Time-dependent Wave Packet Propagation Research Articles

Photodissociation dynamics and UV absorption spectrum of acetone oxide (CH3)2COO.

The photodynamics and B1A' ← X1A' absorption spectrum of acetone oxide, (CH3)2COO, are studied theoretically from first principles. The underlying adiabatic potential energy curves (and surfaces) are computed by a second-order multireference perturbation theory method and diabatized using a diabatization by ansatz scheme. To confirm the results, for selected geometries EOM-CCSD and XMS-RS2C calculations were also performed. The dynamical calculation rests on the multi-configuration time-dependent Hartree wavepacket propagation method. The experimental absorption spectrum is reproduced satisfactorily. This result serves to validate the Hamiltonian model built within the quasi-diabatic representation. Contrary to the smallest Criegee intermediate, CH2OO, it is found that the vibronic coupling between the B and C states of (CH3)2COO plays an essential role in reproducing the experimental absorption spectrum. Time-dependent electronic populations reveal a faster decay than for the smaller system CH2OO. This is interpreted in terms of the stronger coupling between the B and C states in the larger system leading to a shorter lifetime for the B state than in CH2OO.

On the Role of Molecular Polarizability in Positron Coupling to Vibrations in Homonuclear Diatomics

In a previous work [Poveda, Varella, and Mohallem (Poveda et al., Atoms, 2021, 9: 64) it was shown that the bell-like shape of the 0 → 1 vibrational excitation cross section of H2 as a function of the incoming positron energy, with its characteristic sharp onset at threshold, can be accounted for by a simple model which couples the positron to the vibrational mode of the molecule, throught the behavior of the target polarizabitity with the internuclear bond distance. The study, carried out via time-dependent wave-packet dynamics propagation, relies on a two-dimensional potential energy surface involving just the scattering (positron-target) and vibrational (target) coordinates. Here the model is extended to the full three-dimensional configuration space of the positron-diatomic complex, with the cross sections computed within a time-independent close-coupling approach. The present results confirm the previous findings, shedding light on the mechanisms through which a low-energy positron couples to the molecular vibrations.

Quantum and quasi-classical dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state.

The dynamics of the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction on its electronic ground state is investigated by using time-dependent wave packet propagation (TDWP) and quasi-classical trajectory (QCT) simulations. For the moderate collision energies considered (Ec = 0.001 to 0.4 eV, corresponding to a range from 10 K to 4600 K) the total reaction probabilities from the two different treatments of the nuclear dynamics agree very favourably. The undulations present in P(E) from the quantum mechanical treatment can be related to stabilization of the intermediate CO2 complex with lifetimes on the 0.05 ps time scale. This is also confirmed from direct analysis of the TDWP simulations and QCT trajectories. Product diatom vibrational and rotational level resolved state-to-state reaction probabilities from TDWP and QCT simulations agree well except for the highest product vibrational states (v' ≥ 15) and for the lowest product rotational states (j' ≤ 10). Opening of the product vibrational level CO(v' = 17) requires ∼0.2 eV from QCT and TDWP simulations with O2(j = 0) and decreases to 0.04 eV if all initial rotational states are included in the QCT analysis, compared with Ec > 0.04 eV obtained from experiments. It is thus concluded that QCT simulations are suitable for investigating and realistically describe the C(3P) + O2(3Σ-g) → CO(1Σ+) + O(1D) reaction down to low collision energies when compared with results from a quantum mechanical treatment using TDWPs.

Time-dependent quantum wave packet calculation for reaction S−(2P)+H2(1Σg+)→SH−(1Σ)+H(2S) on ab Initio potential energy surface

The time-dependent wave packet propagation method was applied to investigate the dynamic behaviours of the reaction S−(2P)+H2(1Σg+)→SH−(1Σ)+H(2S) based on the electronic ground state (2A′) potential energy surface of the SH2− ionic molecule. The collision energy dependent reaction probabilities and integral cross sections are obtained. The numerical results suggest that there are significant oscillation structures over all the studied range of the collision energies. The vibrational excitation and rotational excitation of the diatomic reagent H2 promote the reactivity significantly as suggested by the numerical total reaction probabilities with the initial rotational quantum number of j = 0, 2, 4, 6, 8, 10, and the vibrational quantum number v = 0, 1, 2, 3, 4. The numerical integral cross sections are quite consistent with the experimental data reported in previous work.

