Trajectory Surface Hopping Calculations Research Articles

Imaging the state-to-state charge-transfer dynamics between the spin-orbit excited Ar+(2P1/2) ion and N2

Ar++N2 → Ar+N2+ has served as a paradigm for charge-transfer dynamics studies during the last several decades. Despite significant experimental and theoretical efforts on this model system, state-resolved experimental investigations on the microscopic charge-transfer mechanism between the spin-orbit excited Ar+(2P1/2) ion and N2 have been rare. Here, we measure the first quantum state-to-state differential cross sections for Ar++N2 → Ar+N2+ with the Ar+ ion prepared exclusively in the spin-orbit excited state 2P1/2 on a crossed-beam setup with three-dimensional velocity-map imaging. Trajectory surface-hopping calculations qualitatively reproduce the vibrationally dependent rotational and angular distributions of the N2+ product. Both the scattering images and theoretical calculations show that the charge-transfer dynamics of the spin-orbit excited Ar+(2P1/2) ion differs significantly from that of the spin-orbit ground Ar+(2P3/2) when colliding with N2. Such state-to-state information makes quantitative understanding of this benchmark charge-transfer reaction within reach.

Imaging of the charge-transfer reaction of spin-orbit state-selected Ar+(2P3/2) with N2 reveals vibrational-state-specific mechanisms.

Charge-transfer reactions are ubiquitous and play important roles in various gaseous environments, but, despite a long history of extensive research, our understanding of their dynamics at the quantum state-to-state level is still lacking. Here we report quantum-state-resolved experiments for the paradigmatic charge-transfer reaction Ar+ + N2 → Ar + N2+ using a three-dimensional velocity-map imaging crossed-beam apparatus with the Ar+ beam prepared exclusively in the spin-orbit state 2P3/2. High-resolution scattering images show strong dependence of rotational and angular distributions on the vibrational quantum number of the N2+ product. Trajectory surface-hopping calculations, which semi-quantitatively reproduce the experimental observations, support the existence of two distinct charge-transfer mechanisms. One of these, in the dominant N2+(v' = 1) channel, is the well-known long-distance harpooning mechanism. However, the highly rotationally excited products in the forward direction are attributed to a hard-collision glory scattering mechanism, which occurs on account of the strong attraction between the collisional partners counterbalanced by the short-range repulsive interaction.

New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conventional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin-orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Ultrafast Ring Closure Reaction of Gaseous cis-Stilbene from S1(ππ*)

cis-Stilbene (cis-St) is a well-known benchmark system for cis-trans photoisomerization. cis-St also produces 4a,4b-dihydrophenanthrene (DHP) in solution with a quantum yield of less than 0.19. The ring closure reaction, however, has never been identified for gaseous cis-St, and a recent computational simulation predicted the quantum yield of DHP to be only 0.04. In the present study, we identified an ultrafast ring closure reaction of gaseous cis-St for the first time using extreme ultraviolet time-resolved photoelectron spectroscopy. Surface hopping trajectory calculations at the SA3-XMS-CASPT2(2,2) level of theory reproduce the features of the observed time-resolved photoelectron spectra and predict the cis-St:DHP:trans-St branching ratio to be 0.55:0.41:0.04, in contrast with previous estimates. The results indicate that photoexcited cis-St favors ring closure over cis-trans isomerization under the isolated condition.

Strong Field Double Ionization of Formaldehyde Investigated Using Momentum Resolved Covariance Imaging and Trajectory Surface Hopping.

We use covariance velocity map imaging of fragment ions from the strong field double ionization of formaldehyde in conjunction with trajectory surface hopping calculations to determine the ionization yields to different singlet and triplet states of the dication. The calculated kinetic energy release for trajectories initiated on different electronic states is compared with the experimental values based on momentum resolved covariance measurements. We determine the state resolved double ionization yields as a function of laser intensity and pulse duration down to 6 fs (two optical cycles).

Non-adiabatic couplings induced complex-forming mechanism in H+MgH+ → Mg++H2 reaction

A chemical process may involve multiple adiabatic electronic states, and non-adiabatic couplings play an important role in the reaction mechanism. In this work, the effect of non-adiabatic couplings in the H+MgH+ → Mg+ + H2 reaction are studied using the time-dependent wave packet method and trajectory surface hopping method. The calculated results show that the reaction follows a direct abstraction process when the non-adiabatic couplings are neglected. However, when non-adiabatic couplings are included in the calculations, a long-lived excited state complex (MgH2+)* can be formed during the reaction. These direct and complex-forming reaction pathways are revealed by trajectory surface hopping calculations. The non-adiabatic couplings induced complex-forming mechanism not only increases the reactivity but also has significant effect on the product vibrational state distribution.

