Nonadiabatic Interactions Research Articles

Recurring Molecular Alignment Induced by Pulsed Nonresonant Laser Fields

We examine the rotational wavepackets created by the nonadiabatic interaction of a linear molecule with a pulsed nonresonant laser field. We map out the recurrences of the wavepackets and of the concomitant alignment as a function of the duration and intensity of the laser pulse. We derive an analytic solution to the time-dependent Schrödinger equation in the short-pulse limit and find it to agree quantitatively with our numerical computations. This indicates that the recurrences are favored under an impulsive transfer of action from the radiative field to the molecule. The recurring wavepackets afford field-free alignment of the molecular axis.

2+1 resonance-enhanced multiphoton ionisation spectroscopy of the high ν2 levels of the [formula omitted] Rydberg state of NH 3(ND 3)

2+1 resonance-enhanced multiphoton ionisation spectra of the B ̃ 1 E″– X ̃ 1 A 1 2 0 n (n⩾6) transitions of NH 3(ND 3) have been recorded, and the room temperature spectra rotationally analysed. The variation with ν 2 of the spectroscopic parameters is discussed. An increased rate of predissociation is observed for the 2 0 11 and 2 0 12 bands of NH 3. This is attributed to a non-adiabatic interaction with a nearby state of A 2″ electronic symmetry, most probably the D ̃ ′1 A 2″ (4 sa 1 ′) Rydberg state enhancing the rate of the known B ̃ 1 E″⇒ A ̃ 1 A 2″ predissociation mechanism.

Numerical techniques for the evaluation of non-adiabatic interactions and the generation of quasi-diabatic potential energy surfaces using configuration interaction methods

CI techniques, based on nearly complete expansions over determinants for subsets of molecular orbitals and electrons, have been extended to evaluate, by finite differences, non-adiabatic interactions arising from the nuclear kinetic energy operator. A functional of the non-adiabatic interactions is defined and, from the minimum condition of the functional, a simple expression is obtained for the transformation matrix to the quasi-diabatic basis. Two different schemes for the minimization of the functional, with and without constraints to the form of the transformation matrix, have been compared. Simple tests are presented to verify the numerical accuracy of the non-adiabatic interactions and to compare the two schemes for the minimization of the functional.

Numerical techniques for the evaluation of non-adiabatic interactions and the generation of quasi-diabatic potential energy surfaces using configuration interaction methods

Numerical techniques for the evaluation of non-adiabatic interactions and the generation of quasi-diabatic potential energy surfaces using configuration interaction methods

Probing the effect of the H2 rotational state in O(1D)+H2→OH+H: Theoretical dynamics including nonadiabatic effects and a crossed molecular beam study

Theoretical estimates of reactive cross sections for O(1D)+H2(X,v=0,j)→OH(X)+H(2S), with H2 rotational quantum numbers j=0 and 1, are obtained for a range of collision energies, Ecol. Crossed molecular beam measurements are also used to infer the ratio, r1,0, of the j=1 and 0 cross sections at Ecol=0.056 eV. The theory indicates that the 1 1A′ potential surface is the most important one. However, the 2 1A′ and 1 1A″ surfaces can also contribute. Adiabatic dynamics on the 1 1A″ surface, particularly at Ecol above its 0.1 eV barrier to reaction plays a role. The 2 1A′ surface, while not correlating with ground electronic state products, can still lead to products via nonadiabatic interactions with the 1 1A′ surface. Many quantum dynamics and quasiclassical classical trajectory calculations are carried out. Accurate, ab initio based potential energy surfaces are employed. Quantum cross sections are based on helicity decoupled wave packet calculations for several values of total angular momentum. Nonadiabatic wave packet and trajectory surface hopping calculations, where appropriate, are carried out. An interesting, subtle picture emerges regarding the energy dependence of r1,0. The theoretical results indicate, somewhat surprisingly, that, for Ecol<0.1 eV,r1,0 can be less than unity owing to the anisotropy of the ground state potential. Electronically excited states and nonadiabatic effects contribute to the overall cross sections for Ecol>0.1 eV, but the full r1,0 is only weakly sensitive to excited states. Our experimentally inferred r1,0 at Ecol=0.056 eV, 0.95±0.02, is in quantitative agreement with our best calculation, which suggests that the effect of potential anisotropy is correctly described by theory. The relation between these results and previous experimental findings is discussed.

