Isotopic fractionation in the photodissociation of N
could explain the considerable variation in the
N/
N ratio in different regions of our galaxy. We previously proposed that such an isotope effect ...is due to coupling of photoexcited bound valence and Rydberg electronic states in the frequency range where there is strong state mixing. We here identify features of the role of the mass in the dynamics through a time-dependent quantum-mechanical simulation. The photoexcitation of N
is by an ultrashort pulse so that the process has a sharply defined origin in time and so that we can monitor the isolated molecule dynamics in time. An ultrafast pulse is necessarily broad in frequency and spans several excited electronic states. Each excited molecule is therefore not in a given electronic state but in a superposition state. A short time after excitation, there is a fairly sharp onset of a mass-dependent large population transfer when wave packets on two different electronic states in the same molecule overlap. This coherent overlap of the wave packets on different electronic states in the region of strong coupling allows an effective transfer of population that is very mass dependent. The extent of the transfer depends on the product of the populations on the two different electronic states and on their relative phase. It is as if two molecules collide but the process occurs within one molecule, a molecule that is simultaneously in both states. An analytical toy model recovers the (strong) mass and energy dependence.
Photodissociation of the nitrogen molecule in the vacuum ultraviolet (VUV) is a major source of reactive nitrogen atoms in the upper atmosphere of Earth and throughout the solar system. Recent ...experimental studies have revealed strong energy dependence of the VUV photodissociation branching ratios to the N(4S3/2)+N(2DJ) and N(4S3/2)+N(2PJ) product channels, the primary dissociation pathways in the 108,000–116,000 cm−1 energy region. This produces N(2DJ) and N(2PJ) excited atoms that differ significantly in their chemical reactivity. The branching ratios oscillate with increase in the VUV excitation energy. We use high-level ab initio quantum chemistry to compute the potential curves of 17 electronic excited states and their nonadiabatic and spin–orbit couplings. The dynamics follow the sequential evolution from the optically excited but bound 1Σu+ singlets. Spin–orbit coupling enables transfer to the dissociative triplet and quintet states. We compute the photodissociation yields through the dense manifold of electronic states leading to both exit channels. The dynamical simulations accurately capture the branching oscillations and enable a detailed look into the photodissociation mechanism. The major contribution to the dissociation is through the two lowest 3Πu states. However, for both isotopomers, at about 110,000 cm−1 there is an abnormally low dissociation rate into the N(4S3/2)+N(2PJ) channel that enables comparable participation of triplet 3Σu− and quintet 5Πu electronic states. This leads to the first peak in the branching ratio. At higher energies, trapping of the population in the 33Πu bound triplet state occurs. This favors dissociation to the lower-energy N(4S3/2)+N(2DJ) channel and results in the observed second switch in branching ratios.
Isotopic fractionation in the photodissociation of N2 could explain the considerable variation in the 14N/15N ratio in different regions of our galaxy. We previously proposed that such an isotope ...effect is due to coupling of photoexcited bound valence and Rydberg electronic states in the frequency range where there is strong state mixing. We here identify features of the role of the mass in the dynamics through a time-dependent quantum-mechanical simulation. The photoexcitation of N2 is by an ultrashort pulse so that the process has a sharply defined origin in time and so that we can monitor the isolated molecule dynamics in time. An ultrafast pulse is necessarily broad in frequency and spans several excited electronic states. Each excited molecule is therefore not in a given electronic state but in a superposition state. A short time after excitation, there is a fairly sharp onset of a mass-dependent large population transfer when wave packets on two different electronic states in the same molecule overlap. This coherent overlap of the wave packets on different electronic states in the region of strong coupling allows an effective transfer of population that is very mass dependent. The extent of the transfer depends on the product of the populations on the two different electronic states and on their relative phase. It is as if two molecules collide but the process occurs within one molecule, a molecule that is simultaneously in both states. An analytical toy model recovers the (strong) mass and energy dependence.
Unraveling the density matrix of a non-stationary quantum state as an explicit function of a few observables provides a complementary view of quantum dynamics. We have recently developed a practical ...way to identify the minimal set of the dominant observables that govern the quantal dynamics even in the case of strong non-adiabatic effects and large anharmonicity Komarova et al., J. Chem. Phys. 155, 204110 (2021). Fast convergence in the number of the dominant contributions is achieved when instead of the density matrix we describe the time-evolution of the surprisal, the logarithm of the density operator. In the present work, we illustrate the efficiency of the proposed approach using an example of the early time dynamics in pyrazine in a Hilbert space accounting for up to four vibrational normal modes, {Q 10a, Q 6a, Q 1, and Q 9a}, and two coupled electronic states, the optically dark B 1 3 u ( n π * ) and the bright B 1 2 u ( π π * ) states. Dynamics in four-dimensional (4D) configurational space involve 19,600 vibronic eigenstates. Our results reveal that the rate of the ultrafast population decay as well as the shape of the nuclear wave packets in 2D, accounting only for {Q 10a,Q 6a} normal modes, are accurately captured with only six dominant time-independent observables in the surprisal. Extension of the dynamics to 3D and 4D vibrational subspace requires only five additional constraints. The time-evolution of a quantum state in 4D vibrational space on two electronic states is thus compacted to only 11 time-dependent coefficients of these observables.