Quasiclassical Trajectory Study of the O(3P) + CO2(1Σg+) Reaction at Hyperthermal Energies

This paper presents the reaction mechanism, cross sections, and product energy partitioning for the O + CO2 reaction, calculated using Born-Oppenheimer molecular dynamics simulations with the quasiclassical trajectory (BOMD-QCT) method. At collision energies up to 9.5 eV, three reactions, oxygen exchange (above ∼1.5 eV), abstraction (above ∼5.5 eV), and dissociation (above ∼7.5 eV) occur, with abstraction and dissociation involving either an insertion-elimination mechanism or a stripping mechanism. The insertion-elimination mechanism involves the formation of a planar CO3 intermediate which lies 0.52 eV above the ground-state CO2; the energetic barrier for oxygen abstraction via this mechanism is 3.52 eV. Interestingly, the insertion-elimination mechanism predominately contributes to the cross sections at collision energies just above the effective energetic threshold for the abstraction and dissociation reactions; at higher collision energies, the contribution from the stripping mechanism increases and eventually dominates. At a collision energy of 9.5 eV, the cross sections for oxygen exchange, abstraction, and dissociation are 4.17 a02, 1.58 a02, and 0.68 a02, respectively. The lower reaction cross sections, higher effective reaction barrier, and product energy distribution of the stripping mechanism were attributed to the short lifetime (28 fs) of the OCOO species compared with that of the CO3 species (45 fs) that arises in the insertion-elimination mechanism. For the exchange reaction, it is found that roughly 40% of the reactant translational energy ends up in CO2 vibration, which provides a single-collision mechanism to produce highly excited CO2. We also studied intersystem crossing effects using trajectory surface hopping calculations and find no changes compared to single surface (triplet) calculations at energies below 7.5 eV; however, at 7.5 eV and higher the abstraction cross sections are changed by as much as 20%, and the (very small) dissociation cross sections are changed by factors of four or more.

Computational Investigation on ESIPT-driven Luminescence of Imidazo[1,2-a]pyridine Derivatives Regulated by Inter/Intramolecular Hydrogen bonding

The three newly synthesized imidazopyridine derivatives bearing inter/intramolecular hydrogen bond were computationally investigated. The quasi stable seven-membered ring systems of the compounds assisted by the intramolecular hydrogen bond exhibited distinct luminescence depending on the surrounding media; in solution, in frozen solution and in solid state. The interesting luminescent properties were studied by means of a series of quantum chemical calculations; i.e., DFT, TDDFT, CASSCF/CASPT2, ADC(2), CC2 and CCSD(T). The stability of the quasi π-conjugated rings was found to be regulated by the delicate balance between intramolecular steric hindrance and intra/intermolecular hydrogen bond strength. The excited state dynamics was explored by the surface hopping trajectory calculations which reproduced the ESIPT process in the first excited singlet state.

Excited-state dynamics of CH2I2 and CH2IBr studied with UV-pump VUV-probe momentum-resolved photoion spectroscopy.

We perform time-resolved ionization spectroscopy measurements of the excited state dynamics of CH2I2 and CH2IBr following photoexcitation in the deep UV. The fragment ions produced by ionization with a vacuum-ultraviolet probe pulse are measured with velocity map imaging, and the momentum resolved yields are compared with trajectory surface hopping calculations of the measurement observable. Together with recent time-resolved photoelectron spectroscopy measurements of the same dynamics, these results provide a detailed picture of the coupled electronic and nuclear dynamics involved. Our measurements highlight the non-adiabatic coupling between electronic states, which leads to notable differences in the dissociation dynamics for the two molecules.

Excited state dynamics of cis,cis-1,3-cyclooctadiene: UV pump VUV probe time-resolved photoelectron spectroscopy.

We present UV pump, vacuum ultraviolet probe time-resolved photoelectron spectroscopy measurements of the excited state dynamics of cis,cis-1,3-cyclooctadiene. A 4.75 eV deep UV pump pulse launches a vibrational wave packet on the first electronically excited state, and the ensuing dynamics are probed via ionization using a 7.92 eV probe pulse. The experimental results indicate that the wave packet undergoes rapid internal conversion to the ground state in under 100 fs. Comparing the measurements with electronic structure and trajectory surface hopping calculations, we are able to interpret the features in the measured photoelectron spectra in terms of ionization to several states of the molecular cation.

