THE LINEAR CORRELATIONS BETWEEN ELECTRONIC TRANSITION ENERGY AND HAMMETT CONSTANTS FOR THE SUBSTITUTED PORPHYRIN-LIKE MACROCYCLE

The properties of absorption spectra are presented and the linear correlations of Hammett constants with the 0-0 transition energy(E_(o,o))of S_←S_o, and the ratios of oscillator strength(f/f)are used to probe the interactions betwee π-electron of aromatic maerocycles or metal ion of complexes with the sub- stituents on β-position of benzene ring for porphyrin-like maerocyclic compounds.

Effect of Electron Correlation and Breit Interaction on Energies, Oscillator Strengths, and Transition Rates for Low-Lying States of Helium

The transition energies, E1 transitional oscillator strengths of the spin-allowed as well as the spin-forbidden and the corresponding transition rates, and complete M1, E2, M2 forbidden transition rates for 1s^(2), 1s2s, and 1s2p states of He I, are investigated using the multi-configuration Dirac–Hartree–Fock method. In the subsequent relativistic configuration interaction computations, the Breit interaction and the QED effect are considered as perturbation, separately. Our transition energies, oscillator strengths, and transition rates are in good agreement with the experimental and other theoretical results. As a result, the QED effect is not important for helium atoms, however, the effect of the Breit interaction plays a significant role in the transition energies, the oscillator strengths and transition rates.

Fixed-node Quantum Monte Carlo: A Novel Approach

In this paper, a novel method for fixed-node quantum Monte Carlo is given. We have derived an expansion of the eigenvalue of the energy for a system and proved that the value of the energy calculated using the traditional fixed-node quantum Monte Carlo method is only the zero order approximation of the eigenvalue of the energy. But when using our novel method, in the case of only increasing less computing amounts (<1%), we can obtain conveniently the first order approximation, second order approximation, and so on. We have calculated the values of the zero, first and second approximation (0, 1 and 2) of the energies of 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O using this novel method. The results indicate that for 11A1 state of CH2, 1Ag (C4h, acet) state of C8 and the ground-state of H2O it needs only the second order approximation to obtain electronic correlation energy with over 97%. This demonstrates that this novel method is very excellent in both the computing accuracy and the amount of calculation required.

Exact Fixed-node Quantum Monte Carlo: Self-optimizing Procedure

In this paper, a novel exact fixed-node quantum Monte Carlo (EFNQMC) algorithm was proposed, which is a self-optimizing and self-improving procedure. In contrast to the previous EFNQMC method, the importance function of this method is optimized synchronistically in the diffusion procedure, but not before beginning the EFNQMC computation. In order to optimize the importance function, the improved steepest descent technique is used, in which the step size is automatically adjustable. The procedure is quasi-Newton type and converges super linearly. The present method also uses a novel trial function, which has correct electron-electron and electron-nucleus cusp conditions. The novel EFNQMC algorithm and the novel trial function are employed to calculate the energies of 1 1A 1 state of CH 2, 1A g state of C 8 and the ground-states of H 2, LiH, Li 2 and H 2O.