Photodissociation of HBr. 1. Electronic structure, photodissociation dynamics, and vector correlation coefficients

Ab initio potential energy curves, transition dipole moments, and spin-orbit coupling matrix elements are computed for HBr. These are then used, within the framework of time-dependent quantum-mechanical wave-packet calculations, to study the photodissociation dynamics of the molecule. Total and partial integral cross sections, the branching fraction for the formation of excited-state bromine atoms Br(2P(1/2)), and the lowest order anisotropy parameters, beta, for both ground and excited-state bromine are calculated as a function of photolysis energy and compared to experimental and theoretical data determined previously. Higher order anisotropy parameters are computed for the first time for HBr and compared to recent experimental measurements. A new expression for the Re[a1(3) (parallel, perpendicular)] parameter describing coherent parallel and perpendicular production of ground-state bromine in terms of the dynamical functions is given. Although good agreement is obtained between the theoretical predictions and the experimental measurements, the discrepancies are analyzed to establish how improvements might be achieved. Insight is obtained into the nonadiabatic dynamics by comparing the results of diabatic and fully adiabatic calculations.     

A diabatic representation including both valence nonadiabatic interactions and spin-orbit effects for reaction dynamics

A diabatic representation is convenient in the study of electronically nonadiabatic chemical reactions because the diabatic energies and couplings are smooth functions of the nuclear coordinates and the couplings are scalar quantities. A method called the fourfold way was devised in our group to generate diabatic representations for spin-free electronic states. One drawback of diabatic states computed from the spin-free Hamiltonian, called a valence diabatic representation, for systems in which spin-orbit coupling cannot be ignored is that the couplings between the states are not zero in asymptotic regions, leading to difficulties in the calculation of reaction probabilities and other properties by semiclassical dynamics methods. Here we report an extension of the fourfold way to construct diabatic representations suitable for spin-coupled systems. In this article we formulate the method for the case of even-electron systems that yield pairs of fragments with doublet spin multiplicity. For this type of system, we introduce the further simplification of calculating the triplet diabatic energies in terms of the singlet diabatic energies via Slater's rules and assuming constant ratios of Coulomb to exchange integrals. Furthermore, the valence diabatic couplings in the triplet manifold are taken equal to the singlet ones. An important feature of the method is the introduction of scaling functions, as they allow one to deal with multibond reactions without having to include high-energy diabatic states. The global transformation matrix to the new diabatic representation, called the spin-valence diabatic representation, is constructed as the product of channel-specific transformation matrices, each one taken as the product of an asymptotic transformation matrix and a scaling function that depends on ratios of the spin-orbit splitting and the valence splittings. Thus the underlying basis functions are recoupled into suitable diabatic basis functions in a manner that provides a multibond generalization of the switch between Hund's cases in diatomic spectroscopy. The spin-orbit matrix elements in this representation are taken equal to their atomic values times a scaling function that depends on the internuclear distances. The spin-valence diabatic potential energy matrix is suitable for semiclassical dynamics simulations. Diagonalization of this matrix produces the spin-coupled adiabatic energies. For the sake of illustration, diabatic potential energy matrices are constructed along bond-fission coordinates for the HBr and the BrCH(2)Cl molecules. Comparison of the spin-coupled adiabatic energies obtained from the spin-valence diabatics with those obtained by ab initio calculations with geometry-dependent spin-orbit matrix elements shows that the new method is sufficiently accurate for practical purposes. The method formulated here should be most useful for systems with a large number of atoms, especially heavy atoms, and/or a large number of spin-coupled electronic states.     

