Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. II. Electron dynamics and outer ionization of the nanoplasma

We explore electron dynamics in molecular (CD4)(1061) clusters and elemental Xen (n=249-2171) clusters, responding to ultraintense (intensity I=10(16)-10(19) W cm(-2)) laser fields. Molecular dynamics simulations (including magnetic field and relativistic effects) and analyses of high-energy electron dynamics and nuclear ion dynamics in a cluster interacting with a Gaussian shaped laser field (frequency 0.35 fs(-1), photon energy 1.44 eV, phase 0, temporal width 25 fs) elucidated the time dependence of inner ionization, the formation of a nanoplasma of unbound electrons within the cluster or its vicinity, and of outer ionization. We determined the cluster size and the laser intensity dependence of these three sequential-parallel electronic processes. The characteristic times for cluster inner ionization (tau(ii)) and for outer ionization (tau(oi)) fall in the femtosecond time domain, i.e., tau(ii)=2-9 fs and tau(oi)=4-15 fs for (CD4)(1061), tau(ii)=7-30 fs and tau(oi)=5-13 fs for Xe(n) (n=479,1061), with both tau(ii) and tau(oi) decreasing with increasing I, in accord with the barrier suppression ionization mechanism for inner ionization of the constituents and the cluster barrier suppression ionization mechanism for outer ionization. The positive delay times Deltatau(OI) between outer and inner ionization (e.g., Deltatau(OI)=6.5 fs for Xen at I=10(16) W cm(-2) and Deltatau(OI)=0.2 fs for (CD4)(1061) at I=10(19) W cm(-2)) demonstrate that the outer/inner ionization processes are sequential. For (CD4)(1061), tau(ii)tau(oi), reflecting on the energetic hierarchy in the ionization of the Xe atoms. Quasiresonance contributions to the outer ionization of the nanoplasma were established, as manifested in the temporal oscillations in the inner/outer ionization levels, and in the center of mass of the nanoplasma electrons. The formation characteristics, dynamics, and response of the nanoplasma in molecular or elemental clusters were addressed. The nanoplasma is positively charged, with a high-average electron density [rho(P)=(2-3)10(22) cm(-3)], being characterized by high-average electron energies epsilon(av) (e.g., in Xe(1061) clusters epsilon(av)=54 eV at I=10(16) W cm(-2) and epsilon(av)=0.56-0.37 keV at I=10(18) W cm(-2), with epsilon(av) proportional, variant I(1/2)). Beyond the cluster boundary the average electron energy markedly increases, reaching electron energies in the range of 1.2-40 keV for outer ionization of Xe(n) (n=249-2171) clusters. The nanoplasma exhibits spatial inhomogeneity and angular anisotropy induced by the laser field. Femtosecond time scales are predicted for the nanoplasma production (rise times 7-3 fs), for the decay (decay times approximately 5 fs), and for the persistence time (30-10 fs) of a transient nanoplasma at I=10(17)-10(18) W cm(-2). At lower intensities of I=10(16) W cm(-2) a persistent nanoplasma with a "long" lifetime of > 50 fs will prevail.     

Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. III. Coulomb explosion of deuterium clusters

