Ab initiostudy of NO2

New Diabatic Potential Energy Surfaces for the Li + H2 Reaction and Time-Dependent Quantum Wave Packet Studies

New global diabatic potential energy surfaces (DPESs) for the ground (12A') and first excited (22A') states for the Li + H2 system were developed, with more than 30,000 energy points at the IC-MRCI+Q level of theory, utilizing the aug-cc-pV5Z basis set for the H atoms and the cc-pCV5Z basis set for the Li atom, fitted by a single neural network (NN) with symmetry. Product state-resolved quantum dynamics calculations of the nonadiabatic reaction Li (2P) + H2 (X 1 ∑g+, v0 = 0, j0 = 0) → LiH (X 1∑+) + H(2S) were carried out using these new DPESs and also the previous HYLC-DPESs. The numerical results suggested that our newly constructed DPESs provided an accurate description of the LiH2 system.

Compensation States Approach in the Hybrid Diabatization Scheme: Extension to Multidimensional Data and Properties

The diabatization of reactive systems for more than just a couple of states is a very demanding problem and generally requires advanced diabatization techniques. Especially for dissociative processes, the drastic changes in the adiabatic wave functions often would require large diabatic state bases, which quickly become impractical. Recently, we addressed this problem by the compensation states approach developed in the context of our hybrid diabatization scheme. This scheme utilizes wave function as well as energy data in combination with a diabatic potential model. In regions where the initial diabatic state basis becomes insufficient for an appropriate representation of the adiabatic states, new model states are generated. The new model states compensate for the state space not spanned by the initial diabatic basis. Such a compensation state is obtained by projecting the initial diabatic state space out of the adiabatic wave function. This yields a very efficient basis representation of the electronic Hamiltonian. The present work presents two new aspects. First, it is shown how other operators like the spin-orbit operator in the framework of the Effective Relativistic Coupling by Asymptotic Representation (ERCAR) can be evaluated in this compact model state space without losing the correct wave function information and accuracy. Second, the extension of the approach to multidimensional potential energy surface models is presented for methyl iodide including the C-I dissociation coordinate and the angular H3C-I bending coordinates.

The role of the sextet potential energy surface in O2 + N inelastic collision processes

We have performed molecular dynamics simulations of inelastic collisions between molecular oxygen and atomic nitrogen, employing the quasi-classical trajectory method on the new doublet, quartet, and sextet analytical potential energy surfaces of NO₂. A complete database of vibrationally detailed rate coefficients is constructed in a wide temperature range for high vibrational states up to ν = 25. In particular, the present work shows that the sextet potential energy surface plays a crucial role in the rovibrational relaxation process of O₂ + N collisions. The state-to-state rate coefficients increase by a factor of 2 to 6 when we consider the contribution of this sextet potential energy surface according to the corresponding weight factor, especially for vibrational energy transfer processes in single quantum jumps and/or high-temperature regimes. Furthermore, we also provide Arrhenius-type accurate fits for the vibrational state-specific rate coefficients of this collision system to achieve the flexible application of rate coefficients in numerical codes concerning air kinetics. Our results have implications for understanding the relaxation mechanism of the collision system with degenerate electronic states.

Accurate Adiabatic and Diabatic Potential Energy Surfaces for the Reaction of He + H2

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.

State-to-State Transition Study of the Exchange Reaction for N(4S) and O2(X3Σg-) Collision by Quasi-Classical Trajectory

Based on the new ²A' and ⁴A' potential energy surfaces of NO₂ fitted by Varga et al., we conducted a quasi-classical trajectory study on the N(⁴S) +O₂(X³Σ_g^- ) → NO(²Π) + O(³P) reaction, focusing on the high vibrational state up to ν = 25. For different rovibrational states of O₂, within the relative translational energy (E_c) range of 0.1-30 eV, the total exchange cross section (ECS) is calculated, and it is found that the initial relative translational energy and vibration excitation have a significant effect on ECSs, while rotational excitation has little influence; the rate coefficient of the high rovibrational state of O₂ molecules at high temperatures is studied, and it is found that when the vibrational level ν of O₂ is in the range of 0-15, the value of log₁₀ k(T, ν, j) with the vibrational level ν is almost linear, while when ν is greater than 15, it becomes gentle with the increase in ν. Finally, the state-to-state rate coefficients are calculated; our results supply the advantageous state-to-state process data in the NO₂ system, and they are useful for further studying the related hypersonic gas flow at very high temperature.

How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely-the resulting "quasidiabatic" states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn-Teller model of nitrogen trioxide and in the induced Renner-Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.