Rapid optical excitation of a molecule produces a nonstationary state localised in the Franck-Condon region. To move out of that region, one needs to propagate both the electronic and the nuclear ...state. We formulate the motion on a grid of nuclear coordinate. The coupling to the electric field is fully included in the Hamiltonian used for propagation. We use perturbation theory to analyse the results of dynamics from one grid point to another. The nonadiabatic coupling terms arise from propagating the electronic states. We apply the formalism to the simple case of a diatomic molecule in an approximate but accurate scheme that allows performing computation on a limited number of grid points. As the coherent dynamics unfolds, we expand the grid in the direction of the wave packet motion with the quantum chemical calculations of the electronic structure performed 'on the fly'. The LiF molecule excited by a one-cycle IR pulse is used as a computational example. The 30-fs propagation through the crossing of the ionic and covalent states is overall adiabatic. The role of electron-nuclear coherences is emphasised.
The vibrational dynamics in a linear triatomic molecule is emulated by a quantum information processing device operating in parallel. The quantum device is an ensemble of semiconducting quantum dot ...dimers addressed and probed by ultrafast laser pulses in the visible frequency range at room temperature. A realistic assessment of the inherent noise due to the inevitable size dispersion of colloidal quantum dots is taken into account and limits the time available for computation. At the short times considered only the electronic states of the quantum dots respond to the excitation. A model for the electronic states quantum dot (QD) dimers is used which retains the eight lowest bands of excitonic dimer states build on the lowest and first excited states of a single QD. We show how up to 8 2 = 64 quantum logic variables can be realistically measured and used to process information for this QD dimer electronic level structure. This is achieved by addressing the lowest and second excited electronic states of the QD’s. With a narrower laser bandwidth (= longer pulse) only the lower band of excited states can be coherently addressed enabling 4 2 = 16 logic variables. Already this is sufficient to emulate both energy transfer between the two oscillators and coherent motions in the vibrating molecule.
On the fly extension of the grid during electron-nuclear dynamics in LiH in different Σ electronic states upon excitation by a 1-cycle IR pulse shown in red.
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•Localized Kinetic energy ...allows quantum dynamical computations on the fly.•Sudden excitation as for few cycle light pulses induces electronic disequilibrium.•On the fly computations track also the electronic multi state dynamics.•The vector potential of the non-adiabatic coupling and its localized form is inherently included.•On the fly computations can be effectively combined with parallel processing.
Multielectronic states quantum dynamics on a grid is described in a manner motivated by on the fly classical trajectory computations. Non stationary electronic states are prepared by a few cycle laser pulse. The nuclei respond and begin moving. We solve the time dependent Schrödinger equation for the electronic and nuclear dynamics for excitation from the ground electronic state. A satisfactory accuracy is possible using a localized description on a discrete grid. This enables computing on the fly for both the nuclear and electronic dynamics including non-adiabatic couplings. Attosecond dynamics in LiH is used as an example.
Abstract
Photodissociation of the nitrogen molecule in the vacuum ultraviolet (VUV) is a major source of reactive nitrogen atoms in the upper atmosphere of Earth and throughout the solar system. ...Recent experimental studies have revealed strong energy dependence of the VUV photodissociation branching ratios to the N(
4
S
3/2
)+N(
2
D
J
) and N(
4
S
3/2
)+N(
2
P
J
) product channels, the primary dissociation pathways in the 108,000–116,000 cm
−1
energy region. This produces N(
2
D
J
) and N(
2
P
J
) excited atoms that differ significantly in their chemical reactivity. The branching ratios oscillate with increase in the VUV excitation energy. We use high-level ab initio quantum chemistry to compute the potential curves of 17 electronic excited states and their nonadiabatic and spin–orbit couplings. The dynamics follow the sequential evolution from the optically excited but bound
1
Σ
u
+
singlets. Spin–orbit coupling enables transfer to the dissociative triplet and quintet states. We compute the photodissociation yields through the dense manifold of electronic states leading to both exit channels. The dynamical simulations accurately capture the branching oscillations and enable a detailed look into the photodissociation mechanism. The major contribution to the dissociation is through the two lowest
3
Π
u
states. However, for both isotopomers, at about 110,000 cm
−1
there is an abnormally low dissociation rate into the N(
4
S
3/2
)+N(
2
P
J
) channel that enables comparable participation of triplet
3
Σ
u
−
and quintet
5
Π
u
electronic states. This leads to the first peak in the branching ratio. At higher energies, trapping of the population in the 3
3
Π
u
bound triplet state occurs. This favors dissociation to the lower-energy N(
4
S
3/2
)+N(
2
D
J
) channel and results in the observed second switch in branching ratios.
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