In this paper we present a theoretical and computational study of the energetics and temporal dynamics of Coulomb explosion of molecular clusters of deuterium (D2)n/2 (n = 480 - 7.6 x 10(4), cluster radius R0 = 13.1 - 70 A) in ultraintense laser fields (laser peak intensity I = 10(15) - 10(20)W cm(-2)). The energetics of Coulomb explosion was inferred from the dependence of the maximal energy EM and the average energy Eav of the product D+ ions on the laser intensity, the laser pulse shape, the cluster radius, and the laser frequency. Electron dynamics of outer cluster ionization and nuclear dynamics of Coulomb explosion were investigated by molecular dynamics simulations. Several distinct laser pulse shape envelopes, involving a rectangular field, a Gaussian field, and a truncated Gaussian field, were employed to determine the validity range of the cluster vertical ionization (CVI) approximation. The CVI predicts that Eav, EM proportional to R0(2) and that the energy distribution is P(E) proportional to E1/2. For a rectangular laser pulse the CVI conditions are satisfied when complete outer ionization is obtained, with the outer ionization time toi being shorter than both the pulse width and the cluster radius doubling time tau2. By increasing toi, due to the increase of R0 or the decrease of I, we have shown that the deviation of Eav from the corresponding CVI value (Eav(CVI)) is (Eav(CVI) - Eav)/Eav(CVI) approximately (toi/2.91tau2)2. The Gaussian pulses trigger outer ionization induced by adiabatic following of the laser field and of the cluster size, providing a pseudo-CVI behavior at sufficiently large laser fields. The energetics manifest the existence of a finite range of CVI size dependence, with the validity range for the applicability of the CVI being R0 < or = (R0)I, with (R0)I representing an intensity dependent boundary radius. Relating electron dynamics of outer ionization to nuclear dynamics for Coulomb explosion induced by a Gaussian pulse, the boundary radius (R0)I and the corresponding ion average energy (Eav)I were inferred from simulations and described in terms of an electrostatic model. Two independent estimates of (R0)I, which involve the cluster size where the CVI relation breaks down and the cluster size for the attainment of complete outer ionization, are in good agreement with each other, as well as with the electrostatic model for cluster barrier suppression. The relation (Eav)I proportional to (R0)I(2) provides the validity range of the pseudo-CVI domain for the cluster sizes and laser intensities, where the energetics of D+ ions produced by Coulomb explosion of (D)n clusters is optimized. The currently available experimental data [Madison et al., Phys. Plasmas 11, 1 (2004)] for the energetics of Coulomb explosion of (D)n clusters (Eav = 5 - 7 keV at I = 2 x 10(18) W cm(-2)), together with our simulation data, lead to the estimates of R0 = 51 - 60 A, which exceed the experimental estimate of R0 = 45 A. The predicted anisotropy of the D+ ion energies in the Coulomb explosion at I = 10(18) W cm(-2) is in accord with experiment. We also explored the laser frequency dependence of the energetics of Coulomb explosion in the range nu = 0.1 - 2.1 fs(-1) (lambda = 3000 - 140 nm), which can be rationalized in terms of the electrostatic model.     

Electron and nuclear dynamics of molecular clusters in ultraintense laser fields. IV. Coulomb explosion of molecular heteroclusters

In this paper we present a theoretical and computational study of the temporal dynamics and energetics of Coulomb explosion of (CD4)(n) and (CH4)(n) (n=55-4213) molecular heteroclusters in ultraintense (I=10(16)-10(19) W cm(-2)) laser fields, addressing the manifestation of electron dynamics, together with nuclear energetic and kinematic effects on the heterocluster Coulomb instability. The manifestations of the coupling between electron and nuclear dynamics were explored by molecular dynamics simulations for these heteroclusters coupled to Gaussian laser fields (pulse width tau=25 fs), elucidating outer ionization dynamics, nanoplasma screening effects (being significant for I< or =10(17) W cm(-2)), and the attainment of cluster vertical ionization (CVI) (at I=10(17) W cm(-2) for cluster radius R(0)< or =31 A). Nuclear kinematic effects on heterocluster Coulomb explosion are governed by the kinematic parameter eta=q(C)m(A)/q(A)m(C) for (CA(4))(n) clusters (A=H,D), where q(j) and m(j) (j=A,C) are the ionic charges and masses. Nonuniform heterocluster Coulomb explosion (eta >1) manifests an overrun effect of the light ions relative to the heavy ions, exhibiting the expansion of two spatially separated subclusters, with the light ions forming the outer subcluster at the outer edge of the spatial distribution. Important features of the energetics of heterocluster Coulomb explosion originate from energetic triggering effects of the driving of the light ions by the heavy ions (C(4+) for I=10(17)-10(18) W cm(-2) and C(6+) for I=10(19) W cm(-2)), as well as for kinematic effects. Based on the CVI assumption, scaling laws for the cluster size (radius R(0)) dependence of the energetics of uniform Coulomb explosion of heteroclusters (eta=1) were derived, with the size dependence of the average (E(j,av)) and maximal (E(j,M)) ion energies being E(j,av)=aR(0) (2) and E(j,M)=(5a/3)R(0) (2), as well as for the ion energy distributions P(E(j)) proportional to E(j) (1/2); E(j)< or =E(j,M). These results for uniform Coulomb explosion serve as benchmark reference data for the assessment of the effects of nonuniform explosion, where the CVI scaling law for the energetics still holds, with deviations of the a coefficient, which increase with increasing eta. Kinematic effects (for eta>1) result in an isotope effect, predicting the enhancement (by 9%-11%) of E(H,av) for Coulomb explosion of (C(4+)H(4) (+))(eta) (eta=3) relative to E(D,av) for Coulomb explosion of (C(4+)D(4) (+))(eta) (eta=1.5), with the isotope effect being determined by the ratio of the kinematic parameters for the pair of Coulomb exploding clusters. Kinematic effects for nonuniform explosion also result in a narrow isotope dependent energy distribution (of width DeltaE) of the light ions (with DeltaE/E(H,av) approximately 0.3 and DeltaE/E(D,av) approximately 0.4), with the distribution peaking at the high energy edge, in marked contrast with the uniform explosion case. Features of laser-heterocluster interactions were inferred from the analyses of the intensity dependent boundary radii (R(0))(I) and the corresponding average D+ ion energies (E(D,av))(I), which provide a measure for optimization of the cluster size at intensity I for the neutron yield from dd nuclear fusion driven by Coulomb explosion (NFDCE) of these heteroclusters. We infer on the advantage of deuterium containing heteronuclear clusters, e.g., (CD4)(n) in comparison to homonuclear clusters, e.g., (D2)(n/2), for dd NFDCE, where the highly charged heavy ions (e.g., C4+ or C6+) serve as energetic and kinematic triggers driving the D+ ions to a high (10-200 keV) energy domain.     