Excited state dynamics of CH2I2 and CH2BrI studied with UV pump VUV probe photoelectron spectroscopy.

We compare the excited state dynamics of diiodomethane (CH2I2) and bromoiodomethane (CH2BrI) using time resolved photoelectron spectroscopy. A 4.65 eV UV pump pulse launches a dissociative wave packet on excited states of both molecules and the ensuing dynamics are probed via photoionization using a 7.75 eV probe pulse. The resulting photoelectrons are measured with the velocity map imaging technique for each pump-probe delay. Our measurements highlight differences in the dynamics for the two molecules, which are interpreted with high-level ab initio molecular dynamics (trajectory surface hopping) calculations. Our analysis allows us to associate features in the photoelectron spectrum with different portions of the excited state wave packet represented by different trajectories. The excited state dynamics in bromoiodomethane are simple and can be described in terms of direct dissociation along the C-I coordinate, whereas the dynamics in diiodomethane involve internal conversion and motion along multiple dimensions.

Performance of trajectory surface hopping method in the treatment of ultrafast intersystem crossing dynamics.

We carried out extensive studies to examine the performance of the fewest-switches surface hopping method in the description of the ultrafast intersystem crossing dynamic of various singlet-triplet (S-T) models by comparison with the results of the exact full quantum dynamics. Different implementation details and some derivative approaches were examined. As expected, it is better to perform the trajectory surface hopping calculations in the spin-adiabatic representation or by the local diabatization approach, instead of in the spin-diabatic representation. The surface hopping method provides reasonable results for the short-time dynamics in the S-T model with weak spin-orbital coupling (diabatic coupling), although it does not perform well in the models with strong spin-orbital coupling (diabatic coupling). When the system accesses the S-T potential energy crossing with rather high kinetic energy, the trajectory surface hopping method tends to produce a good description of the nonadiabatic intersystem crossing dynamics. The impact of the decoherence correction on the performance of the trajectory surface hopping is system dependent. It improves the result accuracy in many cases, while its influence may also be minor for other cases.

QM/MM Photodynamics of Retinal in the Channelrhodopsin Chimera C1C2 with OM3/MRCI

AbstractThe photoisomerization of all‐trans retinal in channelrhodopsins triggers the opening of a cation channel in the membrane of certain green algae. The stimulus resulting from cell depolarization enables the algae to perceive and react to the present lighting conditions. This property makes channelrhodopsins especially interesting for neuroscientific applications in optogenetics. We investigate the initial photoreaction in the channelrhodopsin chimera C1C2 with a combined quantum mechanical/molecular mechanical (QM/MM) strategy. For geometry optimizations, the OM3/RHF and OM3/MRCI/Amber protocols are used. Trajectory surface hopping calculations are performed with OM3/MRCI/Amber and a statistically relevant number of molecules to obtain reaction rates and quantum yields. The utilized models include a direct hydrogen bond of the retinal Schiff base to the proposed counterions in C1C2, i. e. either toward glutamate or aspartate. Static and dynamic aspects are compared to experimental findings including time constants and spectral traces. The calculations provide a rationale for the observed short and long time components in the photokinetics of C1C2 and yield detailed insight into the photoreaction mechanisms that include bicycle pedal and hula twist motions.

Experimental and theoretical studies of the Xe-OH(A/X) quenching system.

New multi-reference, global ab initio potential energy surfaces (PESs) are reported for the interaction of Xe atoms with OH radicals in their ground X2Π and excited A2Σ+ states, together with the non-adiabatic couplings between them. The 2A' excited potential features a very deep well at the collinear Xe-OH configuration whose minimum corresponds to the avoided crossing with the 1A' PES. It is therefore expected that, as with collisions of Kr + OH(A), electronic quenching will play a major role in the dynamics, competing favorably with rotational energy transfer within the 2A' state. The surfaces and couplings are used in full three-state surface-hopping trajectory calculations, including roto-electronic couplings, to calculate integral cross sections for electronic quenching and collisional removal. Experimental cross sections, measured using Zeeman quantum beat spectroscopy, are also presented here for comparison with these calculations. Unlike similar previous work on the collisions of OH(A) with Kr, the surface-hopping calculations are only able to account qualitatively for the experimentally observed electronic quenching cross sections, with those calculated being around a factor of two smaller than the experimental ones. However, the predicted total depopulation of the initial rovibrational state of OH(A) (quenching plus rotational energy transfer) agrees well with the experimental results. Possible reasons for the discrepancies are discussed in detail.

