Large Internuclear Distances Research Articles

Comparison of the nuclear motion in the ultrafast fragmentation of SF 6, CF 4 and CH 3F

Resonant F 1 s excitation of SF 5, CF 4 and CH 3F molecules has been used to initiate ultrafast fragmentation. In all these reactions the fragmentation is fast enough so that atomic-like Auger decay can happen at large internuclear distances. The detection of an atomic-like F 1 s Auger electron allows to focus on the study of this reaction channel. We analyzed the kinetic energy of the F + fragment that is detected after an atomic-like Auger electron has been emitted using high-resolution electron–ion momentum coincidence spectroscopy. In this way we could study the kinetic energy release of the fragmentation as a function of the excitation energy. The results indicate that the nuclear motion within the radical remainder SF 5, CF 3 and CH 3 must be considered to understand the fragmentation dynamics.

Theoretical investigations of the SH + and LiS + cations

Reliable theoretical data on spectroscopy and spin–orbit matrix elements are computed for the lowest electronic states of SH + and LiS + ions. Accurate spectroscopic predictions for their excited electronic states are given. For SH +, polarization minima at large internuclear distances are located in addition to the strongly bound electronic states already known. For LiS +, our calculations confirm that the electronic ground state of this ion is of 3Σ − species and reveal the existence of a 1Δ state presenting a potential well as deep as the potential of the ground state. Moreover, the LiS + electronic excited states potential energy curves possess shallow potential minima in the molecular region and at long-internuclear distances. Generally, these shallow minima may be populated during low energy collisions between the corresponding atomic fragments. Finally, spin–orbit calculations have allowed giving accurate determinations of the spin–orbit splittings for these cations and elucidation of the predissociation mechanisms of SH + leading to the formation of the S + and H species in their electronic ground states. Accordingly, long-lived SH + ions can be found in the X 3Σ −, a 1Δ and b 1Σ + electronic states and the rovibrational levels of LiS + in its electronically excited and ground states should be weakly perturbed.

Strong-field approximation for harmonic generation in diatomic molecules

The generation of high-order harmonics in diatomic molecules is investigated within the framework of the strong-field approximation. We show that the conventional saddle-point approximation is not suitable for large internuclear distances. An adapted saddle-point method that takes into account the molecular structure is presented. We analyze the predictions for the harmonic-generation spectra in both the velocity and length gauges. At large internuclear separations, we compare the resulting cutoffs with the predictions of the three-step semiclassical mechanism. Good agreement is obtained only by using the adapted saddle-point method combined with the velocity gauge.

Validity of the isolated resonance picture forH2autoionizing states

The isolated resonance picture (IRP) is tested by comparing calculations on doubly excited autoionizing states of ${\mathrm{H}}_{2}$ by using two different theoretical approaches: a recent implementation of the exterior complex scaling method and the standard Feshbach method with $B$-spline basis sets. These calculations demonstrate that the IRP can yield poor approximations to autoionization widths when doubly excited states approach the ionization threshold at large internuclear distances, $R$. In contrast, at small $R$ where avoided crossings appear, the IRP produces accurate resonance parameters.

Mechanisms of ultrahigh-order harmonic generation

We analyze mechanisms of high-order harmonic generation from two-center molecules at large internuclear separations in linearly polarized laser fields. Since laser-driven electrons acquire instantaneous kinetic energies of up to 8 times the ponderomotive potential ${U}_{\mathrm{p}}$, recombination at an appropriately placed nucleus leads to ultrahigh-order harmonic emission [P. Moreno, L. Plaja, and L. Roso, Phys. Rev. A 55, R1593 (1997)]. By solving the time-dependent Schr\"odinger equation for model systems, we show that this mechanism is only efficient if the single-particle orbital of the electron is coherently delocalized over the two potential wells. This is realized in the ground state of a one-electron molecular ion. In a neutral molecule or in a molecular ion created by ionization of a neutral molecule at large internuclear distance, the coherence is destroyed by electron-electron correlation.