Wavepacket propagations for the early time dynamics of proton-coupled electron transfer in the charge-transfer state of NH3Cl complex.

A charge-transfer (CT) excited state of NH3Cl, generated by photo-detachment of an electron from the anionic NH3Cl- precursor, can be represented as H2N+-H-Cl- and proceeds to two chemical reactions: one reaction generating NH2 and HCl resulting from a proton transfer (PT) and the other reaction producing NH3 and a Cl atom resulting from an electron transfer (ET); both are coupled to form a typical proton-coupled electron transfer (PCET) process. The early time dynamics of this CT were studied using time-dependent wavepacket propagation on three nonadiabatically coupled electronic states in a reduced three-dimensional space. The electronic states were treated using the XMS-CASPT2/aug-cc-pVTZ ab initio methodology. The population dynamics of the three coupled electronic states were analyzed in detail to reveal the initial stage of the PCET process up to ∼100 fs, while the branching ratio, χ = PT/(ET+PT), was determined after wavepacket propagations of up to 2000 fs. Another main result is the dependence of χ on the vibration levels of the initial precursor anion and the isotope substitution of the connecting H atom with deuterium and tritium. Our study reveals the detailed microscopic features of the PCET process embedded in the CT state of the NH3Cl complex and certain systematic dependences of the branching ratio χ on the above factors.

Effect of initial vibrational excitation on the methane cation sub-femtosecond photodynamics

An ab initio ab quantum dynamics study is attempted to understand the effect of initial vibrational state excitation on the sub-femtosecond photodynamics of the methane cation. A time-dependent wave packet (WP) propagation method is utilised where the WPs are prepared for each initial vibrational state of the neutral species of the title cation and its deuteriated isomer. The ratio of the squared of the nuclear autocorrelation functions (ACFs) of CD and CH on the lowest potential sheet of the state are calculated in full dimensionality, including nonadiabatic coupling of the three electronic sheets. The results predict the above ratio to start at unity and then increase with time before passing through a maximum, irrespective of the initial vibrational state. At the first maximum, such a ratio is found to decrease with the number of nodes of the vibrational wave function while the magnitudes of the ACFs of CD and CH diminish gradually with vibrational excitation. This is enhanced by inclusion of further excited vibrational modes. The present results indicate that nuclear motion on the lowest adiabatic sheet of the states of title cation can be slowed down by initial vibrational state excitation.

Quantum Optimal Control of Rovibrational Excitations of a Diatomic Alkali Halide: One-Photon vs. Two-Photon Processes

We investigated the roles of one-photon and two-photon processes in the laser-controlled rovibrational transitions of the diatomic alkali halide, 7Li37Cl. Optimal control theory calculations were carried out using the Hamiltonian, including both the one-photon and two-photon field-molecule interaction terms. Time-dependent wave packet propagation was performed with both the radial and angular motions being treated quantum mechanically. The targeted processes were pure rotational and vibrational–rotational excitations: (v = 0, J = 0) → (v = 0, J = 2); (v = 0, J = 0) → (v = 1, J = 2). Total time of the control pulse was set to 2,000,000 atomic units (48.4 ps). In each control excitation process, weak and strong optimal fields were obtained by means of giving weak and strong field amplitudes, respectively, to the initial guess for the optimal field. It was found that when the field is weak, the control mechanism is dominated exclusively by a one-photon process, as expected, in both the targeted processes. When the field is strong, we obtained two kinds of optimal fields, one causing two-photon absorption and the other causing a Raman process. It was revealed, however, that the mechanisms for strong fields are not simply characterized by one process but rather by multiple one- and two-photon processes. It was also found that in the rotational excitation, (v = 0, J = 0) → (v = 0, J = 2), the roles of one- and two-photon processes are relatively distinct but in the vibrational–rotational excitation, (v = 0, J = 0) → (v = 1, J = 2), these roles are ambiguous and the cooperative effect associated with these two processes is quite large.

