Zhifeng Cui

An algebraic formula to calculate the three-dimensional Franck–Condon factors including the Duschinsky effect

Based on the contour integral expression of Hermite polynomials, a closed form for the Franck–Condon integrals between multidimensional harmonic oscillators has been presented under the Duschinsky mixing effects. Furthermore, an exact analytical expression for calculation of the three-dimensional six-mode Franck–Condon integral has been derived. In addition, a general explicit formula to calculate the three-dimensional Franck–Condon factors has also been given and applied to study the intensity distribution in the photoelectron spectrum of the H2CO+( 2 B 1)–H2CO( 1 A 1) transition of formaldehyde. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectrum.

Exact evaluation of the multidimensional Franck–Condon integrals based on the contour integral method

Adopting a different method from the Sharp–Rosenstock generating function method and the Doktorov coherent state method, a closed form expression for the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators is derived exactly under the Duschinsky mixing effects on the base of the contour integral form expression of Hermite polynomials. In addition, an analytical expression for the calculation of the four-mode Franck–Condon factors is presented.

Interaction of CO with Kr: Potential energy surface and bound states

The first ab initio potential energy surface of the Kr-CO complex is developed using single and double excitation coupled-cluster theory with noniterative treatment of triple excitations. Mixed basis sets, aug-cc-pVQZ for the C and O atoms and aug-cc-pVQZ-PP for the Kr atom, with an additional (3s3p2d2f1g) set of midbond functions are used. The computed interaction energies in 336 configurations are analytically fitted to a two-dimensional potential model by a least squares fit. The potential has a minimum of -119.68 cm(-1) with Re=7.35a 0 at an approximate T-shaped geometry (theta e=98.5 degrees ). Bound state energies are calculated up to J=12, thus enabling a comprehensive comparison between theory and available experimental data as well as providing detailed guidance for future spectroscopic investigations of higher-lying states. The predicted transition frequencies and spectroscopic constants are in good agreement with the experimental results.

A general analytical expression for the two-dimensional Franck–Condon integral and simulation of the photoelectron spectra of nitrogen dioxide

On the basis of the harmonic oscillator approximation, the two-dimensional four-mode Franck–Condon vibrational overlap integral under mode-mixing effects has been reduced to a product expression of one-dimensional Gaussian integrals with the aid of expanding Hermite polynomials. A more general analytical expression for the calculation of the two-dimensional four-mode Franck–Condon overlap integrals was derived by directly calculating the Gaussian integrals. This analytical expression was applied to investigate the photoelectron spectra of considering mode-mixing and hot band effects. Geometry optimizations and harmonic vibrational frequency calculations were performed on the  2A1 state of NO2 and the  1A1 state of . Franck–Condon analyses and spectral simulations were carried out on the NO2(  2A1)– (  1A1) photodetachment processes. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectra. In addition, the equilibrium geometric parameters of the  1A1 state of were obtained in the spectral simulations: bond length R(ON) = 1.248 ± 0.005 Å and bond angle ∠ (ONO) = 116.8 ± 0.5°.

An experimental study of the lifetimes of excited electronic states of NO2

Abstract The radiative lifetimes of the 2 B 2 electronic state of NO 2 and its relationship with NO 2 pressure and excitation wavelength were measured. The fluorescence decay is exponential at NO 2 pressures below 5×10 −3 Torr, and bi-exponential at pressures higher than this value. The lifetimes are τ 1 =21.6 μs and τ 2 =3.4 μs at 1.4×10 −2 Torr. The apparently anomalously long lifetime of the 2 B 2 state is interpreted using statistical analysis theory.

The Rotational Analysis of the Three New Virbrational Bands of NO2 in the Range 5680–5720 Å

Abstract The three new vibrational bands in the range 5680–5720 A of the fluorescence excitation spectra of NO2 were measured at the normal temperature and were assigned with the rotational quantum numbers. In these bands there are strong spin and rotational forbidden transitions which express the complexity of NO2 spectra.

Theoretical calculations of the 2B1−2A1 subband of NO2

Abstract The vibronic levels of the 2 B 1 ( K′ = 0) state of NO 2 and the fluorescence intensity distribution from these levels is calculated in this Letter using the Rennet-Teller theory. The vibronic quantum number of the upper level of the 454.5 nm subband is found to be ν′ 2 = 17, and the band origin and the fluorescence distribution agree with experimental data.

Theoretical calculation of the spectral fluctuation of the molecular NO2 spectrum

Abstract In this paper we present a novel theory suitable for the calculation of statistical properties of complex molecular spectra. By using this theory the spectral fluctuations of NO 2 VIS spectra are calculated. The existence of irregular spectra in the NO 2 VIS spectra is confirmed.