Time- and frequency-resolved spontaneous emission: Theory and application to the NO2 X̃ 2A′/Ã 2A′ conical intersection

We present a theoretical scheme for the calculation of time- and frequency-resolved spontaneous emission spectra of nonstationary states prepared by a laser pulse, considering explicitly the effect of the frequency filter and the time gate of the measurement instrument. Our scheme treats in a perturbative manner the matter-radiation interaction taking into account the states radiative lifetimes, and utilize the eigenstates of the molecular Hamiltonian up to the maximum excitation energy. We study the fluorescence of a nonstationary state of NO2 created by a Gaussian pulse mainly on the à 2A′ excited adiabatic potential, following an absorption from the ground adiabatic electronic state X̃ 2A′. We analyze the X̃ 2A′/à 2A′ conical intersection effects on the spectra and dynamics in a 2A1(ground)/2B2 (excited) diabatic electronic representation. We have pointed out that the wave packet emits more strongly at times corresponding to partial recurrences, i.e., when it returns to the region of space where it was initially, and that the whole spectrum is red-shifted. The nonadiabatic interactions between the electronic states bring the wave packet from the bright 2B2 state to the quasi-dark 2A1 one, and thus they quench the oscillations of the total emitted energy. Moreover, they cause the broadening of the part of the wave packet that remains on the upper diabatic surface, and this results in a further quenching of the emission. On the contrary, the nonadiabatic interactions have a negligible effects on the times at which the emission peaks occur. The striking effect of the duration of the interval in which the time-gate is opened on the time- and frequency-resolved emission is investigated and discussed.

Charge recombination in contact ion pairs

A theoretical explanation of the recently observed non-Marcus free energy gap dependence of the charge recombination rate in contact ion pairs is presented. The electron transfer event is described as a nonadiabatic depopulation of the initially excited adiabatic state. This model explains the absence of the normal region. Quantitative predictions based on the perturbation theory in the nonadiabatic interaction show good agreement with experimental results.

An ab initio study of spectroscopy and predissociation of ClO

We have computed all the electronic states of ClO arising from the Cl(2P)+O(3P) dissociation limit and several of those connected with Cl(2P)+O(1D). Only two excited states have attractive potentials, A 2Π and 1 4Σ−. The A 2Π state undergoes a well known predissociation, because several as yet unknown potential curves cross the A 2Π one and are coupled to it by nonadiabatic and/or spin-orbit interactions. The calculation of the interaction matrix elements allows to explain the predissociation of A 2Π, due to transitions to the 3 2Π, 12Δ, 2 4Σ− and other less important states, all leading to the Cl(2P)+O(3P) dissociation.

Calculation of Normal Vibrations of the Tetraazaporphin Molecule and Interpretation of Quasiline Spectra

Quasiline fluorescence and fluorescence-excitation spectra of tetraazaporphin and its N-deuterated derivative in n-octane at 77 K have been investigated, and the frequencies of normal vibrations in electronic states S0 and S1 have been determined. Calculation of normal vibrations of these molecules has been done and, on its basis, the experimental data are interpreted. It is shown that in the spectra, predominantly the totally symmetric vibrations of type Ag symmetry of the point D2h symmetry group are active. Some activation of the nontotally symmetric B1g vibrations in the fluorescence-excitation spectra is explained by the nonadiabatic interaction of the vibrational sublevels of the excited electronic state S1 with the purely electronic level S2.

Potential Energy Surface of the à State of NH2 and the Role of Excited States in the N(2D) + H2 Reaction

We present a global potential energy surface for the à state of NH2 (12A‘) based on application of the reproducing kernel Hilbert space (RKHS) interpolation method to high-quality ab initio (multireference configuration−interaction) results. This surface correlates adiabatically to the a1Δ state of NH, with a reaction endoergicity of about 8 kcal/mol, but it can also lead to formation of ground-state NH (exoergic by 29 kcal/mol) via nonadiabatic (Renner−Teller) interactions for linear HNH geometries that lie near the bottom of a 94 kcal/mol deep well that is accessible from N(2D) + H2 by insertion over a 3.4 kcal/mol barrier. This insertion barrier is about 1 kcal/mol higher in energy than the corresponding insertion barrier associated with the ground state of NH2(12A‘ ‘). As a result, the à state contributes measurably to both the thermal rate constant for N(2D) + H2 and the rate for NH(a1Δ) production. Extensive quasiclassical trajectory calculations are performed on the RKHS surface to study the N(2D) + H2 reaction dynamics, with the nonadiabatic rate constant estimated using a capture model. We find that the cross section for ground-state NH production is comparable to that obtained on the ground-state 1A‘ ‘ surface, except for a 1 kcal/mol shift upward in the effective threshold due to the different barrier height. The cross section for NH(a1Δ) production has a higher threshold energy and is about 15% of the ground-state cross section at energies well above threshold.