Ultrafast imaging of laser-controlled non-adiabatic dynamics in NO2 from time-resolved photoelectron emission

Imaging and controlling the ultrafast conical intersection dynamics in NO₂ using the latest advances in attosecond and light-synthesizer technology.

New diabatic potential energy surfaces of the NaH2 system and dynamics studies for the Na(3p) + H2 → NaH + H reaction

The Na(3p) + H2(X1Σg+) → NaH(X1Σ+) + H(2S) reaction plays an important role in the field of diabatic reaction dynamics. A set of new diabatic potential energy surfaces (PESs) of the NaH2 system are structured, which include the diabatic coupling between the lowest two adiabatic states. The electronic structure calculations are performed on the multi-reference configuration interaction level with the cc-pwCVQZ and aug-cc-PVQZ basis sets for Na and H atoms. 32402 geometries are chosen to construct the diabatic data by a unitary transformation based on the molecular property method. The diabatic matrix elements of [Formula: see text], [Formula: see text] and [Formula: see text] ([Formula: see text]) are fitted by the artificial neural network model. The spectroscopic constants of diatoms obtained from the present PESs are consistent with the experimental data. The topographical and intersection characteristics of the [Formula: see text] and [Formula: see text] surfaces are discussed. Based on the new PESs, the time-dependent quantum wave packet calculations are carried out to study the reaction mechanism of the title reaction in detail.

Conical-intersection dynamics and ground-state chemistry probed by extreme-ultraviolet time-resolved photoelectron spectroscopy

Time-resolved photoelectron spectroscopy (TRPES) is a useful approach to elucidate the coupled electronic-nuclear quantum dynamics underlying chemical processes, but has remained limited by the use of low photon energies. Here, we demonstrate the general advantages of XUV-TRPES through an application to NO₂, one of the simplest species displaying the complexity of a non-adiabatic photochemical process. The high photon energy enables ionization from the entire geometrical configuration space, giving access to the true dynamics of the system. Specifically, the technique reveals dynamics through a conical intersection, large-amplitude motion and photodissociation in the electronic ground state. XUV-TRPES simultaneously projects the excited-state wave packet onto many final states, offering a multi-dimensional view of the coupled electronic and nuclear dynamics. Our interpretations are supported by ab initio wavepacket calculations on new global potential-energy surfaces. The presented results contribute to establish XUV-TRPES as a powerful technique providing a complete picture of ultrafast chemical dynamics from photoexcitation to the final products.

Ab initio calculation of femtosecond-time-resolved photoelectron spectra of NO2 after excitation to the A-band

We present calculations of time-dependent photoelectron spectra of NO₂ after excitation to the A-band for comparison with extreme-ultraviolet (XUV) time-resolved photoelectron spectroscopy. We employ newly calculated potential energy surfaces of the two lowest-lying coupled ²A' states obtained from multi-reference configuration-interaction calculations to propagate the photo-excited wave packet using a split-step-operator method. The propagation includes the nonadiabatic coupling of the potential surfaces as well as the explicit interaction with the pump pulse centered at 3.1 eV (400 nm). A semiclassical approach to calculate the time-dependent photoelectron spectrum arising from the ionization to the eight energetically lowest-lying states of the cation allows us to reproduce the static experimental spectrum up to a binding energy of 16 eV and enables direct comparisons with XUV time-resolved photoelectron spectroscopy.

Global diabatic potential energy surfaces for the BeH2 + system and dynamics studies on the Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction

The Be+(2P) + H2(X1Σg +) → BeH+(X1Σ+) + H(2S) reaction has great significance for studying diabatic processes and ultracold chemistry. The first global diabatic potential energy surfaces (PESs) which are correlated with the lowest two adiabatic states 12A' and 22A' of the BeH2 + system are constructed by using the neural network method. Ab initio energy points are calculated using the multi-reference configuration interaction method with the Davidson correction and AVQZ basis set. The diabatic energies are obtained from the transformation of ab initio data based on the dipole moment operators. The topographical characteristics of the diabatic PESs are described in detail, and the positions of crossing between the V d 11 and V d 22 are pinpointed. On new diabatic PESs, the time-dependent quantum wave packet method is carried out to study the mechanism of the title reaction. The results of dynamics calculations indicate the reaction has no threshold and the product BeH+ is excited to high vibrational states easily. In addition, the product BeH+ tends to backward scattering at most collision energies.

Accurate potential energy surfaces for the first two lowest electronic states of the Li (2p) + H2 reaction

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′) (C_2v) → CI → LiH₂ (1²A′) (C_2v) → LiH⋯H → LiH (X¹∑_g⁺) + H. The conical intersection and (2²A′) intermediate may play a vital role in the title reaction.