Extreme ionization of Xe clusters driven by ultraintense laser fields

We applied theoretical models and molecular dynamics simulations to explore extreme multielectron ionization in Xe(n) clusters (n=2-2171, initial cluster radius R(0)=2.16-31.0 A) driven by ultraintense infrared Gaussian laser fields (peak intensity I(M)=10(15)-10(20) W cm(-2), temporal pulse length tau=10-100 fs, and frequency nu=0.35 fs(-1)). Cluster compound ionization was described by three processes of inner ionization, nanoplasma formation, and outer ionization. Inner ionization gives rise to high ionization levels (with the formation of [Xe(q+)](n) with q=2-36), which are amenable to experimental observation. The cluster size and laser intensity dependence of the inner ionization levels are induced by a superposition of barrier suppression ionization (BSI) and electron impact ionization (EII). The BSI was induced by a composite field involving the laser field and an inner field of the ions and electrons, which manifests ignition enhancement and screening retardation effects. EII was treated using experimental cross sections, with a proper account of sequential impact ionization. At the highest intensities (I(M)=10(18)-10(20) W cm(-2)) inner ionization is dominated by BSI. At lower intensities (I(M)=10(15)-10(16) W cm(-2)), where the nanoplasma is persistent, the EII contribution to the inner ionization yield is substantial. It increases with increasing the cluster size, exerts a marked effect on the increase of the [Xe(q+)](n) ionization level, is most pronounced in the cluster center, and manifests a marked increase with increasing the pulse length (i.e., becoming the dominant ionization channel (56%) for Xe(2171) at tau=100 fs). The EII yield and the ionization level enhancement decrease with increasing the laser intensity. The pulse length dependence of the EII yield at I(M)=10(15)-10(16) W cm(-2) establishes an ultraintense laser pulse length control mechanism of extreme ionization products.     

Multiple ionization and Coulomb explosion of mercury clusters in femtosecond laser fields

We report on studies of multiple ionization and fragmentation of free Hg_n (n ≤ 80) clusters in the femtosecond time domain at wavelengths ranging from 255 nm to 800 nm. After excitation by single laser pulses of an intensity of 5 * 10¹¹ W/cm² we observe prompt formation of multiply charged Hg_n clusters. The Hg_n cluster size distribution observed up to n ≈ 80 shows in additon to singly charged also doubly and triply charged clusters with a surprisingly high amount of doubly charged clusters. The measured cluster size distribution is nearly independent of laser wavelengths. For higher laser intensities (2 * 10¹² W/cm²) we observe multiply charged mercury atoms up to Hg⁵⁺. At 10¹³ W/cm² molecules and clusters eventually disappear due to Coulomb explosion and complete Fragmentation. Only atomic ions, singly and multiply charged, with high kinetic energies are then observed.     