Spin-orbit coupled potential energy surfaces and properties using effective relativistic coupling by asymptotic representation

A new method has been reported recently [H. Ndome, R. Welsch, and W. Eisfeld, J. Chem. Phys. 136, 034103 (2012)] that allows the efficient generation of fully coupled potential energy surfaces (PESs) including derivative and spin-orbit (SO) coupling. The method is based on the diabatic asymptotic representation of the molecular fine structure states and an effective relativistic coupling operator and therefore is called effective relativistic coupling by asymptotic representation (ERCAR). The resulting diabatic spin-orbit coupling matrix is constant and the geometry dependence of the coupling between the eigenstates is accounted for by the diabatization. This approach allows to generate an analytical model for the fully coupled PESs without performing any ab initio SO calculations (except perhaps for the atoms) and thus is very efficient. In the present work, we study the performance of this new method for the example of hydrogen iodide as a well-established test case. Details of the diabatization and the accuracy of the results are investigated in comparison to reference ab initio calculations. The energies of the adiabatic fine structure states are reproduced in excellent agreement with reference ab initio data. It is shown that the accuracy of the ERCAR approach mainly depends on the quality of the underlying ab initio data. This is also the case for dissociation and vibrational level energies, which are influenced by the SO coupling. A method is presented how one-electron operators and the corresponding properties can be evaluated in the framework of the ERCAR approach. This allows the computation of dipole and transition moments of the fine structure states in good agreement with ab initio data. The new method is shown to be very promising for the construction of fully coupled PESs for more complex polyatomic systems to be used in quantum dynamics studies.     

Theory of the photodissociation of ozone in the Hartley continuum: potential energy surfaces, conical intersections, and photodissociation dynamics

Ab initio potential energy and transition dipole moment surfaces are presented for the five lowest singlet even symmetry electronic states of ozone. The surfaces are calculated using the complete active space self consistent field method followed by contracted multireference configuration interaction (MRCI) calculations. A slightly reduced augmented correlation consistent valence triple-zeta orbital basis set is used. The ground and excited state energies of the molecule have been computed at 9282 separate nuclear geometries. Cuts through the potential energy surfaces, which pass through the geometry of the minimum of the ground electronic state, show several closely avoided crossings. Close examination, and higher level calculations, very strongly suggests that some of these seemingly avoided crossings are in fact associated with non-symmetry related conical intersections. Diabatic potential energy and transition dipole moment surfaces are created from the computed ab initio adiabatic MRCI energies and transition dipole moments. The transition dipole moment connecting the ground electronic state to the diabatic B state surface is by far the strongest. Vibrational-rotational wavefunctions and energies are computed using the ground electronic state. The energy level separations compare well with experimentally determined values. The ground vibrational state wavefunction is then used, together with the diabatic B<--X transition dipole moment surface, to form an initial wavepacket. The analysis of the time-dependent quantum dynamics of this wavepacket provides the total and partial photodissociation cross sections for the system. Both the total absorption cross section and the predicted product quantum state distributions compare well with experimental observations. A discussion is also given as to how the observed alternation in product diatom rotational state populations might be explained.     

Spin-orbit ab initio investigation of the photolysis of o-, m-, and p-bromotoluene

The photodissociations of o-, m-, and p-bromotoluene were investigated by ab initio and spin-orbit ab initio calculations. The possible photodissociation mechanisms at 266 and 193 nm were clarified by multistate second order multiconfigurational perturbation theory (MS-CASPT2) calculated potential energy curves, vertical excitation energies, and oscillator strengths of low-lying states. The dissociation products with spin-orbit-coupled states of Br(*)((2)P(12)) and Br((2)P(32)) were identified by the MS-CASPT2 method in conjunction with spin-orbit interaction through complete active space state interaction (MS-CASPT2/CASSI-SO) calculations. The effects of methyl rotation and substituent on the photodissociation mechanism were discussed.     

