Photodissociation dynamics in the first absorption band of pyrrole. II. Photofragment distributions for the 1A2(πσ*)←X̃1A1(ππ) transition
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The analysis of the total kinetic energy release (TKER) of the photofragments pyrrolyl + H-atom formed in the photodissociation of pyrrole in the low-lying state 1A2(πσ*) is presented. The TKER distributions contain complementary and often more precise information on the fragmentation process than the broad diffuse absorption spectra. The distributions are calculated quantum mechanically for the diabatic state 1A2(πσ*) either isolated or coupled to the ground electronic state at an exit channel conical intersection. The calculations use the novel ab initio quasi-diabatic potential energy matrix constructed in the work of Picconi and Grebenshchikov [J. Chem. Phys. 148, 104103 (2018)]. The approximate overlap integral-based adiabatic mapping approach is introduced with which the quantum mechanical TKER distributions can be efficiently and accurately reproduced. Finally, the calculated TKERs are compared with the experimental results. The main features of the measured vibrationally resolved distributions are reproduced, and the spectral peaks are assigned and interpreted in detail.Keywords:
Diabatic
Conical intersection
Avoided crossing
The accuracy of three-dimensional adiabatic and diabatic potential energy surfaces is calculated using ab initio methods and is numerically fitted for the two lowest electronic states 1 and 22A' of the LiH2 system, which are very important for the Li (2p) + H2 reaction. The finite difference method is performed to generate the mixing angles, which are used to educe the diabatic potential from the adiabatic potential. The accurate conical intersection (CI) is studied in this work with three different basis sets. The energy of the conical intersection is slightly lower (nearly 0.12 eV) than that of the perpendicular intermediate on the first excited state. By analyzing the potential energy surfaces in this work we can suggest that the most possible reaction pathway for the title reaction is Li (2p) + H2 → LiH2 (22A') (C2v ) → CI → LiH2 (12A') (C2v ) → LiH⋯H → LiH (X1∑g+) + H. The conical intersection and (22A') intermediate may play a vital role in the title reaction.
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Potential energy surface
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An ab initio study of the potential energy curves for BF2+ is reported. The 1Σ+ state is metastable and is characterized by an unusually strong bond with a well depth of 6.06 eV. The origin of this bond is clearly traced to the interaction between the strongly bonding configuration B2+ + F and the repulsive configurations B++F+. Bound metastable states are also present for 1Π and 3Π manifolds. Dipole moments are used to assign types of bonding in each region of internuclear distance for the most important electronic states. An approximate diabatic representation is given for the two low-lying states derived from the 1Σ+ adiabatic curves. This study confirms the utility of an avoided crossing-diabatic coupling plus polarization model for systems of intermediate polarity.
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Diatomic molecule
Avoided crossing
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Potential-energy surfaces of the 1 1A′, 1 1A′′, and 2 1A′′ states of ozone and corresponding transition-dipole-moment surfaces have been computed as a function of the two bond distances and the bond angle. The calculations are based on the complete-active-space self-consistent field (CASSCF) and multiconfigurational second-order perturbation theory (CASPT2) electronic-structure models. For the calculations of the A″1 surfaces, which exhibit a conical intersection, a diabatic representation has been constructed, employing a direct diabatization method implemented at the CASSCF level. The slow variation of the diabatic potentials and transition dipole moments with nuclear geometry allows us to perform the ab initio calculations on a widely spaced grid. The complete potential-energy and transition-dipole-moment surfaces are then efficiently obtained by interpolation. This procedure leads to very significant savings of computing time compared to the mapping of the rapidly varying potentials and derivative couplings in the conventional adiabatic representation. Diabatic potentials at the CASPT2 level have been obtained by applying the adiabatic-to-diabatic transformation constructed at the CASSCF level to the adiabatic CASPT2 potentials. The properties of the resulting adiabatic and diabatic A″1 potential-energy surfaces are discussed, with emphasis on the 1 1A′′–2 1A′′ conical intersection, which is of relevance for the photodissociation dynamics of ozone in the Chappuis band. The computation of the photoabsorption cross section and the comparison between theory and experiment are discussed in the accompanying paper.
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The nonadiabatic nuclear wavepacket dynamics on the coupled two lowest (1)Σ(+) states of the LiF molecule under the action of a control pulse is investigated. The control is achieved by a modulation of the characteristics of the potential energy curves using an infrared field with a cycle duration comparable to the time scale of nuclear dynamics. The transition of population between the states is interpreted on the basis of the coupled nuclear wavepacket dynamics on the effective potential curves, which are transformed from the adiabatic potential curves with use of a diabatic representation that diagonalizes the dipole-moment matrix of the relevant electronic states. The basic feature of the transition dynamics is characterized in terms of the notion of the collision between the dynamical crossing point and nuclear wavepackets running on such modulated potential curves, and the transition amplitude is mainly dominated by the off-diagonal matrix element of the time-independent electronic Hamiltonian in the present diabatic representation. The importance of the geometry dependence of the intrinsic dipole moments as well as of the diabatic coupling potential is illustrated both theoretically and numerically.