Incorporation of a wave-packet propagation method into theS-matrix framework: Investigation of the effects of excited state dynamics on intense-field ionization

We propose a theoretical method for investigation of ionization of atoms and molecules in intense laser fields that copes with the effects of excited state dynamics (or intramolecular electronic dynamics). The time-evolving wave packet composed of only bound electronic states, $\ensuremath{\mid}{\ensuremath{\Phi}}_{i}(t)⟩$, is introduced into a framework of the intense-field $S$-matrix theory. Then, the effects of both Coulomb field and radiation field on the bound electron(s) are well described by $\ensuremath{\mid}{\ensuremath{\Phi}}_{i}(t)⟩$, while the effects of a radiation field on a freed electron are also treated in a nonperturbative way. We have applied the theory to ionization of H and $\mathrm{H}_{2}{}^{+}$ in ultrashort intense laser pulses. Although only a small number of Gaussian functions are used in the expansion of $\ensuremath{\mid}{\ensuremath{\Phi}}_{i}(t)⟩$, the present method can quantitatively reproduce the features of enhanced ionization of $\mathrm{H}_{2}{}^{+}$ obtained by an accurate grid propagation method. This agreement supports the view that field-induced population transfer between the lowest two electronic states triggers the enhancement of ionization at large internuclear distances. We also applied the method to calculate the photoelectron momentum distribution of H in an intense near-infrared field. A broad low intensity component due to ``rescattering'' appears in the distribution of the momentum perpendicular to the polarization direction of an applied laser field, as observed in the experiments of single ionization of noble gas atoms. The present method provides a practical way of properly describing the nonperturbative nature of field-induced dynamics of an electron (or electrons) in the presence of both Coulomb and radiation fields.

Stable and metastable states of SN−

Highly correlated ab initio methods were used in order to generate the potential energy functions (PEFs) of the bound electronic states of the SN− anion and the long-range parts of the PEFs of its excited states and their mutual spin–orbit couplings. The SN (X2Π and a4Π) potential energy curves are also computed. In addition to the two bound electronic states of SN− (i.e. X3Σ− and 1Δ) already known, our calculations show that the 3Δ state is lying energetically below its quartet parent neutral state (a4Π). The depletion of the J = 3 component of SN−(3Δ) will mainly occur via weak interactions with the electron continuum wave. At large internuclear distances, SN−(5Π) state is predicted to possess a shallow polarization minimum supporting long-lived SN− ions. Finally, the reaction between S−(2Pu) and N(4Su) involves the electronic states of SN− and their mutual couplings, in competition with the autodetachment processes.

Laser-induced electron recollision inH2and electron correlation

Single and double ionization processes are calculated for a 1D model of ${\mathrm{H}}_{2}$ from numerical solution of the time-dependent Schr\"odinger equation in the presence of an intense $I\ensuremath{\leqslant}5\ifmmode\times\else\texttimes\fi{}{10}^{15}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$, ultrashort $(10\phantom{\rule{0.3em}{0ex}}\text{cycles})$ $800\phantom{\rule{0.3em}{0ex}}\mathrm{nm}$ laser pulse. Laser-induced electron recollision, LIERC, is identified from a systematic analysis of bound and continuum populations in the two-electron wave function. Recollision is shown to be responsible for double ionization at lower intensities, $I<{10}^{15}\phantom{\rule{0.3em}{0ex}}\mathrm{W}∕{\mathrm{cm}}^{2}$ and persists also in the first two excited states of ${\mathrm{H}}_{2}$, the $A\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}$ and $B\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}$ states. The effects of the symmetry (antisymmetry) of the two-electrons wave function is found to be dominant at large internuclear distances where enhanced ionization is operative, especially in the $A\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{u}^{+}$, where the exclusion principle suppresses double ionization from LIERC. Furthermore, at large distances, double ionization is shown to occur with equal excitation of the highest occupied and lowest unoccupied molecular orbitals of the ${\mathrm{H}}_{2}^{+}$ core ion. Negligible core excitation occurs at equilibrium.

Collisional and thermal ionization of sodium Rydberg atoms: II. Theory for nS, nP and nD states with n = 5–25

A stochastic model of associative ionization in collisions of Rydberg atoms with ground-state atoms is presented. The conventional Duman–Shmatov–Mihajlov–Janev (DSMJ) model treats the ionization as excitation of Rydberg electron to the continuum by the electric-dipole field generated by exchange interaction within the quasi-molecular ion. The stochastic model essentially extends this treatment by taking into account redistribution of population over a range of Rydberg states prior to ionization, which is caused by non-adiabatic processes in overlapping multiple level crossings of quasi-molecular Rydberg states. The redistribution is modelled as diffusion of electrons in the Rydberg energy spectrum using a Fokker–Planck-type equation. The process of l-mixing of Rydberg states at large internuclear distances and twisting of the collision trajectories on attractive potentials are taken into account. The choice of the collision velocity distribution is also shown to be important. Associative ionization rates have been calculated for Na**(nl) + Na collisions with n = 5–25 and l = 0, 1, 2, and compared with the available experimental data and the calculations performed using the nonlinear DSMJ model. At relatively low n the stochastic model yields a substantially better agreement with the experimental data than the DSMJ model, while the results of both models converge at large n.

