•The electron affinity of HCCl was calculated at the CCSD(T) level and extrapolated to the complete basis set limit.•The Duschinsky matrix and displacement vector were calculated at the CCSD(T)/aug-cc-pV5Z level of theory.•The photoelectron spectra of HCCl− anion are explored using a harmonic oscillator model and including Duschinsky effect.•The singlet and triplet electronic transitions of HCCl− are merged together.Halomethylenes (such as HCCl) are particularly critical intermediates in many gas-phase reaction environments. The structures, spectra, and reactivity of environment-related molecules have been of many studies interest. In the present work, geometry optimization and frequency calculations have been carried out on the X˜2A″ state of HCCl− and the X˜1A′ and a˜3A″ states of HCCl at CCSD(T) theory. The single point energy, electron affinity and term energy of HCCl have been computed up to the CCSD(T)/aug-cc-pV5Z level and extrapolated to the complete basis set limit. The Duschinsky matrix and displacement vector have been considered at the CCSD(T) level of theory and the result shows that the normal mode mixing effects play a main role for HCCl(a˜3A″)–HCCl−(X˜2A″) transition, and which can be neglected for the HCCl(X˜1A′)–HCCl−(X˜2A″) process. Franck–Condon analysis and spectral simulations have been performed on the singlet and triplet photo-detachment processes, respectively. We have merged the singlet and triplet transitions together for the first time and the results show that the simulated spectra are very consistent with the previous experimental one.

•We derived an analytical expression to calculate the three-dimensional Franck–Condon integrals.•The photoelectron spectrum of PO2- was simulated and the role of Duschinsky effects and hot bands were clarified.•The equilibrium geometry of PO2- was deduced in the spectral simulation.Calculations of Franck–Condon factors are crucial for interpreting vibronic spectra of molecules and studying nonradiative processes. We have derived straightforwardly a more general analytical expression for the calculation of the three-dimensional Franck–Condon overlap integrals on the basis of harmonic oscillator approximation under the influence of mode mixing effects. This new analytical expression was applied to study the photoelectron spectra of PO2-. The theoretical spectrum obtained by employing CCSD(T) values is in excellent agreement with the observed one. An ‘irregular spacing’ observed in the experimental photoelectron spectrum of PO2- is interpreted as contributing from a hot-band sequence of the bending vibration ω2 and combination bands of the stretching vibration ω1 and the bending vibration ω2. In addition, the equilibrium geometry parameters, r(O–P) = 1.495 ± 0.005 Å and ∠(O–P–O) = 119.5 ± 0.5°, of theX∼1A1 state of PO2-, are derived by employing an iterative Franck–Condon analysis procedure in the spectral simulation.

Calculations of Franck–Condon factors are crucial for interpreting vibronic spectra of molecules and studying nonradiative processes. On the base of the closed form expression of the Franck–Condon integrals between arbitrary multidimensional harmonic oscillators under the Duschinsky mixing effects, a more general algebraic expression for the calculation of the three-dimensional four-mode Franck–Condon factors was derived straightforwardly and applied to study the photoelectron spectrum of D2CO+(B∼2A1). Geometry optimization and harmonic vibrational frequency calculations were performed on the X∼1A1 state of D2CO at B3LYP, QCISD, CCSD and CASSCF levels, and the B∼2A1 state of D2CO+ at CIS, TD-B3LYP, and CASSCF levels. Franck–Condon analyses and spectral simulations were carried out on the D2CO+(B∼2A1)-D2CO(X∼1A1) photoionization process. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in excellent agreement with the observed spectrum. In addition, the equilibrium geometric parameters of the B∼2A1 state of D2CO+ were obtained in the spectral simulations.

Geometry optimization and harmonic vibrational frequency calculations were performed on the X˜2A″ states of CH3OO/CD3OO and X˜1A′ states of CH3OO−/CD3OO− at the B3LYP, QCISD and CCSD levels. The electron affinity energies of CH3OO/CD3OO were calculated at various theory levels. Franck–Condon analyses and spectral simulations were carried out on the X˜2A″-X˜1A′ photodetachment processes. The spectral simulations of vibrational structures based on the computed Franck–Condon factors are in agreement with the observed spectra.

Geometry optimization and harmonic vibrational frequency calculations were performed on the X∼2A″ and A∼2A′ states of HOO and X∼1A′ state of HOO−. The electron affinity and the term energy (X∼2A″–A∼2A′) of HOO were calculated at various theory levels. Franck–Condon analyses and spectral simulations were carried out on the X∼2A″–X∼1A′ and A∼2A′–X∼1A′ 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 geometrical parameters of the X∼1A′ state of HOO− and A∼2A′ state of HOO were obtained in the spectral simulations.

B3LYP, CCSD, and QCISD geometry optimization and harmonic vibrational frequency calculations were performed on the X˜2A1 state of SO2+ and X˜1A1 state of SO2. Spectral simulations were carried out on the first photoelectron band of SO2. The geometric parameters of SO2+(X˜2A1) were obtained: ReRe(OS) = 0.1420 ± 0.0003 nm and θeθe(OSO) = 132.80 ± 0.05°, in the spectral simulation.

Geometry optimization and harmonic vibrational frequency calculations have been performed on the X˜1A1 state of O3 and X˜2B1 state of O3-. Franck–Condon analyses and spectral simulation were carried out on the first photoelectron band of O3-. The theoretical spectrum obtained by employing CCSD(T)/6-311+G(2d, p) values are in excellent agreement with the observed one. In addition, the equilibrium geometry parameters, re(OO) = 0.1355 ± 0.0005 nm and θe(O–O–O) = 113.5 ± 0.5°, of the X˜2B1 state of O3-, are derived by employing an iterative Franck–Condon analysis procedure in the spectral simulation.