Nonadiabatic transitions: what we learned from old masters and how much we owe them.

This chapter discusses the impact of two-state models of nonadiabatic coupling by Landau, Zener, Stuckelberg, Rosen, and Teller on the current theory of nonadiabatic interaction. In particular, the idea of analytical continuation of classical dynamical variables into complex-valued phase space and time is emphasized. The development of the basic models over the past 30 years has provided us with a useful means of investigating the nonadiabatic molecular dynamics; this is illustrated by the references to our earlier and most recent work.

Experimental and theoretical investigation of theHH¯1Σg+state inH2,D2,and HD, and theB″B¯1Σu+state in HD

525-27 for D2 , v521-23 for HD!. A second tunable laser in the range 550-735 nm was used to excite the Hlevels in the isotopomers H2 ,D 2, and HD. A third laser at 355 nm probed the excitation of the Hlevels by dissociative ionization, producing ions for signal detection. For H 2 82 quantum levels were calibrated (v52 -15, J5 0-5 ! and 107 levels for D2 (v56 -22, J5 0-5 !. These level energies are compared with ab initio calculations including adiabatic and relativistic effects. Agreement between observation and calculation is of the order of 1 cm 21 for H2 and 0.5 cm 21 for D2 throughout the rovibrational manifold. In the HD isotopomer the H ¯1 S g state nonadiabatically interacts with the B1 S u state. This mixing represents an example of strong g-u symmetry breaking. Apart from Hlevels ( v54 -19, J5 0-3 ! also Blevels ( v59 -20, J5 0-3 ! were observed. Theoretical results for HD account for the nonadiabatic interaction with the Bstate, based on a new ab initio calculation of the B9B1 S u potential and the coupling with the HH ¯1 S g state. Except for some levels near the potential barrier also for HD the experimentally calibrated levels agree with the ab initio calculated energies within 1.5 cm 21 . @S1050-2947~99!06007-2#

Resonance-enhanced two-photon dissociation ofH2through nonadiabatically coupled intermediate and final states

Nonperturbative time-dependent calculations of the resonance-enhanced two-photon dissociation probability of ${\mathrm{H}}_{2}$ in two frequency laser fields from the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}(v=0,j=0)$ level to the final continua of $\mathrm{GK}{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $I{}^{1}{\ensuremath{\Pi}}_{g}$ states have been made as functions of the laser frequencies. The two fields are taken to have linear parallel polarizations with identical sine-squared time dependences of the amplitudes. The first field of frequency ${\ensuremath{\omega}}_{1}$ is near resonant with the two closely spaced excited intermediate levels $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}(v=14,j=1)$ and $C{}^{1}{\ensuremath{\Pi}}_{u}^{+}(v=3,j=1),$ which are strongly coupled to each other through nonadiabatic interaction as well as by radiative Raman coupling. Thus two intermediate levels with mixed ${\ensuremath{\Sigma}}^{+}\ensuremath{-}{\ensuremath{\Pi}}^{+}$ character are created. The molecule finally dissociates through coherent excitation to a number of near-resonant discrete rovibrational bound levels of $H\overline{H}{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ and $J{}^{1}{\ensuremath{\Delta}}_{g}^{+}$ embedded into the continua of GK and I states as well as by direct transition to these continua, by absorption of a second photon of frequency ${\ensuremath{\omega}}_{2}.$ The nonadiabatic interactions of the bound levels of $H\overline{H}$ and J states, with the respective continuum of GK and I states, give these levels a predissociating character. The interference of the direct transition amplitudes to the continua, and those through the various overlapping predissociating resonances, gives rise to a resultant structure in the dissociation probability with the variation of ${\ensuremath{\omega}}_{2}.$ The bound levels used are either (a) a group of three closely spaced vibrational-rotational levels, $H\overline{H}{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ $(v=4,$ $j=0$ and 2), $J{}^{1}{\ensuremath{\Delta}}_{g}(v=4,j=2);$ and (b) the next group of three closely spaced levels, $H\overline{H}{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ $(v=5,$ $j=0$ and 2), $J{}^{1}{\ensuremath{\Delta}}_{g}(v=5,j=2).$ Far from resonance with any predissociating level, the dissociation probability becomes equal to the value obtained by considering only the direct transitions to the continua. For different fixed values of ${\ensuremath{\omega}}_{1},$ the variation of the dissociation probability against ${\ensuremath{\omega}}_{2}$ reflects the characteristics of the excitation of the intermediate resonances with mixed B and C character. On or near resonance, the excitation of the predissociating levels of the J electronic state plays a crucial role in determining the dissociation line shape, whereas the excitation of the predissociating levels of the $H\overline{H}$ electronic state do not affect the dissociation line shape significantly.