Theoretical transition probabilities for the OH Meinel system

The authors present a new potential energy curve, electric dipole moment function, and spin-orbit coupling function for OH in the X 2Pi state, based on high-level ab initio calculations. These properties, combined with a spectroscopically parametrized lambda-type doubling Hamiltonian, are used to compute the Einstein A coefficients and photoabsorption cross sections for the OH Meinel transitions. The authors investigate the effect of spin-orbit coupling on the lifetimes of rovibrationally excited states. Comparing their results with earlier ab initio calculations, they conclude that their dipole moment and potential energy curve give the best agreement with experimental data to date. The results are made available via EPAPS Document No. E-JCPSAG-017709.     

Classical and quantum studies of the photodissociation of a HX (X=Cl,F) molecule adsorbed on ice

The photodissociation dynamics of a HX (X = Cl,F) molecule adsorbed on a hexagonal ice surface at T = 0 K is studied using time-dependent quantum wave packets and quasiclassical trajectories. The relevant potential energy surfaces are calculated using high-level ab initio methods. We present here two dimensional calculations for the dynamics of the hydrogen photofragment for both HCl and HF molecules. The purpose of this paper is to compare the photodissociation dynamics of the two molecules which are adsorbed on the ice surface with different equilibrium geometries. The total photodissociation cross section and the angular distribution are calculated. The comparison with classical trajectory calculations provides evidence for typical quantum effects and reveals rainbow structures.     

Ab initio adiabatic and diabatic energies and dipole moments of the CaH+ molecular ion

The diabatic and adiabatic potential-energy curves and permanent and transition dipole moments of the highly excited states of the CaH(+) molecular ion have been computed as a function of the internuclear distance R for a large and dense grid varying from 2.5 to 240 au. The adiabatic results are determined by an ab initio approach involving a nonempirical pseudopotential for the Ca core, operatorial core-valence correlation, and full valence configuration interaction. The molecule is thus treated as a two-electron system. The diabatic potential energy curves have been calculated using an effective metric combined to the effective Hamiltonian theory. The diabatic potential-energy curves and their permanent dipole moments for the (1)∑(+) symmetry are examined and corroborate the high imprint of the ionic state in the adiabatic representation. Taking the benefit of the diabatization approach, correction of hydrogen electron affinity was taken into account leading to improved results for the adiabatic potentials but also the permanent and transition electric dipole moments.     

Restricted open-shell Kohn-Sham theory: simulation of the pyrrole photodissociation

The authors study the photodissociation reactions of pyrrole and N-methylpyrrole using first-principles molecular dynamics. The first excited state is described with restricted open-shell Kohn-Sham theory. They find a small barrier in the excited state potential energy surface. The possibility of energy redistribution near the Franck-Condon region leads to two different reaction channels in on-the-fly simulations on a single diabatic potential energy surface. The results are discussed in comparison with previous ab initio calculations and with experiments.     

Rovibrational dynamics of the strontium molecule in the A(1)Σ(u)+, c(3)Π(u), and a(3)Σ(u)+ manifold from state-of-the-art ab initio calculations

State-of-the-art ab initio techniques have been applied to compute the potential energy curves for the electronic states in the A(1)Σ(u)(+), c(3)Π(u), and a(3)Σ(u)(+) manifold of the strontium dimer, the spin-orbit and nonadiabatic coupling matrix elements between the states in the manifold, and the electric transition dipole moment from the ground X(1)Σ(g)(+) to the nonrelativistic and relativistic states in the A+c+a manifold. The potential energy curves and transition moments were obtained with the linear response (equation of motion) coupled cluster method limited to single, double, and linear triple excitations for the potentials and limited to single and double excitations for the transition moments. The spin-orbit and nonadiabatic coupling matrix elements were computed with the multireference configuration interaction method limited to single and double excitations. Our results for the nonrelativistic and relativistic (spin-orbit coupled) potentials deviate substantially from recent ab initio calculations. The potential energy curve for the spectroscopically active (1)0(u)(+) state is in quantitative agreement with the empirical potential fitted to high-resolution Fourier transform spectra [A. Stein, H. Kno?ckel, and E. Tiemann, Eur. Phys. J. D 64, 227 (2011)]. The computed ab initio points were fitted to physically sound analytical expressions, and used in converged coupled channel calculations of the rovibrational energy levels in the A+c+a manifold and line strengths for the A(1)Σ(u)(+)←X(1)Σ(g (+) transitions. Positions and lifetimes of quasi-bound Feshbach resonances lying above the (1)S(0) + (3)P(1) dissociation limit were also obtained. Our results reproduce (semi)quantitatively the experimental data observed thus far. Predictions for on-going and future experiments are also reported.     