Herman-Kluk semiclassical dynamics of molecular rotations in laser fields

The action-angle mapping algorithm [R. Saha and M. Ovchinnikov, J. Chem. Phys. 124, 204112 (2006)] is utilized to provide a Herman-Kluk semiclassical initial value representation (SC-IVR) treatment of quantum dynamics of systems with non-Cartesian degrees of freedom. The non-Cartesian system under investigation is a linear rotor molecule in static electric and pulsed laser field. The results demonstrate that the SC-IVR procedure described in this work provides an accurate representation of quantum rotational dynamics of the system.     

Electron hydration dynamics in water clusters: A direct ab initio molecular dynamics approach

Electron attachment dynamics of excess electron in water cluster (H2O)n (n = 2 and 3) have been investigated by means of full-dimensional direct ab initio molecular dynamics (MD) method at the MP26-311++G(d,p) level. It was found that the hydrogen bond breaking due to the excess electron is an important process in the first stage of electron capture in water trimer. Time scale of electron localization and hydrogen bond breaking were determined by the direct ab initio MD simulation. The initial process of hydration in water cluster is clearly visualized in the present study. In n = 3, an excess electron is first trapped around the cyclic water trimer with a triangular form, where the excess electron is equivalently distributed on the three water molecules at time zero. After 50 fs, the excess electron is concentrated into two water molecules, while the potential energy of the system decreases by -1.5 kcal/mol from the vertical point. After 100 fs, the excess electron is localized in one of the water molecules and the potential energy decreases by -5.3 kcal/mol, but the triangular form still remained. After that, one of the hydrogen bonds in the triangular form is gradually broken by the excess electron, while the structure becomes linear at 100-300 fs after electron capture. The time scale of hydrogen bond breaking due to the excess electron is calculated to be about 300 fs. Finally, a dipole bound state is formed by the linear form of three water molecules. In the case of n = 2, the dipole bound anion is formed directly. The mechanism of electron hydration dynamics was discussed on the basis of theoretical results.     

Photoionization of isooctane and n-octane in intense laser fields. I. Effect of irradiance on ionization rates

The population of ejected electrons following multiphoton ionization of neat liquids isooctane and n-octane is investigated over a large range of ionizing irradiance I(ex). Transient absorption (TA) at 1200 nm in both neat liquids is measured in a 60 mum path at time delays of 0.7 and 2.5 ps following an intense 400 nm (3.1 eV) ionizing pulse. As the irradiance of this pulse is varied over the range from 4 to 410 TWcm(2), the dependence of TA on I(ex) exhibits the periodic structure theoretically predicted for multiphoton channel openings and closings. At low I(ex) (<9 TWcm(2)), TA in isooctane is proportional to I(ex) (n) where n=3, consistent with nonresonant, near threshold ionization (liquid phase ionization potential=8.6 eV). At I(ex)>9 TWcm(2), n declines with increasing I(ex) up to I(ex)=13 TWcm(2), at which point n abruptly increases to 4. The pattern is repeated at I(ex)>13 TWcm(2), albeit with n declining from 4 and then abruptly increasing to 5 as I(ex) becomes greater than 100 TWcm(2). A similar trend is observed in n-octane. The dependence of the TA on I(ex) in the regions of channel openings and closings is compared to the nonperturbative, strong field approximation developed by Reiss [Phys. Rev. A 22, 1786 (1980)].     

Electron impact ionization of small silver and copper clusters

Using a quadrupole mass spectrometer, relative cross sections for electron impact ionization of neutral Ag _n and Cu _n clusters withn=1 ... 4 have been measured for electron energies between threshold and 125 eV. From the results, the following ionization energies were obtained: Ag₂: 7.26±0.1 eV, Ag₃: 6.19±0.2 eV, Ag₄: 6.33±0.3 eV, Cu₂: 7.46±0.15 eV, Cu₃: 6.14±1.0 eV, Cu₄: 7.00±0.6 eV. With only two exceptions, these values agree with other data published for Ag₂, Cu₂, Cu₃ and Cu₄.     

