Ab initio calculation and quasi‐classical dynamics study of the two lowest potential energy surfaces of the O(1D)+HBr system*

The lowest singlet 1¹A′ and 1¹A″ potential energy surfaces (PES) of the O(¹D)+HBr system have been ab initio computed. The complete active space self‐consistent field (CASSCF) method was used in most of the calculations, considering all the valence orbitals as active. The calculations were complemented with both analytical gradient calculations to characterize the stationary points and multireference configuration interaction (MRCI) calculations at selected nuclear geometries to improve the determination of the barrier heights and of the energetics. Electronic energy values for both PESs were then independently fitted by polynomial expansions in bond order coordinates. On the fitted surfaces quasi‐classical trajectories were separately run. Single‐surface calculations behave qualitatively different for the ground and the excited PES at low collision energies. A satisfactory agreement with existing experimental data was obtained by using the ground PES while calculations performed on the excited 1¹A″ PES worsened the agreement. However, when collision energy is increased, detailed experimental distributions are less well reproduced by calculations on the ground PES. This may imply the participation via nonadiabatic transitions of the 2¹A′ PES at higher energies while the adiabatic ground singlet PES well describes reactive scattering at low collision energy. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Detailed electron spectrometric study of the ionization of H2 by He* (21 S, 23 S)

The energy spectra of electrons released in thermal energy (≈ 50 meV) ionizing collisions of He*(2¹ S, 2³ S) with H₂ have been measured with high resolution and low background. Based on a detailed data analysis, we report accurate H ₂ ⁺ (v′) vibrational populationsP(v′) for both He*(2¹ S)+H₂(v′=0–10) and He*(2³ S)+H₂(v′=0–15) and the spectral shapeS(ε) for the individual vibrational peaks. The vibrational populationsP(v′) are quite similar to the Franck-Condon factorsf _v ′0 for unperturbed H₂(v″=0)→H ₂ ⁺ (v′) transitions, but, more in detail, the ratiosP(v′)/f _v ′0 show a characteristically differentv′-dependence for He*(2³ S), He*(2¹ S), and HeI_α(58.4 nm) ionization. The vibrational level separations in the He*(2¹ S, 2³ S)+H₂ spectra agree with those in the HeI photoelectron spectrum to within 1–2 meV. The spectral shapesS(ε) are characteristically different for He*(2¹ S)+H₂ and He*(2³ S)+H₂, reflecting the respective differences in the entrance channel potentials, as determined previously in ab initio calculations and from scattering experiments.     

Theoretical study of ScCO2+

The structure, binding energy, and vibrational frequencies have been determined for ScCO₂⁺. The inserted OSc⁺CO structure in the ¹A′ state is the most stable isomer and lies 43.2 kcal/mol below the ground-state Sc⁺+ CO₂ asymptote. The linear η¹-O Sc⁺(SINGLE BOND)OCO ³Δ state is bound by a charge-quadrupole interaction and has a binding energy of 13.9 kcal/mol. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 63: 523–528, 1997     

On the lowest electronic states of the C2F radical

The adiabatic energy surfaces of the lowest three electronic states [²(²A′ and ²A′)] and ²Σ⁺[²A′] of the C₂F radical were investigated by the Hartree-Fock multiconfiguration self-consistent field (HF—MCSCF) ab initio method using a large set of atomic natural orbitals (ANO) and an extended configuration space, and the results were shown to be in agreement with the predictions of valence theory for this radical. The electronic ground state was found to have a bent equilibrium structure, hence contradicting the Walsh rule which predicts for the isoelectronic molecules a ² linear state. The three states were found to be nearly degenerate and the potential energy surfaces of the two lowest electronic states exhibit an avoided crossing at an energy ∼2000 cm⁻¹ above the ground-state minimum, lower than the highest vibrational fundamental. The strong adiabatic interaction which is responsible for the ordering of the electronic states and their equilibrium geometry involves not only the bending coordinate as normally found for Renner-Teller pairs of states, but also the C—C stretching coordinate, due to the near degeneracy of the ²Σ⁺ and the ² lowest electronic states at linear geometries. © 1996 John Wiley & Sons, Inc.     

