discussed the properties of the quantum states generated by DMRG smatrix-product statesd and the properties of the density matrices that are essential for its success. The Fortran programe of infinite- and finite-DMRG is designed, and is performed to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. Additionaly, the conformational stability, intramolecular and intermolecular H-bond strength, vibrational absorption (VA) and vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol and their complexes with water are investigated in the two last sections. There are three conclusions can be drawn:(â… ) The equations that the DMRG needed are derivated from the model Harmilton. For example, the formula how to add site to block system and enviroment, how to get the Harmilton of the superblock and the density matrix, are discussed in detail. We designe the Fortran programe of infinite- and finite-DMRG, and use it to calculate the ground state energes of S=1/2 Heisenberg model and polyacene, polyphenanthrene. The results of our programe are very closed to the results of exact diagonalization, when considering little system.(â…¡) The electronic energies, the vibrational absorption harmonic frequencies, IR intensities and VCD spectra of eight (S)-glycidol conformers are calculated. The effection of intramolecular H-bond and ring structure on the stablity of molecule is discussed. The red-shift of O-H stretching frequency is using to determine whether there is intramolecular H-bond in a molecule. The absolute structure of (S)-glycidol can be determined by the vibrational circular dichroism (VCD) spectra for conformers of (S)-glycidol.(â…¢) The energies, the vibrational absorption harmonic frequencies and VCD spectra of six (S)-glycidol-water complexes are calculated. The calculated results indicate that the VCD spectra are sensitive to conformational changes of both monomer and complexes and that alter complex formation with a chiral molecule, an achiral molecule becomes active in VCD spectra. Using the theoretical prediction, we demonstrate that the VCD technique is a powerful approach for determining conformational behavior of chiral molecules.