Nonadiabatic interaction effects on population transfer inH2by stimulated Raman transition with partially overlapping laser pulses

We have theoretically investigated the population transfer in a four-level ${\mathrm{H}}_{2}$ system by stimulated Raman transition from the ground $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}({\ensuremath{\nu}}_{g}{=0,J}_{g}=0)$ level to higher rovibrational levels $({\ensuremath{\nu}}_{f}{,J}_{f})$ of the $X{}^{1}{\ensuremath{\Sigma}}_{g}^{+}$ state via the excited intermediate $B{}^{1}{\ensuremath{\Sigma}}_{u}^{+}({\ensuremath{\nu}}_{i}{=14,J}_{i}=1)$ and $C{}^{1}{\ensuremath{\Pi}}_{u}^{+}({\ensuremath{\nu}}_{i}{=3,J}_{i}=1)$ levels coupled with each other by nonadiabatic interaction, using time-dependent overlapping pump and Stokes laser fields. The density-matrix treatment, which permits the convenient inclusion of the spontaneous emissions from the intermediate levels, has been employed to describe the dynamics of the two-photon Raman resonance process. The present study performs the calculations of final populations (after both the pulses are over) of the ground and terminal levels for Q-branch ${(J}_{f}=0)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ and first overtone $({\ensuremath{\nu}}_{f}=2)$ transitions and the S-branch ${(J}_{f}=2)$ fundamental $({\ensuremath{\nu}}_{f}=1)$ transition as a function of time delay between the two pulses for the cases of on-resonance as well as off-resonance excitations in a wide range $(2\ifmmode\times\else\texttimes\fi{}{10}^{5}--2\ifmmode\times\else\texttimes\fi{}{10}^{7}{\mathrm{W}/\mathrm{c}\mathrm{m}}^{2})$ of peak intensities ${I}_{P}^{0}$ ${(I}_{S}^{0})$ of the pump (Stokes) fields. Both fields are assumed to have the same temporal shape, duration, peak intensities, and linear parallel polarizations. The accurate values of spontaneous radiative relaxation rates of the intermediate levels to the initial and final levels, taking into account their J and M dependence, are explicitly included in our calculations. The pulse width (full width at half maximum) ${\ensuremath{\tau}}_{p}$ is taken as 170 ns so that total spontaneous decay can occur during the pulse duration. The transfer efficiency is found to be very sensitive to the peak intensities of the laser pulses in each case of transition considered. Special attention is paid to the effects of the nonadiabatic (NA) interaction between $B(14,1)$ and $C(3,1)$ levels on population transfer efficiency. Calculations are also done in some particular cases using the adiabatic Born-Oppenheimer (ABO) approximation. The results with ABO approximation are found to differ remarkably from those obtained including NA interaction. Our calculations for the four-level ${\mathrm{H}}_{2}$ system reveal that almost complete population is transferred in counterintuitive pulse order for both on-resonance and off-resonance excitations with intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$ For intuitive pulse sequence also a large population transfer is achieved for on-resonance excitation at intermediate values of ${I}_{P}^{0}$ ${(I}_{S}^{0})$ and for off-resonance excitation at intermediate and high values of ${I}_{P}^{0}$ ${(I}_{S}^{0}).$

IR-spectroscopy of CO on iron ultrathin films

In contrast to the well-known surface enhanced Raman scattering (SERS) the surface enhanced infrared absorption (SEIRA) of molecules adsorbed on metal island films is hardly investigated. The results of our experiments add at least one important fact for a better understanding of the chemical contribution to SEIRA. Under ultrahigh vacuum conditions we measured IR-transmission spectra of in-situ grown iron films on MgO(001) on which CO was adsorbed. The MgO(001) surface was prepared by cleavage in UHV. Deposition of iron leads to growth of epitaxial islands. After CO exposure IR-transmission spectra taken at normal incidence show strong absorption lines in the C–O stretch region with number, intensities, positions, and shapes dependent on Fe-film morphology and Fe-film thickness. For each of the films under investigation the strongest C–O line shows an asymmetric (Fano-like) shape which reveals non-adiabatic interaction of vibrations with a continuum of other excitations, i.e. free electron transitions. The dynamic dipole moment is enhanced by about two orders regarding adiabatic values. However, with grazing incidence IR reflection spectroscopy of CO on thick and annealed iron films we observe symmetric lines and intensities without any extra enhancement. Obviously, the Fano-like non-adiabatic interaction is somewhat like the chemical effect in SEIRA.