Difluorocarbene Studied with Threshold Photoelectron Spectroscopy (TPES): Measurement of the First Adiabatic Ionization Energy (AIE) of CF2

The first photoelectron band of difluorocarbene CF₂, has been studied by threshold photoelectron (TPE) spectroscopy. CF₂ was prepared by microwave discharge of a flowing mixture of hexafluoropropene, C₃F₆, and argon. A vibrationally resolved band was observed in which at least twenty‐two components were observed. In the first PE band of CF₂, the adiabatic ionization energy differs significantly from the vertical ionization energy because, for the ionization CF₂⁺ (X?²A₁)+e^? ← CF₂ (X?¹A₁), there is an increase in the FCF bond angle (by ≈20°) and a decrease in the C? F bond length (by ≈0.7 Å). The adiabatic component was not observed in the experimental TPE spectrum. However, on comparing this spectrum with an ab initio/Franck–Condon simulation of this band, using results from high‐level ab initio calculations, the structure associated with the vibrational components could be assigned. This led to alignment of the experimental TPE spectrum and the computed Franck–Condon envelope, and a determination of the first adiabatic ionization energy of CF₂ as (11.362±0.005) eV. From the assignment of the vibrational structure, values were obtained for the harmonic and fundamental frequencies of the symmetric stretching mode (ν₁′) and symmetric bending mode (ν₂′) in CF₂⁺ (X?²A₁).     

Ab initio study of low-lying electronic states of the PF2 radical

The equilibrium geometries, excitation energies, force constants, and vibrational frequencies of the low-lying electronic states X²B₁, ²A₁, ²B₂, and ²A₂ of the PF₂ radical have been calculated at the MRSDCI level with a double zeta plus polarization basis set. Our calculated geometry, force constants, and vibrational frequencies for the X²B₁ state are in good agreement with experimental data. The electronic transition moments, oscillator strengths for the ²A₁ → X²B₁ and ²A₂ → X²B₁ transitions, and radiative lifetimes for the ²A₁ and ²A₂ states are calculated based on the MRSDCI wave functions. © 1994 by John Wiley & Sons, Inc.     

Theoretical prediction on HAlS+ and HSAl+ cations using multiconfiguration second‐order perturbation theory

Some low‐lying states of the HAlS⁺ and HSAl⁺ cations have been studied for the first time by large‐scale theoretical calculations using three methods: complete active space self‐consistent field (CASSCF), complete active second‐order perturbation theory (CASPT2), and density functional theory Becke's three‐parameter hybrid function with the nonlocal correlation of Lee–Yang–Parr (B3LYP) with the contracted atomic natural orbital (ANO‐L) and cc‐pVTZ basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO‐L and B3LYP/cc‐pVTZ levels. The ground and the first excited states of linear HAlS⁺ are predicted to be X²Π and A²Σ⁺ states, respectively. For the linear HSAl⁺ structure, the first excited state is A²Σ⁺. The X²Π state of linear HSAl⁺ is a second‐order saddle point, because it has two imaginary frequencies. Two bent global minima M1 and M2 were found along the 1²A′ and 1²A″ PESs, respectively. The CASPT2/ANO‐L potential energy curves of isomerization reactions were calculated as a function of HAlS bond angle. According to our calculations, the ground‐state HAlS⁺ is linear, whereas the ground‐state HSAl⁺ is bent. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

An ab initio theoretical study of the optical spectrum of CF2

The ab initio calculation methods have been used to calculate the spectral and electronic characteristics of difluorocarbene in the ground electronic state (¹A₁), the lowest-lying singlet (¹B₁) and triplet (³B₁) states. The optimized equilibrium geometries, rotational constants, harmonic vibrational frequencies and energy gaps, electronic charges, dipole moments of these states have been computed with different basis sets. The calculated vibrational frequency of ³B₁ state (v₂=522 cm^?1) and the energy separation (2.26 eV) between ³B₁ and ¹A₁ states are in good agreement with the experimental results (519 cm^?1, 2.46 eV respectively). According to the calculations the previous assignment of vibrational symmetries of ¹B₁ state was corrected, and some experimentally undetermined vibrational frequencies were predicted.     

à 2A1 → X̃ 2B1 emission spectrum of cis-1,2-difluoroethylene cation and the non-radiation decay of the à states of the haloethylene cations in the gaseous phase

The results of the search for the à → X? radiative relaxation of haloethylene cations in the gaseous phase are reported. Only in the case of cis-1,2-difloroethylene cation was an emission spectrum detected. It is identified as the à ²A₁ → X? ²B ₁ band system on the basis of photoelectron spectroscopic measurements. An assignment of the emission bands yields the vibrational frequencies of four of the A₁ fundamentals (under C₂, symmetry) for the X? state and one for the à state. Well resolved Ne(I) photoelectron spectra of cis- and trans-1,2-difluoroethylene are presented, from which some vibrational frequencies for these cations in the X? and à states are also obtained. The lifetimes of cis-1,2-difluoroethylene cation in the lowest vibrational levels of the à ²A₁ state have been measured. The decay of this cation is unusual as these levels are depleted both by, radiative, and pathways leading to fragment ions (C₂HF⁺). The lack of detectable emissions with other fluoro-, chloro- and bromo-ethylene cations is discussed and the likely symmetries of the à states are proposed.     

