PPP Parameterization Study Derived From High-level Ab-initio Calculations

Organic conjugated molecules have relatively smallπ→π* energy gaps and fluidπelectrons, and have become the source of advanced materials. They obtain much attention by theoretical chemists. Conjugated hydrocarbons have been studied early by quantum chemistry due to their easy simplification with several approximations. A lot of semiempirical quantum chemical methods have been set up to calculate conju-gated molecules; among them there is the important Pariser-Parr-Pople (PPP) model, which has a relatively high accuracy for electronic spectra and other physical proper-ties. Recently, conjugated polymers have been widely studied as a kind of significant materials. New high-quality theoretical methods are needed instead of high-level ab initio methods, which are too expensive for polymers, and PPP method is suitable for large conjugated systems due to its relatively low cost.Obviously, the accuracy of PPP method depends on the quality of its parameteriza-tion. Existing parameters of PPP model are usually optimized by fitting the integrals of STOs or absorption spectra of several small molecules. The lowest excitation energies calculated with these models usually agree only qualitatively with high-level ab initio calculations or experimental observations, with the largest deviations being as large as 1 eV. In this work, we propose a new approach for PPP parameterization and thus another way to improve the accuracy of the PPP method, which is entirely based on accurate CASPT2 results for several low-lying excited-state potential energy surfaces of ethylene and its cation.In this work, each of the four PPP parameters will be expressed analytically as a carefully chosen mathematical function of the interatomic distance, which is calibrated against CASPT2 data. For various conjugated molecules, including oligo-polyenes, small aromatic rings, anti-aromatic rings, diradicals, even polyene series and polyacene series, our newly-parameterized PPP model is found to be superior to the conventional PPP models, with the low-lying excitation energies often approaching the accuracy of high-level CASPT2, MRMP and coupled cluster (CC) values. Besides this, our new parameterization can reproduce correct electron structures as well as a lot of physical properties, such as dipole moments, oscillator strengths, etc.Our new PPP model can be applied to study electronic excitations in small to medium-size conjugated hydrocarbons, and the accuracy can be expected to approach the high-level multireference electron-correlation methods. Another value of this work is to have practised a valid method for the study of polymers. One can set out new parameterization of semiempirical models by fitting the results of high-level ab initio calculations, and then perform semiempirical calculations with the parameterization for large molecules which high-level ab initio methods cannot reach.The main context of this dissertation can be summarized as follows:In chapter 1, all of the mathematics tools been used in this thesis are summarized, in-cluding matrix diagonalization methods:Jacobi algorithm, Lanczos algorithm, David-son algorithm and block-Davidson algorithm, and optimization methods:the simplex method, the sequential univariate method, the steepest descents method, conjugate gra-dients method, the Newton-Raphson method and Quasi-Newton methods. Some useful strategies are also introduced, including the calculation of numerical gradient and con-vergence criteria.In chapter 2, the development histories of quantum mechanics and quantum chem-istry are indicated. The principle of PPP model and the common parameterizations are also introduced in this chapter.In chapter 3, the parameterization of this work is introduced in details, including the selection of states in ethylene, of the high-level ab initio methods and of the functions used for fitting. The final fitted expressions for these parameters and the accuracies are also shown in this chapter.In chapter 4, the new PPP parameterization is validated with several kinds of conju-gated hydrocarbons. PPP calculations with common parameterization as well as several high-level ab initio calculations are performed in the same geometry for comparison.In chapter 5, the low-lying excited singlets of oligo-polyenes, including not only the well-known near-degenerate 11Bu+and 21Ag- states but also the neglected 11Bu-, have been studied systematically with the new PPP parameterization and ab initio methods. The electron structures and physical properties as well as excitation energies have been calculated. And the advantages and disadvantages of these theoretical methods have been discussed in this chapter.