Dynamics of the C(3P) + Ethylene Reaction: A Trajectory Surface Hopping Study.

The direct dynamics trajectory surface hopping (DDTSH) method has been employed to study the reaction of C(3P) with ethylene (C2H4). Our trajectory simulations show that at a reagent collision energy of 7.36 kcal/mol, there are two possible product channels: propargyl (H2CCCH) + H and carbene (CH2) + acetylene (HCCH). Estimated branching ratios based on trajectory propagations indicate that propargyl radical formation is the dominant channel contributing (94.1 ± 5.2) % of the overall products formation with (5.9 ± 1.7)% contribution from the minor CH2 + HCCH channel. These findings are consistent with earlier experimental observations and theoretical predictions that propargyl (H2CCCH) formation is the dominant channel for the C(3P) + C2H4 collision reaction. Our trajectory simulations, however, unravel five distinctly different dynamical pathways, unlike earlier experimental and theoretical predictions of only two pathways proposed for the formation of propargyl radical, and three different dynamics are followed for the CH2 + HCCH channel (this channel was not detected experimentally). The computed translational energy distribution for the propargyl + H channel is narrower and showed peak maximum at a lower energy compared to the experimental one. While the center of mass product angular distribution based on our trajectory propagation is nearly isotropic in nature indicating formation of long-lived intermediate complexes, the experimental one was reported to be backward-forward distributed with more intensity in the forward direction indicating the formation of an osculating complex. Our trajectory surface hopping calculations confirm that the effect of intersystem crossing (ISC) is not important for the title reaction presumably because of weak spin-orbit coupling values (<10 cm-1) for the (C + C2H4) system. No trace of cyclic products formation was obtained from our trajectory simulations, which however was predicted to be a minor (2%) product channel, experimentally.

Dynamics of Azobenzene Dimer Photoisomerization: Electronic and Steric Effects.

While azobenzenes readily photoswitch in solution, their photoisomerization in densely packed self-assembled monolayers (SAMs) can be suppressed. Reasons for this can be steric hindrance and/or electronic quenching, e.g., by exciton coupling. We address these possibilities by means of nonadiabatic molecular dynamics with trajectory surface hopping calculations, investigating the trans → cis isomerization of azobenzene after excitation into the ππ* absorption band. We consider a free monomer, an isolated dimer and a dimer embedded in a SAM-like environment of additional azobenzene molecules, imitating in this way the gradual transition from an unconstrained over an electronically coupled to an electronically coupled and sterically hindered, molecular switch. Our simulations reveal that in comparison to the single molecule the quantum yield of the trans → cis photoisomerization is similar for the isolated dimer, but greatly reduced in the sterically constrained situation. Other implications of dimerization and steric constraints are also discussed.

Roaming mediated nonadiabatic dynamics in molecular hydrogen elimination from propane at 157 nm

The photofragmentation dynamics study using Tully’s fewest switches trajectory surface hopping calculations, based on MRCIS(6,6)/6-31++G∗∗ potential energy surfaces, energy gradients and nonadiabatic couplings, reveals the occurrence of roaming mediated nonadiabatic pathways for the elimination of molecular hydrogen from propane at 157nm. 1,2- and 1,3-molecular hydrogen eliminations, the minor dissociation channels, exclusively follow roaming (of partially dissociated H atom) mediated nonadiabatic pathway (S1→S0) to the ground electronic state followed by an atomic hydrogen abstraction from another carbon atom in the ground singlet (S0) state. 1,1- and 2,2-molecular hydrogen eliminations on the other hand, the major dissociation processes, proceed either adiabatically in the first excited singlet (S1) electronic state or through the internal conversion S1→S0 followed by direct two-body fragmentation in the ground singlet (S0) state, with equal probability.

Crossed Molecular Beams and Quasiclassical Trajectory Surface Hopping Studies of the Multichannel Nonadiabatic O((3)P) + Ethylene Reaction at High Collision Energy.