Long-range interaction between polar Rydberg atoms

The most attractive and the most repulsive potential-energy curves for interaction between two Rydberg atoms in a broad superposition of internal angular momentum states are studied. The extreme Stark states have the largest dipole moments and provide the dominant contribution to the interaction which is then expressed as a long-range expansion involving the permanent multipole moments Qj of each polar atom. Analytical expressions are obtained for all Qj associated with principal quantum number n of H(n) and permit the long-range expansion for the H(n)–H(n′) first-order interaction to be explicitly expressed analytically in terms of n, n′ and internuclear distance R. Possible quasi-molecular formation is investigated. Direct calculations show that the H(n = 2)–H(n′ = 2) interaction is capable of supporting 47 bound vibrational levels. As n increases, the long-range interaction becomes increasingly attractive so that molecular formation at large internuclear distances is expected to be scarcely possible for these extreme Stark levels.

High-resolution pulsed-field-ionization zero-kinetic-energy photoelectron spectroscopic study of the two lowest electronic states of the ozone cation O3+

The pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectrum of jet-cooled O3 has been recorded in the range 101,000-104,000 cm(-1). The origins of the X 1A1-->X+ 2A1 and X 1A1-->A+ 2B2 transitions could be determined from the rotational structure of the bands, the photoionization selection rules, the photoionization efficiency curve, and comparison with ab initio calculations. The first adiabatic ionization energy of O3 was measured to be 101,020.5(5) cm(-1) [12.524 95(6) eV] and the energy difference between the X+ 2A1 (0,0,0) and A+ 2B2 (0,0,0) states was determined to be DeltaT0=1089.7(4) cm(-1). Whereas the X-->X+ band consists of an intense and regular progression in the bending (nu2) mode observed up to v2+=4, only the origin of the X-->A+ band was observed. The analysis of the rotational structure in each band led to the derivation of the r0 structure of O3+ in the X+ [C2v,r0=1.25(2) A,alpha0=131.5(9) degrees ] and A+[C2v,r0=1.37(5) A,alpha0=111.3(38) degrees ] states. The appearance of the spectrum, which is regular up to 102,300 cm(-1), changes abruptly at approximately 102,500 cm(-1), a position above which the spectral density increases markedly and the rotational structure of the bands collapses. On the basis of ab initio calculations, this behavior is attributed to the onset of large-amplitude motions spreading through several local minima all the way to large internuclear distances. The ab initio calculations are consistent with earlier results in predicting a seam of conical intersections between the X+ and A+ states approximately 2600 cm(-1) above the cationic ground state and demonstrate the existence of potential minima at large internuclear distances that are connected to the main minima of the X+ and A+ states through low-lying barriers.

Polarizability functions of diatomic homonuclear molecules: Semiempirical approach

A semiempirical method is discussed to construct the polarizability functions for a diatomic homonuclear molecule as a piecewise-continuous function that exhibits physically correct behavior at small and large internuclear distances and agrees with the polarizability function near the nuclear equilibrium position of the molecule. The method is applied to calculate the polarizability functions of N$_2$ and O$_2$ molecules in the range of internuclear distances (0, ∞).

Quantum mechanical study of electronic and nuclear dynamics of molecules in intense laser fields