Imaging the alignment angular distribution: State symmetries, coherence effects, and nonadiabatic interactions in photodissociation

We establish a rigorous theoretical connection between measurements of the angular distribution of atomic photofragment alignment and the underlying dynamics of molecular photodissociation. We derive laboratory and molecular-frame angular momentum state multipoles as a function of photofragment recoil angles. These state multipoles are expressed in terms of alignment anisotropy parameters, which provide information on state symmetries, coherence effects, and nonadiabatic interactions. The method is intended for analysis of experimental data obtained with two-photon spectroscopy and ion imaging techniques, although it is readily modified for treating Doppler or time-of-flight mass spectrometer peak profiles. We have applied this method to the photodissociation of Cl2 at 355 nm, where we observe strong alignment in the ground state chlorine atom photofragments. Our analysis demonstrates that there are important contributions to the alignment from both incoherent and coherent perpendicular excitation. We also show that the existence of atomic alignment due to coherence requires that nonadiabatic transitions occur at long range.

Potential energy curves of ICl and non-adiabatic interactions studied by the spin-orbit CI method

Excited state potential curves of ICl have been obtained by the spin–orbit CI method to describe the non-adiabatic interactions. Variations of each wavefunction are analyzed and three avoided crossings are characterized between 0 +(III)/0 +(IV), 0 +(II)/0 +(IV), and 0 +(II)/0 +(III) at R=2.85, 3.14 and 3.62 Å, respectively. The second avoided crossing, that was suggested before by Tiemann et al. is proved here for the first time. Our 1Π 1, 1(II) state crosses with the B state just inside the second avoided crossing, supporting the experimental analyses made by Gordon et al. and Tiemann et al. Applying to the B state photodissociation, our potential curves yield the wavelength dependence of the branching ratios, I( 2P 3/2)+Cl( 2P 3/2)/I( 2P 3/2)+Cl( 2P 1/2), in good agreement with experimental results. Photodissociation from the second absorption band is also discussed based on our theoretical and recent experimental results.

Observation of the I′ 1Πg outer well state in H2 and D2

We observed bound levels of the I′ state in H2 and D2, confined in the outer well of the lowest Πg1 adiabatic potential close to its (1s+2p) dissociation limit, with an equilibrium internuclear distance of ≈8 a.u. Rovibronic levels (v=0–2, J=1–5 for H2 and v=0–5, J=1–6 for D2) are populated with pulsed lasers in resonance enhanced XUV+IR (extreme ultraviolet+infrared) excitation, and probed by a third laser pulse. Level energies are measured with an accuracy of ≈0.03 cm−1, and are in reasonable agreement with predictions from ab initio calculations in adiabatic approximation; the smallness of Λ-doublet splitting indicating that nonadiabatic interactions with Σg+1 states are generally weak. Additional resonances are observed close to the n=2 dissociation limit, some of which can be assigned as high vibrational levels of the EF 1Σg+ state.

Complete g– u symmetry breaking in highly excited valence states of the HD molecule

We performed a study of rovibrational energy levels of the H ̄ 1Σ + g and B ̄ 1Σ + u states in HD in a three-photon experiment involving extreme ultraviolet (XUV), visible, and ultraviolet laser radiation. An analysis of level shifts with respect to adiabatic energies, deduced from level energies in H 2 and D 2, shows strong non-adiabatic interaction between these two states, implying complete g– u symmetry breaking over a wide range of v and J quantum numbers.

Quantum and semiclassical dynamics of differential optical collisions

We apply quantum and semiclassical theories to differential optical collisions Na(32S1/2) + Kr + Na(32P1/2,3/2) + Kr. Our results provide a basis to analyze recent experiments in which for the first time optical collisions were investigated with angular resolution under crossed-beam conditions. A characteristic feature of the differential cross sections is the pronounced oscillatory structure due to interferences of different Condon paths. These Stueckelberg oscillations form an extremely sensitive probe of the collisional dynamics and of the molecular interactions. We demonstrate perspectives to determine geometric properties of the collision complex by excitation with polarized light. By final state analysis nonadiabatic (spin-orbit, rotational) interactions can be studied with complete control of the path. In summary it is shown that the method of differential detection of optical collisions opens a variety of new accesses to atomic and molecular subcollisions.