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Stochastic matrix
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We intend to study the non-adiabatic interactions among the three lowest adiabatic states (12A', 12A'', and 22A') of F+H2 triatomic reactive system in hyperspherical coordinates for a fixed hyperradius at ρ = 7.5 bohr as functions of hyperangles, θ (0° ≤ θ ≤ 90°) and ϕ (0° ≤ ϕ ≤ 360°). The adiabatic potential energy surfaces are calculated using MRCI level of methodology whereas the non-adiabatic coupling terms between those states are calculated from the analytic gradient methods implemented in MOLPRO quantum chemistry package. The ground (12A') and the first excited (12A'') states exhibit conical intersection (CI) and seam of CI along C2v geometries, whereas the first (12A'') and the second (22A') excited states undergo Renner-Teller coupling at linear geometries. We carry out adiabatic-to-diabatic transformation (ADT) by solving ADT equations to obtain ADT angles for constructing single-valued, continuous and symmetric 3 × 3 diabatic potential energy matrix so that subsequent accurate scattering calculations can be performed.
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Avoided crossing
Adiabatic theorem
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The accurate adiabatic and diabatic potential energy surfaces, which are for the two lowest states of He + H2, are presented in this study. The Molpro 2012 software package is used, and the large basis sets (aug-cc-pV5Z) are selected. The high-level MCSCF/MRCI method is employed to calculate the adiabatic potential energy points of the title reaction system. The triatomic reaction system is described by Jacobi coordinates, and the adiabatic potential energy surfaces are fitted accurately using the B-spline method. The equilibrium structures and electronic energies for the H2 are provided, and the corresponding different levels of vibrational energies of the ground state are deduced. To better express the diabatic process of the whole reaction, avoid crossing points being calculated and conical intersection also being optimized. Meanwhile, the diabatic potential energy surfaces of the reaction process are constructed. This study will be helpful for the analysis of histopathology and for the study in biological and medical mechanisms.
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We present a new diabatic representation of the coupled potential energy surfaces for Na(3p 2P)+H2→Na(3s 2S)+H2 or NaH+H. The new representation is designed to yield, upon diagonalization, realistic values for the two lowest energy 2A′ adiabatic states at both asymptotes of the chemical reaction as well as near the conical intersection in the three-body interaction region. It is economical to evaluate and portable. It is suitable for dynamics calculations on both the quenching process and the electronically nonadiabatic chemical reaction.
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Exothermic reaction
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The adiabatic potential energies for the lowest three states of a Li2H system are calculated with a high level ab initio method (MCSCF/MRCI) with a large basis set (aV5Z). The accurate three dimensional B-spline fitting method is used to map the global adiabatic potential energy surfaces, using the existing adiabatic potential energies, for the lowest two adiabatic states of the title reaction system. The different vibrational states and corresponding energies are studied for the diatomic molecule of reactant and products. In order to clearly understand the nonadiabatic process, the avoided crossing area and conical intersection are carefully studied. For further study of the nonadiabatic dynamic reaction, the diabatic potential energy surfaces are deduced in the present work.
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Diatomic molecule
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Potential energy surface
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A general neural network (NN)-fitting procedure based on nonadiabatic couplings is proposed to generate coupled two-state diabatic potential energy surfaces (PESs) with conical intersections. The elements of the diabatic potential energy matrix (DPEM) can be obtained directly from a combination of the NN outputs in principle. Instead, to achieve higher accuracy, the adiabatic-to-diabatic transformation (ADT) angle (mixing angle) for each geometry is first solved from the NN outputs, followed by individual NN fittings of the three terms of the DPEM, which are calculated from the ab initio adiabatic energies and solved mixing angles. The procedure is applied to construct a new set of two-state diabatic potential energy surfaces of ClH2. The ab initio data including adiabatic energies and derivative couplings are well reproduced. Furthermore, the current diabatization procedure can describe well the vicinity of conical intersections in high potential energy regions, which are located in the T-shaped (C2v) structure of Cl-H2. The diabatic quantum dynamical results on diabatic PESs show large differences as compared with the adiabatic results in high collision energy regions, suggesting the significance of nonadiabatic processes in conical intersection regions at high energies.
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A diabatic representation is presented of the coupled potential-energy surfaces for Na(3p P-2) + H2 yields Na (3s S-2) + H2 or NaH + H. The representation is designed to yield, upon diagonalization, realistic values for the two lowest energy adiabatic states at both asymptotes of the chemical reaction as well as near the conical intersection in the three-body interaction region. It is economical to evaluate and portable. It is suitable for dynamics calculations on both the quenching process and the electronically nonadiabatic chemical reaction.
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Conical intersection
Asymptote
Representation
Exothermic reaction
Diatomic molecule
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