Theoretical investigation on o-, m-, and p-chlorotoluene photodissociations at 193 and 266 nm

Photodissociations of the o-, m-, and p-chlorotoluene at 193 and 266 nm were investigated by ab initio calculations with and without spin-orbit interaction. The experimentally observed photodissociation channels were clearly assigned by multistate second order multiconfigurational perturbation theory (MS-CASPT2) calculated potential energy curves. The dissociation products with spin-orbit-coupled states of Cl*(2P1/2) and Cl(2P3/2) were identified by MS-CASPT2 in conjunction with spin-orbit interaction through complete active space state interaction (MS-CASPT2/CASSI-SO) calculations. The effects of methyl rotation and substituent on the photodissociation mechanism were discussed in detail.     

Theoretical investigation of the dissociation dynamics of vibrationally excited vinyl bromide on an ab initio potential-energy surface obtained using modified novelty sampling and feed-forward neural networks

The reaction dynamics of vibrationally excited vinyl bromide have been investigated using classical trajectory methods on a neural network potential surface that is fitted to an ab initio database of 12 122 configuration energies obtained from electronic structure calculations conducted at the MP4(SDQ) level of theory using a 6-31G(d,p) basis set for the carbon and hydrogen atoms and Huzinaga's (43334334) basis set augmented with split outer s and p orbitals (4332143214) and a polarization f orbital with an exponent of 0.5 for the bromine atom. The sampling of the 12-dimensional configuration hyperspace of vinyl bromide prior to execution of the electronic structure calculations is accomplished by combining novelty-sampling methods, chemical intuition, and trajectory sampling on empirical and neural network surfaces. The final potential is obtained using a two-layer feed-forward neural network comprising 38 and 1 neurons, respectively, with hyperbolic tangent sigmoid and linear transfer functions in the hidden and output layers, respectively. The fitting is accomplished using the Levenberg-Marquardt algorithm with early stopping and Bayesian regularization methods to avoid overfitting. The interpolated potentials have a standard deviation from the ab initio results of 0.0578 eV, which is within the range generally regarded as "chemical accuracy" for the purposes of electronic structure calculations. It is shown that the potential surface may be easily and conveniently transferred from one research group to another. The files required for transfer of the vinyl bromide surface can be obtained from the Electronic Physics Auxiliary Publication Service. Total dissociation rate coefficients for vinyl bromide are obtained at five different excitation energies between 4.50 and 6.44 eV. Branching ratios into each of the six open reaction channels are computed at 24 vibrational energies in the range between 4.00 and 6.44 eV. The distribution of vibrational energies in HBr formed via three-center dissociation from vinyl bromide is determined and compared with previous theoretical and experimental results. It is concluded that the combination of ab initio electronic structure calculations, novelty sampling with chemical intuition and trajectories on empirical analytic surfaces, and feed-forward neural networks provides a viable framework in which to execute purely ab initio molecular-dynamics studies on complex systems with multiple open reaction channels.     