Abstract The dynamical behaviour of H 2 + in near-infrared, intense laser fields ( I >10 13 W/cm 2 and λ >700 nm) is examined with accurate evaluation of the electronic and nuclear wave packet by the dual transformation method we developed to deal with the dynamics in Coulombic systems. Using “field-following” time-dependent adiabatic states defined as eigenfunctions of the “instantaneous” electronic Hamiltonian, we have clarified the dynamics of the bound electron, ionization, Coulomb explosion, and molecular vibration of H 2 + . The present analysis of H 2 + indicates that the multi-electron dynamics and nuclear dynamics of polyatomic molecules in intense fields can be described by using the potential surfaces of time-dependent adiabatic states and the nonadaiabatic coupling elements between those states. To obtain time-dependent adiabatic states of a molecule, the electronic Hamiltonian including the interaction with the instantaneous laser electric field is diagonalized by ab initio molecular orbital (MO) methods. While the time-dependent adiabatic potentials calculated by MO methods are used to evaluate the multichannel nuclear dynamics until the next ionization process, the charge distributions on individual atomic sites can be used to judge whether ionization occurs or not at a given light intensity. We have applied the time-dependent adiabatic state approach to reveal characteristic features of the dynamics of structural deformations of CO 2 and its cations in a near-infrared intense laser field (∼10 15 W cm −2 ). In the CO 2 and CO 2 + stages, ionization occurs before the field intensity becomes high enough to deform the molecule. In the CO 2 2+ stage, simultaneous symmetric two-bond stretching occurs as well as one-bond stretching. Two-bond stretching is induced by an intense field in the lowest time-dependent adiabatic state |1〉 of CO 2 2+ , and this two-bond stretching is followed by the occurrence of a large-amplitude bending motion mainly in the second-lowest adiabatic state |2〉 nonadiabatically created from |1〉 at large internuclear distances by the field. It is concluded that the experimentally observed stretched and bent structure of CO 2 3+ just before Coulomb explosions originates from the structural deformation of CO 2 2+ . We also applied the present approach to investigate dissociative ionization of C 2 H 5 OH in near-infrared, intense laser fields. The calculated ratio of the probability of C–O bond cleavage to that of C–C bond cleavage becomes smaller with decreases in the pulse length, as was observed in the experiment by Itakura et al. [J. Chem. Phys. 119 (2003) 4179]. In the case where the C–C axis is parallel to the polarization direction of an applied laser field, upper C–C bond dissociative adiabatic states are created owing to field-induced nonadiabatic transitions even if the pulse length is as short as 30 fs. This example clearly shows that field-induced nonadiabatic transition plays a decisive role in the reaction dynamics of molecules in intense laser field.

On the computation of (2‐2) three‐center Slater‐type orbital integrals of 1/r12 using Fourier‐transform‐based analytical formulas

AbstractWe describe a computational scheme devised for using Fourier‐transform‐based analytic formulas for three‐center integrals of r, wherein each electron is described by a two‐center product of Slater‐type orbitals. The asymptotic behavior of the auxiliary functions, which are related to modified spherical Bessel functions and to exponential integrals, is investigated, and recursive computational schemes are derived that are shown to be numerically stable for high summation indices and large internuclear distances. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Molecular frame photoelectron angular distributions in dissociative photoionization ofH2 in theregion of the Q1 and Q2 doubly excited states

Dissociative photoionization ofH2 induced by VUV linearly polarized synchrotron radiationP has been studiedusing the (VH+,Ve,P) vector correlation method. The ion–electron kinetic energy correlationdiagrams obtained for the three photon excitation energieshν = 20, 28.5and 32.5 eV enable us to identify and select the dominant dissociative photoionization processes. TheIχ(θe,ϕe) molecular frame photoelectron angular distributions for any orientationχ of the molecular axis with respect to the polarization are reported for direct photoionization ofH2 into theH2+(2Σg+) ionic groundstate at hν = 20 eVand for the dominant DPI processes involving autoionization of theH2(Q1 1Σu+(1)) andH2(Q2 1Πu(1)) doubly excitedstates into the H2+(2Σg+) and H2+(2Σu+) continua at hν = 28.5 and 32.5 eV. They show the dominant excitation of ap σu partial wave inautoionization of the Q1(1Σu+(1)) state into the H2+(1s σg) ionic stateand that of a d πg partial wavein autoionization of the Q2(1Πu(1)) state into the H2+(2p σu) continuum. A molecular frame forward–backward electron emission anisotropy is observedwhen ionization takes place at large internuclear distance.

Self-interaction in natural orbital functional theory

Spurious self-interaction is shown to be responsible for essentially exact H 2 potential energy curves calculated using simple one-electron density matrix functionals. For molecules with more than two electrons, bond-stretching potentials are unrealistically shallow due to overcorrelation that is most severe in the separated-atom limit. In addition, too much population is shifted into orbitals beyond the formal valence shell. Both problems are remedied by a facile self-interaction correction. At large internuclear distance, the corrected potentials are superior to those obtained from Hartree–Fock and density functional theories.