Computation of the S1 ← S0 Vibronic Absorption Spectrum of Formaldehyde by Variational Gaussian Wavepacket and Semiclassical IVR Methods.

The vibronic absorption spectrum of the electric dipole forbidden and vibronically allowed S1(1 A2) ← S0(1 A1) transition of formaldehyde is calculated by Gaussian wavepacket and semiclassical methods, along with numerically exact reference calculations, using the potential energy surface of Fu, Shepler, and Bowman ( J. Am. Chem. Soc. 2011, 133, 7957). Specifically, the variational multiconfigurational Gaussian (vMCG) approach and the Herman-Kluk semiclassical initial value representation (HK-SCIVR) are compared to assess the accuracy and convergence of these methods, benchmarked against numerically exact time-dependent wavepacket propagation (TDWP) on the reference potential energy surface. The vMCG calculation is shown to converge quite well with about 100 variationally evolving Gaussian functions and using a local cubic expansion instead of the conventional local harmonic approximation. By contrast, the HK-SCIVR approach with ∼105 trajectories reproduces the vibrationally structured spectral envelope correctly but yields a strongly broadened spectrum. The comparison of the computed absorption spectrum with experiment shows that the relevant vibronic progressions are reasonably reproduced by all computations, but deviations of the order of 10-100 cm-1 occur, underscoring that both electronic structure calculations and dynamical approaches remain challenging in the calculation of typical small-molecule excited-state spectra by trajectory-based methods.

Initial excited state structural dynamics of lumiflavin upon ultraviolet excitation

Excited state photophysics of flavin compounds has attracted great attention due to their involvement in several photobiological processes as a cofactor in photoreceptor enzymes. In this work, we have determined the initial excited state structural dynamics of flavin related compound, lumiflavin (LF), upon ultraviolet (UV) excitation through resonance Raman intensity analysis. A quantitative measurement of resonance Raman cross-sections across the 265 nm absorption band (257–275 nm) of LF have been performed, and Raman excitation profiles (REPs) are constructed for all the Raman active modes. The REPs and absorption cross sections have been simulated using time-dependent wave packet propagation (TDWP) formalism to extract the ultrafast dynamics of LF within 50 fs after photoexcitation. The total internal reorganization energy is estimated to be 470 cm−1, which is clear evidence for the significant structural distortion in the excited state from that of the ground state. By comparing the excited state structural changes between S1 state and 265 nm excited state, we found that different molecular distortions occur following photoexcitation to those two different states. The total reorganization energy is obtained to be 1542 cm−1, in which the maximum contribution comes from the inertial response of water (1070 cm−1). Additionally, our simulation also yields an instantaneous response of the first solvation shell within an ultrafast timescale, τ ∼ 30 fs, following photoexcitation. The current study provides the basis for future investigations to determine the excited state properties of flavin compounds upon UV excitations.

H2/LiF(001) diffractive scattering under fast grazing incidence using a DFT-based potential energy surface

Grazing incidence fast molecule diffraction (GIFMD) has been recently used to study a number of surfaces, but this experimental effort has not been followed, to present, by a subsequent theoretical endeavor. Aiming at filling this gap, in this work, we have carried out GIFMD simulations for the benchmark system H 2 /LiF(001). To perform our study, we have built a six-dimensional potential energy surface (6D-PES) by applying a modified version of the corrugation reducing procedure (CRP) to a set of density functional theory (DFT) energies. Based on this CRP interpolated PES, we have conducted quantum dynamics calculations using both the multiconfiguration time-dependent Hartree and the time-dependent wave packet propagation methods. We have compared the results of our GIFMD simulations with available experimental spectra. From this comparison, we have uncovered a prominent role of the interaction between the quadrupole moment of H 2 and the electric field associated with LiF(001) for specific incidence crystallographic directions. We show that, on the one hand, the molecule's initial rotation strongly affects its diffractive scattering and, on the other hand, the scattering is predominantly rotationally elastic over a wide range of incidence conditions typical for GIFMD experiments.

Ultrafast Nuclear Dynamics of Photoexcited Guanosine-5'-Monophosphate in Three Singlet States.