The Jahn-Teller effect in CH3Cl+(X̃2E): a combined high-resolution experimental measurement and ab initio theoretical study

The energy levels of CH(3)Cl(+)X?(2)E showing strong spin-vibronic coupling effect (Jahn-Teller effect) have been measured up to 3500 cm(-1) above the ground vibrational state using one-photon zero-kinetic energy photoelectron and mass-analyzed threshold ionization spectroscopic method. Theoretical calculations have been also performed to calculate the spin-vibronic energy levels using a diabatic model and ab initio adiabatic potential energy surfaces (PESs). In the theoretical calculations the diabatic potential energy surfaces are expanded by the Taylor expansions up to the fourth-order including the multimode vibronic interactions. The calculated spin-orbit energy splitting (224.6 cm(-1)) for the ground vibrational state is in good agreement with the experimental data (219 ± 3 cm(-1)), which indicates that the Jahn-Teller and the spin-orbit coupling have been properly described in the theoretical model near the zero-point energy level. Based on the assignments predicted by the theoretical calculations, the experimentally measured energy levels were fitted to those from the diabatic model by optimizing the main spectroscopic parameters. The PESs from the ab initio calculations at the level of CASPT2/vq(t)z were thus compared with those calculated from the experimentally determined spectroscopic parameters. The theoretical diagonal elements in the diabatic potential matrix are in good agreement with those determined using the experimental data, however, the theoretical off-diagonal elements appreciably deviate from those determined using the experimental data for geometric points far away from the conical intersections. It is also concluded that the JT effect in CH(3)Cl(+) mainly arises from the linear coupling and the mode coupling between the CH(3) deform (υ(5)) and CH(3) rock (υ(6)) vibrations. The mode couplings between the symmetric C-Cl stretching vibration υ(3) with υ(5) and υ(6) are also important to understand the spin-vibronic structure of the molecule.     

Theoretical study of the UV photodissociation of Cl2: potentials, transition moments, extinction coefficients, and Cl*/Cl branching ratio

Potential energy curves for the X (1)Sigma(g) (+) ground state and Omega=0(u) (+), 1(u) valence states and dipole moments for the 0(u) (+), 1(u)-X transitions are obtained in an ab initio configuration interaction study of Cl(2) including spin-orbit coupling. In contrast to common assumptions, it is found that the B (3)Pi(0(+)u)-X transition moment strongly depends on internuclear distance, which has an important influence on the Cl(2) photodissociation. Computed energy curves and transition moments are employed to calculate the A, B, C<--X extinction coefficients, the total spectrum for the first absorption band, and the Cl(*)((2)P(1/2))/Cl((2)P(3/2)) branching ratio as a function of excitation wavelength. The calculated data are shown to be in good agreement with available experimental results.     

Accurate ab initio potential for the Na+...I* complex

High-level ab initio calculations employing the multireference configuration interaction and coupled clusters methods with a correlation-consistent sequence of basis sets have been used to obtain accurate potential energy curves for the complex of the sodium cation with the iodine atom. Potential curves for the first two electronic Lambda-S states have very different characters: the potential for the 2pi state has a well depth of approximately 10 kcal/mol, while the 2sigma state is essentially unbound. This difference is rationalized in terms of the anisotropic interaction of the quadrupole moment of the iodine atom with the sodium cation, which is stabilizing in the case of the 2pi state and destabilizing in the case of the 2sigma state. The effects of spin-orbit coupling have been accounted for with both ab initio and semiempirical approaches, which have been found to give practically the same results. Inclusion of spin-orbit interactions does not affect the X(omega = 32) ground state, which retains its 2pi character, but it results in two omega = 12 spin-orbit states, with mixed 2sigma and 2pi characters and binding energies roughly half of that of the ground spin-orbit state. Complete basis set (CBS) extrapolations of potential curves, binding energies, and equilibrium geometries were also performed, and used to calculate a number of rovibronic parameters for the Na+...I* complex and to parameterize model potentials. The final CBS-extrapolated and zero-point vibrational energy-corrected binding energy is 10.2 kcal/mol. Applications of the present results for simulations of NaI photodissociation femtosecond spectroscopy are discussed.     