Accurate diabatic potential energy surfaces for the Li (2p) + H₂ → LiH (X) + H reaction are produced.

Diabatic potential energy surfaces of MgH2+ and dynamic studies for the Mg+(3p) + H2 → MgH+ + H reaction

The global diabatic potential energy surfaces for the Mg⁺(3p) + H₂ → MgH⁺ + H reaction are structured for the first time.

Global diabatic potential energy surfaces and quantum dynamical studies for the Li(2p) + H2(X(1)Σ(+)g) → LiH(X(1)Σ(+)) + H reaction

The global diabatic potential energy surfaces which are correlated with the ground state 1A' and the excited state 2A' of the Li(2p) + H2 reaction are presented in this study. The multi-reference configuration interaction method and large basis sets (aug-cc-pVQZ for H atom and cc-pwCVQZ for Li atom) were employed in the ab initio single-point energy calculations. The diabatic potential energies were generated by the diabatization scheme based on transition dipole moment operators. The neural network method was utilized to fit the matrix elements of the diabatic energy surfaces, and the root mean square errors were extremely small (3.69 meV for , 5.34 meV for and 5.06 meV for ). The topographical features of the diabatic potential energy surfaces were characterized and the surfaces were found to be sufficiently smooth for the dynamical calculation. The crossing seam of the conical intersections between the and surfaces were pinpointed. Based on this new analytical diabatic potential energy surfaces, time-dependent wave packet calculation were conducted to investigate the mechanism of the title reaction. At low collision energies, the product LiH molecule tends to forward scattering, while at high collision energies, the forward and backward scatterings exist simultaneously.

Ab initio constructed diabatic surfaces of NO2 and the photodetachment spectra of its anion

A thorough investigation has been performed for electronic structure, topological effect, and nuclear dynamics of NO2 molecule, where the adiabatic potential energy surfaces (PESs), conical intersections between the ground (X(2)A1) and the first excited state (A(2)B2), and the corresponding non-adiabatic coupling terms between those states are recalculated [Chem. Phys. 416, 11 (2013)] to achieve enough accuracy in dynamics. We employ beyond Born-Oppenheimer theory for these two state sub-Hilbert space to carry out adiabatic to diabatic transformation (ADT) to obtain the ADT angles and thereby, to construct single-valued, smooth, and continuous diabatic PESs. The analytic expressions for the adiabatic PESs and ADT angles are provided to represent a two-state three-mode diabatic Hamiltonian of NO2 for performing nuclear dynamics to calculate the photo-electron spectra of its anion. It appears that not only Jahn-Teller type coupling but also Renner-Teller interaction contributes significantly on the overall spectrum. The coupling between the electronic states (X(2)A1 and A(2)B2) of NO2 is essentially through the asymmetric stretching mode, where the functional form of such interaction is distinctly symmetric and non-linear.

Space-time contours to treat intense field-dressed molecular states. I. Theory

A molecular system exposed to an intense external field is considered. The strength of the field is measured by the number L of electronic states that become populated during this process. In the present article the authors discuss a rigorous way, based on the recently introduced space-time contours [R. Baer, et al., J. Chem. Phys. 119, 6998 (2003)], to form N coupled Schrodinger equations where N<L, which maintains the effects due to the remaining (L-N) populated states. It is shown that whereas the size of L is unlimited, the main requirement concerning N is that the original group of N field-free states forms a Hilbert subspace in the spatial region of interest. From previous studies it is known that a group of states forms a Hilbert subspace if and only if the corresponding topological D matrix is diagonal [M. Baer, et al., Farad, Discuss 127, 337 (2004)].

Elastic and charge transfer processes in H+ + CO collisions

Proton and hydrogen atom time-of-flight spectra in collision energy range of E(trans) = 9.5-30 eV show that the endoergic charge transfer process in the H+ + CO system is almost an order of magnitude less probable than the elastic scattering [G. Niedner-Schatteburg and J. P. Toennies, Adv. Chem. Phys. LXXXII, 553 (1992)]. Ab initio computations at the multireference configuration interaction level have been performed to obtain the ground- and several low-lying excited electronic state potential energy curves in three different molecular orientations namely, H+ approaching the O-end and the C-end (collinear), and H+ approaching the CO molecule in perpendicular configuration with fixed CO internuclear distance. Nonadiabatic coupling terms between the ground electronic state (H+ + CO) and the three low-lying excited electronic states (H + CO+) have been computed and the corresponding diabatic potentials have been obtained. A time-dependent wavepacket dynamics study is modeled first involving only the ground and the first excited states and then involving the ground and the three lowest excited states at the collision energy of 9.5 eV. The overall charge transfer probability have been found to be approximately 20%-30% which is in qualitative agreement with the experimental findings.