We report measurement of resonance Raman (RR) spectra of guanosine-5'-monophosphate (GMP), a DNA nucleotide at excitation wavelengths throughout its ππ* absorption band (Bb) in the 210-230 nm range. From these data, we constructed wavelength-dependent Raman intensity excitation profiles (REPs) for all observed modes. These profiles and the absorption spectrum were then modeled using self-consistent simulations based on the time-dependent wave packet propagation formalism. We inferred the initial structural dynamics of GMP immediately after photoexcitation in terms of dimensionless displacements. The simulations also provide linewidth-broadening parameters that in turn report on the time scale of dynamics. We compared deduced structural changes in the purine ring upon photoabsorption into the Bb state with those deduced for the two lowest lying ππ* (La and Lb at 280 and 248 nm, respectively) excited states of GMP. We find that excitation to the Lb state lengthens C6-N1 and C2═N3 bonds, which lie along the formation coordinate of various oxidative adducts but Bb excitation does not. We also find that photoabsorption by the Bb state weakens the C8-N9 bond and thus might assist imidazole ring opening via cleavage of the same bond. Electronic excitation to different ππ* states of the guanine chromophore results in contrasting structural changes; although absorption by the La and Lb states induces expansion of pyrimidine and contraction of imidazole rings, excitation results in overall shrinkage of both the rings. Computed absolute changes in internal coordinates imply that photoexcitation to any of the three singlet states of GMP does not lead directly to the formation of a cation radical of guanine.

Effect of internal excitations of reagent diatom on initial state-selected dynamics of C + OH reaction on its second excited (14A″) electronic state

ABSTRACTInitial state-selected total reaction probabilities and integral reaction cross sections (ICSs) of, C(3P) + OH (X2Π) → CO(a3Π) + H (2S), reaction on its second excited electronic state (14A″) are calculated with the aid of a time-dependent wave packet propagation method within the coupled states approximation. Partial wave contributions for the total angular momentum quantum number, J=0–48, were necessary to obtain converged ICSs for OH (v=0, j=0) upto a collision energy of ∼0.25 eV. In case of rotationally and vibrationally excited OH, many more partial wave contributions had to be included. Dense oscillatory structures are found in total reaction probabilities due to the formation of quasibound collision complexes inside the wells (of depth ∼2.25 eV and ∼1.85 eV) present on the potential energy surface. While reagent vibrational excitation promotes the reaction, no such general trend is found with rotational excitation. The results of the present study are compared with the literature data. Mechanistic details of the C + OH reaction occurring on its ground, first and second excited electronic states are compared and discussed.

Dynamics and resonances of the H(2S) + CH+(X1Σ+) reaction in the electronic ground state: a detailed quantum wavepacket study.

Initial state-selected and energy resolved channel-specific reaction probabilities, integral cross sections and thermal rate constants of the H(2S) + CH+(X1Σ+) reaction are calculated within the coupled states approximation by a time-dependent wave packet propagation method. The new ab initio global potential energy surface (PES) of the electronic ground state (1 2A') of the system, recently reported by Li et al. [J. Chem. Phys., 2015, 142, 124302], is employed for this purpose. All partial wave contributions up to the total angular momentum J = 60 are considered to obtain the converged integral reaction cross section up to a collision energy of 1.0 eV. Thermal rate constants are calculated by averaging the reaction cross sections over the Boltzmann distribution of energies and compared with the available theoretical and experimental results for the temperature range 10-1000 K. Investigation of the channel-specific reaction attributes shows that the H abstraction (CH+ destruction) channel is highly favored over the H exchange channel. The effect of rotational and vibrational excitations of the CH+ reagent on the dynamics is also studied. The resonances formed during the course of the reaction are also identified by calculating the transition state spectrum and characterized in terms of the eigenfunctions and lifetimes. More than 260 vibrational levels are obtained and their eigenfunctions are calculated, which are represented in terms of the nodal assignments and the eigenenergies. They reveal both the local and hyperspherical behavior for the bound and quasibound states of the CH2+ complex in the ground 1 2A' surface. The lifetime analysis of the quasibound states indicates that the CH2+ resonances survive for as long as ∼400 fs at high energies (E ∼ 2.0 eV) and are expected to decay faster with further increasing energy. Finally, the type of mechanism for the formation of the product (C+ + H2) is elucidated.