Electron bubbles in helium clusters. I. Structure and energetics

In this paper we present a theoretical study of the structure, energetics, potential energy surfaces, and energetic stability of excess electron bubbles in ((4)He)(N) (N=6500-10(6)) clusters. The subsystem of the helium atoms was treated by the density functional method. The density profile was specified by a void (i.e., an empty bubble) at the cluster center, a rising profile towards a constant interior value (described by a power exponential), and a decreasing profile near the cluster surface (described in terms of a Gudermannian function). The cluster surface density profile width (approximately 6 A) weakly depends on the bubble radius R(b), while the interior surface profile widths (approximately 4-8 A) increase with increasing R(b). The cluster deformation energy E(d) accompanying the bubble formation originates from the bubble surface energy, the exterior cluster surface energy change, and the energy increase due to intracluster density changes, with the latter term providing the dominant contribution for N=6500-2 x 10(5). The excess electron energy E(e) was calculated at a fixed nuclear configuration using a pseudopotential method, with an effective (nonlocal) potential, which incorporates repulsion and polarization effects. Concurrently, the energy V(0) of the quasi-free-electron within the deformed cluster was calculated. The total electron bubble energies E(t)=E(e)+E(d), which represent the energetic configurational diagrams of E(t) vs R(b) (at fixed N), provide the equilibrium bubble radii R(b) (c) and the corresponding total equilibrium energies E(t) (e), with E(t) (e)(R(e)) decreasing (increasing) with increasing N (i.e., at N=6500, R(e)=13.5 A and E(t) (e)=0.86 eV, while at N=1.8 x 10(5), R(e)=16.6 A and E(t) (e)=0.39 eV). The cluster size dependence of the energy gap (V(0)-E(t) (e)) allows for the estimate of the minimal ((4)He)(N) cluster size of N approximately 5200 for which the electron bubble is energetically stable.     

Classical dynamics of 3D Hydrogen molecular ion in intense laser fields

The classical trajectory method is used to study the dynamics of 3D Hydrogen molecular ion interacting with intense laser fields. In the 3D classical model, a three-body Hamiltonian with one-dimensional nuclear motion restricted to the direction of the laser field is considered. The motion of electron and nucleus is described by the classical Hamiltonian canonical equations. The probabilities of ionization, dissociation and Coulomb explosion as functions of time are calculated and the average distances from electron to the mass-center for various laser parameters are implemented by symplectic method. The dynamics of in two-color laser fields are also investigated. We compare our results with the corresponding quantum-mechanical calculations and find they produce similar qualitative features in many cases.     

Comparative study of multielectron ionization of alkyl halides induced by picosecond laser irradiation

The interaction of C2H5X, 1-C3H7X, 1-C4H9X, where X = I, Br, Cl, with strong (1 x 10(13)-1.2 x 10(14) W/cm2) 35 ps laser pulses at 1064 nm is studied by means of time-of-flight mass spectrometry. The multielectron ionization following the C-X bond elongation has been verified for the studied molecules. By combination of the intensity dependence of the ion yields, the estimated kinetic energies of the released fragment ions, and their angular distributions, we have identified the different dissociation channels of the transient multiply charged parent ions. From the dependence on the laser intensity of the ratio of the doubly charged halogen ions to the singly charged ones, it is concluded that the molecular coupling with the laser field increases with the molecular size.     

Two-photon ionization thresholds of matrix-assisted laser desorption/ionization matrix clusters

Direct two-photon ionization of the matrix has been considered a likely primary ionization mechanism in matrix-assisted laser desorption/ionization (MALDI) mass spectrometry. This mechanism requires that the vertical ionization threshold of matrix materials be below twice the laser photon energy. Because dimers and larger aggregates may be numerous in the early stages of the MALDI plume expansion, their ionization thresholds are important as well. We have used two-color two-photon ionization to determine the ionization thresholds of jet cooled clusters of an important matrix, 2,5-dihydroxy benzoic acid (DHB), and mixed clusters with the thermal decomposition product of DHB, hydroquinone. The thresholds of the clusters were reduced by only a few tenths of an eV compared to the monomers, to an apparent limit of 7.82 eV for pure DHB clusters. None of the investigated clusters can be directly ionized by two nitrogen laser photons (7.36 eV), and the ionization efficiency at the thresholds is low.     