Analytical ab initio potential-energy surfaces for the ground and the first singlet excited states of HeH2

Analytical potential-energy surfaces have been constructed for the ground and the first excited states of HeH₂. The functions fit ab initio MRD CI calculations with standard deviations of 0.05 and 0.13 eV for the ground and the excited surface respectively. Classical trajectory calculations for collisions of ⁴Hc with HD(B ¹Σ_u⁺, υ = 3, J = 2) at the temperature T = 297 K yields the electronic quenching cross section σ_Q = 6.5 A² and the vibrational cross section σ_3→2 = 3.8 A². The results are in qualitative agreement with the experimental values of Fink, Akins and Moore.     

Quasiclassical trajectory study of the rotational distribution for the O+NO(v = 0) fundamental vibrational excitation

Quasiclassical trajectories have been run to study the fundamental one‐quantum vibrational transition formed from collisions of ground‐state nitric oxide with atomic oxygen at temperatures of 500, 750, and 1000 K. Two adiabatic potential energy surfaces of different symmetry (²A′ and ²A″ of NO₂) have been utilized. The rate constant for the title process is given along with the rotational distributions, and the results shown to corroborate previous atmospheric models that describe the nascent state by a Maxwell–Boltzmann distribution at the local temperature. © 2011 Wiley Peiodicals, Inc. Int J Chem Kinet 43: 345–352, 2011     

The radiative lifetime of the A1II state of BH

Second-order polarization propagator calculations of the X¹Σ⁺ → A¹II transition moment as well as the radiative lifetime of the A¹II state of BH are reported. The calculated vibrational lifetimes are τ(v′ = 0) = 121 ns, τ(v′ = 1) = 129 ns, and τ(v′ = 2) = 137 ns. The τ(v′ = 0 lifetime agrees with the most recent experiment of τ(v′ = 0) = 125 ± 5 ns. We show that the electronic oscillator strength computed at the ground state equilibrium is rather different from the band absorption oscillator strength f₀₀, which demonstrates that theoretical electronic oscillator strengths should not be expected to agree with experimentally determined band oscillator strengths.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

CASPT2 study on low‐lying states of HMgO and HOMg

The HMgO and magnesium monohydroxide (HOMg) have been reinvestigated using the complete active space self‐consistent field (CASSCF) and multiconfiguration second‐order perturbation theory (CASPT2) methods with the contracted atomic natural orbital (ANO) basis sets. The geometries of all stationary points along the potential energy surfaces (PESs) were optimized at the CASSCF/ANO levels. The ground and the first excited states of HMgO are predicted to be X²Π and A²Σ⁺ states, respectively. It was predicted that the ground state of HOMg is X²Σ⁺ state. The A²Π state of HOMg has unique imaginary frequency. A bent local minimum M1 was found for the first time along the 1²A″ PES and the A²Π state of HOMg should be the transition state of the isomerization reactions for M1 ? M1. The CASPT2/ANO potential energy curves of isomerization reactions were calculated as a function of HMgO bond angle. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Rotational relaxation in S1 glyoxal: Cross sections and a search for propensity rules

Details of rotational energy transfer from a few selected K′J′ levels in the zero point vibrational level of ¹Au(S₁) glyoxal vapor have been studied. The cross section for destruction of an initial K′J′ level by rotational relaxation in collision with ground electronic state glyoxal is about 240 A² or 4.5 times gas kinetic. Much of the rotational transfer within the S₁ state occurs with large ΔK′ and ΔJ′. No strong propensities for △K′ = 0, ± 1, ± 2, or ± 3 with small ΔJ′ changes occur in collisions with ground electronic state glyoxal. The study was made by examination of the rotational structure in the 5₁⁰ emission band at various pressures after excitation in the 0,0 band of the S₁—S₀ system with the 454.5 nm argon ion line.     

Rotationally resolved laser-induced fluorescence and zeeman quantum beat spectroscopy of the V 1B2 state of jet-cooled CS2