Diabatic investigation for the NaRb molecule

An extensive diabatic investigation of the NaRb species has been carried out for all excited states up to the ionic limit Na^‐Rb⁺. An ab initio calculation founded on the pseudopotential, core polarization potential operators and full configuration interaction has been used with an efficient diabatization method involving a combination of variational effective hamiltonian theory and an effective overlap matrix. Diabatic potential energy curves and electric dipole moments (permanent and transition) for all the symmetries Σ⁺, Π, and Δ have been studied for the first time. Thanks to a unitary rotation matrix, the examination of the diabatic permanent dipole moment (PDM) has shown the ionic feature clearly seen in the diabatic ¹Σ⁺ potential curves and confirming the high imprint of the Na^‐Rb⁺ ionic state in the adiabatic representation. Diabatic transition dipole moments have also been computed. Real crossings have been shown for the diabatic PDM, locating the avoided crossings between the corresponding adiabatic energy curves.     

Spin-orbit ab initio investigation of the photolysis of bromoiodomethane.

The photodissociation of bromoiodomethane has been investigated by spin-orbit ab initio calculations. The experimentally observed A- and B-bands and the corresponding photoproducts were assigned by multistate second-order multiconfigurational perturbation theory in conjunction with spin-orbit interaction through complete active space state interaction potential energy curves, vertical excitation energies, and oscillator strengths of low-lying excited states. The present conclusions with respect to the dissociation process in the B-band are different compared with those of previous studies. The reaction between the iso-CH(2)Br-I and iso-CH(2)I-Br species has also been studied. Finally, a set of stable excited states was identified for both isomers. These species might be of importance in the recombination process that follows the photodissociation in a solvent.     

Quartet states of the acetylene cation: electronic structure calculations and spin-orbit coupling terms

Highly correlated ab initio methods have been used to generate one-dimensional cuts of the six-dimensional potential energy surfaces of the quartet and lowest doublet states for the HCCH(+) ion along the CH, CC, and cis and trans bending coordinates. Transition dipole moments and spin-orbit matrix elements are deduced. For the lowest 1 (4)Sigma(u) (+) state, the calculations predict a possible photon emission through the 1 (4)Pi(g)<--1 (4)Sigma(u) (+) transition competing with internal conversion and predissociation processes. The potential surfaces are used together with spin-orbit matrix elements to discuss the metastability and the predissociation processes forming the C(2)HC(2)H(+)+H(+)H products. Multistep spin-orbit induced predissociation pathways are suggested.     

Structural and spectroscopic study of the LiRb molecule beyond the Born-Oppenheimer approximation

Adiabatic and diabatic potential energy curves and the permanent and transition dipole moments of the low-lying electronic states of the LiRb molecule dissociating into Rb(5s, 5p, 4d, 6s, 6p, 5d, 7s, 6d) + Li(2s, 2p) have been investigated. The molecular calculations are performed with an ab initio approach based on nonempirical pseudopotentials for Rb(+) and Li(+) cores, parametrized l-dependent core polarization potentials and full configuration interaction calculations. The derived spectroscopic constants (R(e), D(e), T(e), ω(e), ω(e)x(e), and B(e)) of the ground state and lower excited states are in good agreement with the available theoretical works. However, the 8-10(1)Σ(+), 8-10(3)Σ(+), 6(1,3)Π, and 3(1,3)Δ excited states are studied for the first time. In addition, to the potential energy, accurate permanent and transition dipole moments have been determined for a wide interval of internuclear distances. The permanent dipole moment of LiRb has revealed ionic characters both relating to electron transfer and yielding Li(-)Rb(+) and Li(+)Rb(-) arrangements. The diabatic potential energy for the (1,3)Σ(+), (1,3)Π, and (1,3)Δ symmetries has been performed for this molecule for the first time. The diabatization method is based on variational effective Hamiltonian theory and effective metric, where the adiabatic and diabatic states are connected by an appropriate unitary transformation.     

Controlled dynamics at an avoided crossing interpreted in terms of dynamically fluctuating potential energy curves

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.