Probing molecular symmetry effects in the ionization of N2 and O2 by intense laser fields

High-resolution electron spectroscopy is used to explore the role played by molecular symmetry in determining the morphology of the energy spectra of electrons ejected when N2 and O2 are irradiated by intense laser fields. In O2, the low-energy part of the electron spectrum is curtailed due to the destructive interference brought about by the antibonding nature of the O2 valence orbital. The high-energy tail of the spectrum is also suppressed by virtue of electron rescattering being of little consequence in O2. In contrast, in N2, which has a bonding valence orbital, the electron dynamics follow the pattern that has been established for atomic ionization in strong optical fields.     

Electron impact ionization efficiency curves of van der Waals clusters

The study of van der Waals clusters is an area of growing interest and is being widely studied for a number of reasons. The measurement of the ionization efficiency (IE) curves have yielded a wealth of information by enabling ionization and appearance energies of ions to be determined which are essential for the calculation of thermochemical data. In the case of van der Waals clusters, the measurement ofIE curves enables one to determine the qualitative trends in the ionization potentials as a function of cluster size. In additionIE curves have also offered valuable insight into ionization related processes occurring in clusters. This paper will cover some of the more recent studies of Penning ionization, exciton induced decay and Coulomb explosion in van der Waals clusters through the use of electron impactIE curves.     

Electron bombardment fragmentation of size selected molecular clusters

(CO₂) _n , (NO) _n and (NH₃) _n clusters are generated in a supersonic molecular beam and size selected by scattering from an He beam. By measurements of angular dependent mass spectra, TOF distributions and the angular dependence of the scattered signal quantitative information on the fragmentation probability by electron impact is derived. The van der Waals systems (CO₂) _n and (NO) _n appear only at masses which are simply multiples of the monomer mass. The preferred cluster ion is the monomer ion for all investigated cluster sizes withn=2 to 4. The fragment pattern for the quasi-hydrogen bonded (NH₃) _n -cluster shows, beside a large number of fragment masses, a preference for protonated ions. The results are explained in terms of simple models based on the structural change from the neutral to the ionized configuration and the fragmentation pattern of the monomer followed by ionmolecule reactions.     

The dynamics of phase changes in molecular clusters

The significant advantages offered by systems of molecular clusters in the study of homogeneous nucleation are discussed. Determinations of nucleation rates in clusters can be followed experimentally in supersonic jets or computationally in molecular dynamics simulations. Extraordinarily high rates may be encountered, both in freezing and in solid-state transitions. From such information can be inferred the interfacial free energies, σ_sl and σ_SS, mechanisms of solid-state transitions. and an explanation of why certain crystalline phases not found in bulk systems can be seen in large molecular clusters.     

Electron impact and single photon ionization cross sections of neutral silver clusters

Neutral silver atoms and small clusters Ag _n (n=1...4) were generated by sputtering, i.e. by bombarding a polycrystalline silver surface with Ar⁺ ions of 5 keV. The sputtered particles were ionized by a crossed electron beam and subsequently detected by a quadrupole mass spectrometer. In alternative to the electron impact ionization, the same neutral species were also ionized by single photon absorption from a pulsed VUV laser (photon energy 7.9 eV), and the photoionization cross sections were evaluated from the laser intensity dependence of the measured signals. By in situ combining both ionization mechanisms, absolute values of the ratio σ _e (Ag _n )/σ _e (Ag) between the electron impact ionization cross sections of silver clusters and atoms could be determined for a fixed electron energy of 46 eV. These values can then be used to calibrate previously measured relative ionization functions. By calibrating the results using literature data measured for silver atoms, we present absolute cross sections for electron impact ionization of neutral Ag₂, Ag₃ and Ag₄ as a function of the electron energy between threshold and 125 eV.     

First-principle molecular dynamics calculation of selenium clusters

The equiliblium structures of small selenium clusters are obtained via first-principle molecular dynamics calculations based on the linearized-augmented-plane-wave (LAPW) method. Resulting equiliblium structures show a good agreement with experimental data and other firstprinciple calculations.