The rotationally resolved laser-induced fluorescence (LIF) excitation spectrum of V system bands (V¹B₂≈X¹Σ¹_g transition) of CS₂ cooled in a supersonic jet has been observed. In a supersonic jet of CS₂/Ar or He mixture, the rotational temperature of CS₂ is reduced to less than 10 K, and thus the LIF excitation spectrum is simplified significantly. Two types of rotational structure are found; one is composed of P and R branch transitions from even J″ levels and the other is of P, Q, and R branch transitions from even as well as J″. The bands with the former rotational structure are assigned to transitions to K′ = O levels of ¹B₂ state, the bands with the latter structure to transitions to K′ = 1 levels from the (O, 1¹, O) level of the electronic ground state, i.e. vibrationally hot bands. This assignment is supported by the further evidence that these hot bands disappear when the supersonic jet includes a third-body gas such as NH₃ which enhances the vibrational relaxation of CS₂. Calculation of transition moments for respective leads to the conclusion that the upper levels of the V system bands are located in the region close to or higher than the potential barrier of the bending vibration of excited CS₂. The radiative lifetime of CS₂ in single rovibronic levels of the ¹B₂ state is in the range of 2–8 μs which is of the same order of magnitude as that calculated from the absorption coefficient. It tends to be longer for higher J levels or for higher vibronic levels. Zeeman quantum beating is observed in the fluorescence decay of excited CS₂ for a number of rovibronic levels under a weak magnetic field, and thus a magnetic moment associated with each rovibronic level can be determined. The g values are around 0.02 and tend to be smaller in higher J levels for some vibronic states. Based on the the observed radiative lifetime and the g value, it is suggested that the ¹B₂ state is perturbed by a spin-rotation interaction with two spin components, A₁ and B₁ of the ³A₂ orbital state besides a strong spin-orbit coupling with the R ³B₂ state.     

Nonadiabatic photodissociation dynamics

The photodissociation dynamics of the triatomic (or pseudo‐triatomic) system in the nonadiabatic multiple electronic states is investigated by employing a time‐dependent quantum wave packet method, while the time propagation of the wave packet is carried out using the split‐operator scheme. As a numerical example, the photodissociation dynamics of CH₃I in three electronic states ¹Q₁(A′), ¹Q₁(A″), and ³Q₀₊ is studied and CH₃I is treated as a pseudotriatomic model. The absorption spectra and product vibrational state distributions are calculated and compared with previous theoretical work. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

MRSDCI studies of low-lying electronic states of the CF 2 + ion

Summary The equilibrium geometries, excitation energies, force constants and vibrational frequencies for four low-lying electronic statesX ² A ₁,² B ₁,² B ₂ and² A ₂ of the CF ₂ ⁺ ion have been calculated at the MRSDCI level with a double zeta plus polarization basis set. Our calculated excitation energies for these states and vibrational frequencies for the ground state are in good agreement with experimental data via photoelectron spectroscopy of the CF₂ radical (carbene). The electronic transition dipole moments, oscillator strengths for the² B ₁ X ² A ₁ and² B ₂ X ² A ₁ transitions, radiative lifetimes for the² B ₁ and² B ₂ states and the spin properties for theX ² A ₁ state are calculated based on the MRSDCI wavefunctions.     

The lifetimes of gas phase CO2˙− and N2O˙− calculated from the transition probability of the autodetachment process A− → A + e−

A procedure to calculate the quantum mechanical transition probability of a unimolecular primary chemical process, A^? → A + e^? is investigated for the circumstance where A^? and A have different numbers of vibrational and rotational degrees of freedom (one is linear, the other not). A procedure is introduced to deal with the coupling between the vibrational and rotational motions. The proposed method was applied to calculating the lifetimes of CO₂^˙? and N₂O^˙? in the gas phase. The geometry optimizations and frequency calculations for CO₂, CO₂^˙?, N₂O, and N₂O^˙? are performed at HF, MP2, and QCISD(T) levels with 6-31G* or 6–31+G* basis sets, in order to obtain reliable geometric and spectroscopic information on these systems. Lifetimes are calculated for several of the lower vibrational–rotational states of the anions, as well as for the Boltzmann distribution of states at 298 K. The lifetime of the lowest vibrational–rotational state of CO₂^˙?, is 1.03 × 10^?4 s, and of the lowest vibrational state with rotational levels weighted by Boltzmann distribution at 298 K, 1.50 × 10^?4 s. These values are in good agreement with the experimental number, 9.0 ± 2.0 × 10^?5 s, and support the experimental evidence that CO₂^˙? was formed in its ground vibrational level by the techniques used. The lifetime of CO₂^˙? calculated with Boltzmann distribution over its vibrational and rotational levels at 298 K, is 1.51 × 10^?5 s. There are no direct measurements of the lifetime of N₂O^˙?, but it was estimated to be greater than 10^?4 s from experimental evidence. The predicted lifetimes of N₂O^˙?, at its lowest vibrational–rotational state (0 K) and lowest vibrational state with rotational levels weighted by the Boltzmann distribution at 298 K, are 238 and 19.1 s, respectively. The lifetime of N₂O^˙? at thermal equilibrium at 298 K is 6.66 × 10^?2 s, indicating that electron loss from the excited vibrational states of N₂O^˙? is significant. This study represents the first theoretical investigation of CO₂^˙? and N₂O^˙? lifetimes. © 1994 John Wiley & Sons, Inc.