The combustion relevant O((3)P) + C2H4 reaction stands out as a prototypical multichannel nonadiabatic reaction involving both triplet and singlet potential energy surfaces (PESs), which are strongly coupled. Crossed molecular beam (CMB) scattering experiments with universal soft electron ionization mass spectrometric detection have been used to characterize the dynamics of this reaction at the relatively high collision energy Ec of 13.7 kcal/mol, attained by crossing the reactant beams at an angle of 135°. This work is a full report of the data at the highest Ec investigated for this reaction. From laboratory product angular and velocity distribution measurements, angular and translational energy distributions in the center-of-mass system have been obtained for the five observed exothermic competing reaction channels leading to H + CH2CHO, H + CH3CO, CH3 + HCO, CH2 + H2CO, and H2 + CH2CO. The product branching ratios (BRs) have been derived. The elucidation of the reaction dynamics is assisted by synergic full-dimensional quasiclassical trajectory surface-hopping calculations of the reactive differential cross sections on coupled ab initio triplet/singlet PESs. This joint experimental/theoretical study extends and complements our previous combined CMB and theoretical work at the lower collision energy of 8.4 kcal/mol. The theoretically derived BRs and extent of intersystem crossing (ISC) are compared with experimental results. In particular, the predictions of the QCT results for the three main channels (those leading to vinoxy + H, methyl + HCO and methylene + H2CO formation) are compared directly with the experimental data in the laboratory frame. Good overall agreement is noted between theory and experiment, although some small, yet significant shortcomings of the theoretical differential cross section are noted. Both experiment and theory find almost an equal contribution from the triplet and singlet surfaces to the reaction, with a clear tendency of the degree of ISC to decrease with increasing Ec and with theory slightly overestimating the extent of ISC.

Surface-hopping trajectories for OH(A(2)Σ(+)) + Kr: extension to the 1A″ state.

We present a new trajectory surface hopping study of the rotational energy transfer and collisional quenching of electronically excited OH(A) radicals by Kr. The trajectory surface hopping calculations include both electronic coupling between the excited 2(2)A' and ground 1(2)A' electronic states, as well as Renner-Teller and Coriolis roto-electronic couplings between the 1(2)A' and 1(2)A″, and the 2(2)A' and 1(2)A″ electronic states, respectively. The new calculations are shown to lead to a noticeable improvement in the agreement between theory and experiment in this system, particularly with respect to the OH(X) rotational and Λ-doublet quantum state populations, compared with a simpler two-state treatment, which only included the electronic coupling between the 2(2)A' and 1(2)A' states. Discrepancies between the predictions of theory and experiment do however remain, and could arise either due to errors in the potential energy surfaces and couplings employed, or due to the limitations in the classical treatment of non-adiabatic effects.

Reaction dynamics of oxygen atoms with unsaturated hydrocarbons from crossed molecular beam studies: primary products, branching ratios and role of intersystem crossing

We review the progress made in the understanding of the dynamics of the reactions of ground state oxygen atoms, O(3P), with unsaturated hydrocarbons (acetylene, ethylene, allene, propyne and propene) which are of great relevance, besides from a fundamental point of view, in combustion chemistry and of interest also in atmosphere- and astro-chemistry. Advances in this area have been made possible by an improved crossed molecular beams (CMBs) instrument with rotating mass spectrometric detection and time-of-flight analysis which features product detection by low-energy electron soft-ionisation for increased sensitivity and universal detection power. This apparatus offers the capability of identifying virtually all primary reaction channels, characterising the dynamics, and determining the branching ratios (BRs) for these polyatomic multichannel nonadiabatic reactions. The reactive scattering results are rationalised with the assistance of theoretical information from other laboratories on the stationary points and product energetics of the relevant ab initio potential energy surfaces (PESs). For the simpler prototypical systems, such as O(3P) + ethylene, detailed comparisons with synergic state-of-the-art quasiclassical trajectory surface-hopping calculations on full dimensional ab initio coupled triplet and singlet PESs have recently been possible. For more complex systems, such as O(3P) + propene, comparisons with the results of synergic statistical calculations of BRs on ab initio coupled triplet and singlet PESs, have also been carried out very recently. The combined experimental/theoretical approach has allowed for a better understanding of the mechanism of these reactions. And overall has deepened considerably our understanding of chemical reactivity; in addition, these studies provide an important bridge between CMBs dynamics and thermal kinetics as well as valuable information for improving combustion and astrochemistry models.