Higher order (A+E)⊗e pseudo-Jahn–Teller coupling

The pseudo-Jahn-Teller (PJT) coupling of a nondegenerate state A with a twofold degenerate state E by a degenerate vibrational mode e is studied for a general system with a C(3) main rotational axis. The PJT coupling terms up to sixth order are derived by symmetry considerations for this general (A+E) multiply sign in circle e case. The obtained expression for the 3 x 3 diabatic potential energy matrix is found to be closely related to the expression recently developed for the higher order Jahn-Teller case [A. Viel and W. Eisfeld, J. Chem. Phys. 120, 4603 (2004)]. The dynamical PJT coupling, which can arise for states of appropriate symmetry if one of the vibrational modes induces a change of the nuclear point group between D(3h), C(3v), C(3h), and C(3), is discussed. The effect of the higher order PJT coupling is tested by a two-dimensional model study based on the e bending mode of NH(3)(+). The models are analyzed by fitting the two-dimensional potential energy surfaces. The significance of the higher order terms on the nonadiabatic dynamics is demonstrated by quantum wave packet propagations.

Calculation of nonadiabatic couplings in density-functional theory

This paper proposes methods for calculating the derivative couplings between adiabatic states in density-functional theory (DFT) and compares them with each other and with multiconfigurational self-consistent field calculations. They are shown to be accurate and, as expected, the costs of their calculation scale more favorably with system size than post-Hartree-Fock calculations. The proposed methods are based on single-particle excitations and the associated Slater transition-state densities to overcome the problem of the unavailability of multielectron states in DFT which precludes a straightforward calculation of the matrix elements of the nuclear gradient operator. An iterative scheme employing linear-response theory was found to offer the best trade-off between accuracy and efficiency. The algorithms presented here have been implemented for doublet-doublet excitations within a plane-wave-basis and pseudopotential framework but are easily generalizable to other excitations and basis sets. Owing to their fundamental importance in cases where the Born-Oppenheimer separation of motions is not valid, these derivative couplings can facilitate, for example, the treatment of nonadiabatic charge transfers, of electron-phonon couplings, and of radiationless electronic transitions in DFT.

Chemical reaction dynamics beyond the Born-Oppenheimer approximation

To predict the branching between energetically allowed product channels, chemists often rely on statistical transition state theories or exact quantum scattering calculations on a single adiabatic potential energy surface. The potential energy surface gives the energetic barriers to each chemical reaction and allows prediction of the reaction rates. Yet, chemical reactions evolve on a single potential energy surface only if, in simple terms, the electronic wavefunction can evolve from the reactant electronic configuration to the product electronic configuration on a time scale that is fast compared to the nuclear dynamics through the transition state. The experiments reviewed here investigate how the breakdown of the Born-Oppenheimer approximation at a barrier along an adiabatic reaction coordinate can alter the dynamics of and the expected branching between molecular dissociation pathways. The work reviewed focuses on three questions that have come to the forefront with recent theory and experiments: Which classes of chemical reactions evidence dramatic nonadiabatic behavior that influences the branching between energetically allowed reaction pathways? How do the intramolecular distance and orientation between the electronic orbitals involved influence the nonadiabaticity in the reaction? How can the detailed nuclear dynamics mediate the effective nonadiabatic coupling encountered in a chemical reaction?

Effects of higher order Jahn-Teller coupling on the nuclear dynamics

In this paper effects of higher order Jahn-Teller coupling terms on the nonadiabatic dynamics are studied. Of particular interest is the case when the potential energy surfaces of the degenerate state show pronounced anharmonicity. In order to demonstrate the effects a two-dimensional E multiply sign in circle e Jahn-Teller model system is treated which is based on the e(') stretching vibration of the photoactive (2)E(') state of NO(3) as a realistic example. The sixth order E multiply sign in circle e Jahn-Teller Hamiltonian is derived in the diabatic representation which is valid for any system with a C(3) rotation axis. This diabatization scheme is compared to lower-order Jahn-Teller Hamiltonians and to symmetry adapted as well as ad hoc approximations. Lower-order potentials result in pronounced quantitative and qualitative differences in the dynamics, including differences in the evolution of mean values, the autocorrelation functions (and thus the corresponding spectra), and the electronic population evolution. In the particular example treated, the results of fourth and fifth order potentials are very similar to the sixth order reference system. In contrast, the approximate sixth order Hamiltonians, though the corresponding adiabatic surfaces seem to be nearly identical, results in pronounced differences. The possible consequences for the dynamics of realistic systems with higher dimensionality are briefly discussed.