Ab Initio Calculation of the Polarizability for the Ground State XΣ+ and the First Low-Lying Excited States a3Σ+ and A1Σ+ of LiH and NaH

The dipole polarizabilities of the ground X1Σ+ and the lowest-lying A1Σ+ singlet states of LiH and NaH have been investigated at the ab initio level by using the time-dependent gauge invariant method (TDGI). For the ground-state dipole polarizability of LiH and NaH, and the triplet a3Σ+ excited state of LiH, an alternative method, namely, the coupled cluster with single, double, and a perturbative treatment of the connected triple excitations (CCSD(T)), has been computed for comparison. We found that the long in-plane component αzz of the excited A1Σ+ state of NaH exhibits an unusual calculated negative value, due to the large negative contribution of the X1Σ+ state. At the TDGI level, the convergence of the calculated electric properties with respect to the number of the spectroscopic states has been carefully investigated. The dipole polarizability components as a function of the diatomic distances up to dissociation have also been computed. The results obtained are particularly relevant to the understanding of the variation of the polarizability for small and large internuclear distances. The properties computed in this work are in very good agreement with the experimental and theoretical data available in the literature. With regard to the a3Σ+ and A1Σ+ excited states, most of the calculated electric properties are new for LiH and NaH.

Description of molecular dynamics in intense laser fields by the time-dependent adiabatic state approach: application to simultaneous two-bond dissociation of CO2 and its control.

We theoretically investigated the dynamics of structural deformations of CO(2) and its cations in near-infrared intense laser fields (approximately 10(15) W cm(-2)) by using the time-dependent adiabatic state approach. To obtain "field-following" adiabatic potentials for nuclear dynamics, the electronic Hamiltonian including the interaction with the instantaneous laser electric field is diagonalized by the multiconfiguration self-consistent-field molecular orbital method. In the CO(2) and CO(2+) stages, ionization occurs before the field intensity becomes high enough to deform the molecule. In the CO(2)(2+) stage, simultaneous symmetric two-bond stretching occurs as well as one-bond stretching. Two-bond stretching is induced by an intense field in the lowest time-dependent adiabatic state |1> of CO(2)(2+), and this two-bond stretching is followed by the occurrence of a large-amplitude bending motion mainly in the second-lowest adiabatic state |2> nonadiabatically created at large internuclear distances by the field from |1>. It is concluded that the experimentally observed stretched and bent structure of CO(2)(3+) just before Coulomb explosions originates from the structural deformation of CO(2)(2+). We also show in this report that the concept of "optical-cycle-averaged potential" is useful for designing schemes to control molecular (reaction) dynamics, such as dissociation dynamics of CO(2), in intense fields. The present approach is simple but has wide applicability for analysis and prediction of electronic and nuclear dynamics of polyatomic molecules in intense laser fields.

Analytical expressions for two-Coulomb-centre wavefunctions at large internucleardistances

Two-Coulomb-centre quasiradial and quasiangular wavefunctions asymptotic forlarge distances between the fixed positive charges (nuclei) are derived for theentire space of the negative particle (electron). Explicit expressions of thewavefunctions are presented for some low-lying states. Excellent agreement isfound between the expressions presented here and numerically calculatedwavefunctions when the internuclear distance is greater than the size of the shellon either centre.

Potential energy curves and dipole transition moments for excited electronic states of XeKr and ArNe

Relativistic core-potential calculations have been carried out on Ω states resulting from the interaction of Xe* (5p56s, 3P, 1P) with ground-state Kr atoms as well as for the system Ar* (3p54s, 3P, 1P) with ground-state Ne, using different basis sets and configuration interaction procedures. The present calculations on ArNe, employing larger sets of Rydberg functions than those of the previous calculations, yield totally repulsive potentials for the excited states of ArNe. Similar calculations on XeKr obtain shallow minima (600–860 cm−1) in the potential energy curves of the excited states at large internuclear distances (6.9–7.8 bohr). Dipole transition moments have been calculated and strong radiative transitions are predicted from excited states to the ground state. The 1(I) state, correlating with the metastable P23 state of Xe is found to have a small but nonzero dipole transition moment at short and intermediate nuclear distances leading to a radiative lifetime for the v=0 level of this state of 21.0 μs.