Photodissociation dynamics of weakly bound HeH2+ in intense light fields

Photoinduced dynamics of a weakly bound triatomic molecule $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ exposed to electromagnetic radiation is investigated by time-dependent quantum wave-packet propagation. Adopting a two-dimensional linear H-H-He model, the three lowest-lying potential energy surfaces (PESs) and corresponding dipole moment surfaces are constructed. One of the two characteristic excited PESs of $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the charge-transfer reaction ${{\mathrm{H}}_{2}}^{+}+\mathrm{He}\ensuremath{\rightarrow}{\mathrm{H}}_{2}+\mathrm{H}{\mathrm{e}}^{+}$ and the other corresponds to the first excited state of ${{\mathrm{H}}_{2}}^{+}$ perturbed by the presence of He. When $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ is exposed to a femtosecond intense ultraviolet light pulse ($I=4\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\mathrm{W}\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}2}, \ensuremath{\lambda}=400\phantom{\rule{0.16em}{0ex}}\mathrm{nm}$), both of the two excited PESs are found to be coupled with the light field and a variety of reaction pathways become opened so that HeH, $\mathrm{He}{\mathrm{H}}^{+}, {\mathrm{H}}_{2},\phantom{\rule{0.16em}{0ex}}{{\mathrm{H}}_{2}}^{+},\phantom{\rule{0.16em}{0ex}}\mathrm{H},\phantom{\rule{0.16em}{0ex}}{\mathrm{H}}^{+}$, He, and $\mathrm{H}{\mathrm{e}}^{+}$ are produced. Simulations also show that the anharmonic coupling between the two stretching vibrational modes in $\mathrm{He}{{\mathrm{H}}_{2}}^{+}$ leads to the stabilization of the ${{\mathrm{H}}_{2}}^{+}$ moiety against the decomposition into $\mathrm{H}+{\mathrm{H}}^{+}$ compared with bare ${{\mathrm{H}}_{2}}^{+}$. The theoretical findings of the formation of $\mathrm{He}{\mathrm{H}}^{+}$ composed of the most abundant elements in the universe are also discussed in view of the theoretical modeling of the chemical reactions proceeding in the primordial gas and in the interstellar medium.

Non-adiabatic effects in the Ã2B2 and states of CH2F2+ through coupling vibrational modes

Vibronic coupling between the two energetically close-lying excited electronic states (Ã2B2 and ) of CH2F2+ is studied in this article. A reduced dimensional model Hamiltonian is constructed in a diabatic representation and using standard vibronic coupling theory. A detailed topographical analysis of the coupled surfaces is presented here and nuclear dynamics study on these surfaces is also studied by using time-dependent wavepacket propagation approach.

Ab Initio Benchmark Study of Nonadiabatic S1-S2 Photodynamics of cis- and trans-Hexatriene.

The dynamics of the nonadiabatically coupled lowest singlet excited states of cis- and trans-hexatriene are studied theoretically, in a comprehensive electronic structure and quantum dynamical investigation. At the ground state equilibrium geometry the relevant S2 and S1 states carry the A1 (Ag) and B2 (Bu) symmetry labels, for the cis (trans) isomer. Various high-level electronic structure methods are used, including the recently reparametrized DFT/MRCI method, and the results are critically compared. Key parameters of interest are the vertical energy gap and the strength of vibronic coupling between the interacting electronic states. To estimate their influence, suitable comparison calculations are performed. The results are used as the basis for quantum dynamical calculations on the UV absorption spectrum and electronic population transfer involving the S1 and S2 states. Up to nine nonseparable degrees of freedom are included in the calculations. The experimental UV absorption spectrum in the 5-5.2 eV energy range can be very well reproduced. The time-dependent wavepacket propagations reveal a population transfer on the order of 30-50 fs, which becomes increasingly complete with more degrees of freedom included in the calculation. The results are briefly compared with analogous data for the s-trans-butadiene system treated by some of us recently.

Quantum wavepacket dynamics of the N([formula omitted]) + NO([formula omitted]) reaction and its isotopic variants: Integral cross sections and thermal rate constants

We investigate the initial state-selected dynamics of the title reaction on its ground (1 3A″) and first excited (1 3A′) triplet potential energy surfaces (PESs) by a time-dependent wavepacket propagation method, employing the ab initio analytical PESs developed by Gamallo et al. (2003). All partial wave contributions up to the total angular momentum J=140 are found to be necessary for the scattering of NO diatom in its vibrational and rotational ground state up to a collision energy ∼0.9eV. The converged initial state-selected reaction attributes viz., reaction probabilities, integral cross sections and thermal rate constants are obtained within the centrifugal sudden (CS) approximation and the convergence of the results are carefully checked by varying all parameters used in the numerical calculations. The dynamical results are compared with the other reported theoretical and experimental findings. Investigation on the energy-resolved channel-specific reaction probabilities infers that the N2 formation channel is very much favorable than the N-exchange channel. The reaction proceeds via some metastable resonances, observed from the oscillatory probability curves, which is more in the latter channel compared to the former. The effect of rotational and vibrational excitations of the reagent (NO diatom) on the dynamics is examined. We also examine the effect of isotopic substitution of N-atom (14N by 15N) on the reaction dynamics.

Dynamic Symmetry Breaking Hidden in Fano Resonance of a Molecule: S1 State of Diazirine Using Quantum Wave Packet Propagation.

Fano resonance in the predissociation of the S1 state of diazirine was studied by applying a time-dependent wave packet propagation method, and dynamic symmetry breaking (DSB) around the stationary structure of S1 was disclosed in a detailed analysis of this theoretical result. The DSB was found to originate in coupling between the asymmetric C-N2 stretching and CH2 wagging modes, suggesting that there is a slight time gap between ring opening and the concurrent dragging of two H atoms of the CH2 moiety. Although the depth of the double well due to DSB is just 0.011 eV, its presence noticeably affects the early time dynamics and observed spectrum.

Photophysics of barrelene: The Jahn-Teller and pseudo-Jahn-Teller effects

The static and dynamic aspects of Jahn-Teller(JT) and pseudo-Jahn-Teller(PJT) interactions between ground (X˜2A2′) and first three excited electronic states (A˜2E′, B˜2E″ and C˜2A′1 ) of bicyclo- [2,2,2]-octa-2,5,7-triene (barrelene) radical cation (Bl+) are theoretically investigated here. This belongs to the (E + E) ⊗ e and (E + A) ⊗ e JT-PJT class of compounds as described by the symmetry of the electronic states and the molecular point group. The complex vibronic dynamics on the coupled electronic states of the cation is simulated by both time-independent and time-dependent wave packet propagation method using multi configuration time-dependent Hartree scheme. The JT effects in the A˜ and B˜ electronic states and the PJT coupling between the B˜ and C˜ electronic states of Bl+ are found very strong. The final theoretical results are compared with the experimental results.

Structural evolution of the methane cation in subfemtosecond photodynamics.

An ab initio quantum dynamics study has been performed to explore the structural rearrangement of ground state CH4 (+) in subfemtosecond resolved photodynamics. The method utilizes time-dependent wave-packet propagation on the X˜(2)T2 electronic manifold of the title cation in full dimensionality, including nonadiabatic coupling of the three electronic sheets. Good agreement is obtained with recent experiments [Baker et al., Science 312, 424 (2006)] which use high-order harmonic generation to probe the attosecond proton dynamics. The novel results provide direct theoretical support of the observations while unravelling the underlying details. With the geometrical changes obtained by calculating the expectation values of the nuclear coordinates as a function of time, the structural evolution is predicted to begin through activation of the totally symmetric a1 and doubly degenerate e modes. While the former retains the original Td symmetry of the cation, the Jahn-Teller active e mode conducts it to a D2d structure. At ∼1.85 fs, the intermediate D2d structure is further predicted to rearrange to local C2v minimum geometry via Jahn-Teller active bending vibrations of t2 symmetry.