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.     

Coulomb explosion of nitrogen and oxygen molecules through non-Coulombic states

We have systematically studied Coulomb explosion of nitrogen and oxygen molecules in intense 8 and 24 fs laser pulses. In the experiment, we explicitly separated all explosion pathways through coincident measurements. The high resolution kinetic energy releases (KERs) and the exotic angular distributions of atomic ions provide direct evidence that Coulomb explosion occurs through non-Coulombic states. In the theory, we calculated dissociation potential energy curves (PECs) of nitrogen and oxygen molecules and their multicharged molecular ions using multiconfiguration second-order perturbation theory. The results indicate that Coulomb potentials are close to the accurate PECs of multicharged molecular ions only when the internuclear distance is larger than 3 ?. In comparison with the experimental observations and the theoretical calculations, we determined the internuclear distance when Coulombic explosion occurs. It is near the equilibrium distance of the neutral molecules in the case of 8 fs laser pulses and expands gradually with the increase of the charge state of the molecular ions in the case of 24 fs laser pulses.     

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.     

Communication: Delayed asymmetric Coulomb fission of molecular clusters: application of a dielectric liquid-drop model

Delayed asymmetric Coulomb fission in size-selected molecular dication clusters has been recorded for the first time. Observations on (NH(3))(n)(2+) clusters show that fragmentation accompanied by charge separation can occur on a microsecond time scale, exhibits considerable asymmetry, and involves a kinetic energy release of ～0.9 eV. The fission process has been modeled by representing the fragments as charged dielectric spheres and the calculated maximum in the electrostatic interaction energy between the fragments gives a good account of the measured kinetic energy release. A simple kinetic model shows that instrumental factors may contribute to the observation of asymmetric fragmentation.     

Kinetic energy distribution of multiply charged ions in Coulomb explosion of Xe clusters

We report on the calculations of kinetic energy distribution (KED) functions of multiply charged, high-energy ions in Coulomb explosion (CE) of an assembly of elemental Xe(n) clusters (average size (n) = 200-2171) driven by ultra-intense, near-infrared, Gaussian laser fields (peak intensities 10(15) - 4?×?10(16) W cm(-2), pulse lengths 65-230 fs). In this cluster size and pulse parameter domain, outer ionization is incomplete∕vertical, incomplete∕nonvertical, or complete∕nonvertical, with CE occurring in the presence of nanoplasma electrons. The KEDs were obtained from double averaging of single-trajectory molecular dynamics simulation ion kinetic energies. The KEDs were doubly averaged over a log-normal cluster size distribution and over the laser intensity distribution of a spatial Gaussian beam, which constitutes either a two-dimensional (2D) or a three-dimensional (3D) profile, with the 3D profile (when the cluster beam radius is larger than the Rayleigh length) usually being experimentally realized. The general features of the doubly averaged KEDs manifest the smearing out of the structure corresponding to the distribution of ion charges, a marked increase of the KEDs at very low energies due to the contribution from the persistent nanoplasma, a distortion of the KEDs and of the average energies toward lower energy values, and the appearance of long low-intensity high-energy tails caused by the admixture of contributions from large clusters by size averaging. The doubly averaged simulation results account reasonably well (within 30%) for the experimental data for the cluster-size dependence of the CE energetics and for its dependence on the laser pulse parameters, as well as for the anisotropy in the angular distribution of the energies of the Xe(q+) ions. Possible applications of this computational study include a control of the ion kinetic energies by the choice of the laser intensity profile (2D∕3D) in the laser-cluster interaction volume.     

Fragmentation of doubly charged argon clusters

Fragmentation of doubly charged argon clusters is reported. Neutral argon clusters are excited with monochromatized synchrotron radiation in the energy regime of the argonL ₃/L ₂ absorption edges (240–260 eV) leading predominantly to cluster dication formation. All charged particles are detected in a photoelectron-photoion-photoion-concidence (PEPIPICO) experiment. Symmetric and asymmetric charge separation reactions (Coulomb explosion) are identified for clusters below the critical size of stable dication formation. The peak shapes of the coincidence signals are investigated as a function of neutral cluster size. Characteristic changes in peak shape are observed which are used to derive fragmentation mechanisms involving sequential evaporation of neutrals before and after charge separation. The spectra indicate in accordance with low kinetic energy releases occurring in charge separation of large dissociative cluster dications (Ar _n ²⁺ , withn>50) that due to large charge separation distances the momenta of both singly charged fragments are not any more directed into opposite direction, as it is typical for Coulomb explosion. The results are compared to collision induced fragmentation of mass selected argon cluster dications as well as photon stimulated desorption spectra of condensed argon.     

Velocity map imaging and theoretical study of the Coulomb explosion of CH3I under intense femtosecond IR pulses

The Coulomb explosion of CH(3)I in an intense (10-100 TW cm(-2)), ultrashort (50 fs) and nonresonant (804 nm) laser field has been studied experimentally and justified theoretically. Ion images have been recorded using the velocity map imaging (VMI) technique for different singly and multiply charged ion fragments, CH(3)(p+) (p = 1) and I(q+) (q ≤ 3), arising from different Coulomb explosion channels. The fragment kinetic energy distributions obtained from the measured images for these ion fragments show significantly lower energies than those expected considering only Coulomb repulsion forces. The experimental results have been rationalized in terms of one-dimensional wave packet calculations on ab initio potential energy curves of the different multiply charged species. The calculations reveal the existence of a potential energy barrier due to a bound minimum in the potential energy curve of the CH(3)I(2+) species and a strong stabilization with respect to the pure Coulombic repulsion for the higher charged CH(3)I(n+) (n = 3, 4) species.     

Wavelength-dependent Coulomb explosion in carbon disulphide (CS2) clusters: generation of energetic multiply charged carbon and sulphur ions

A gigawatt laser-induced Coulomb explosion has been observed in carbon disulphide (CS(2)) clusters generating energetic, multiply charged [C](m+) (m = 1-4) and [S](n+) (n = 1-6) atomic ions of carbon and sulphur. The Coulomb explosion shows wavelength dependence. Comparison of these results with our earlier work shows that the polarizability and dipole moment might help in energy absorption from the laser field but they are not mandatory conditions for this low-intensity Coulomb explosion. The results show that in a field of 10(9) W/cm(2), absorption of 266 and 355 nm laser radiation by CS(2) clusters leads to multiphoton dissociation/ionization whereas at 532 nm the whole cluster explodes generating multiply charged atomic ions.     

Fragmentation Behavior and Ionization Potentials of Lead Clusters Pb_n(n≤30)

The properties of Pbn(n=2―30) clusters including binding energies,second differences in energy,and HOMO-LUMO gaps,especially fragmentation energies and ionization potentials,have been studied by ab initio calculation.The main fragmentation products of Pbn+ are shown to be Pb+Pbn-1+ for n≤14 and two small cluster fragments for larger ones with n14.The Pb13+ appears frequently as the products in the fragmentations of large clusters.Also,the calculated ionization potentials of the clusters are consistent with the experiment data.     

Coulomb explosion of ammonia clusters induced by intense nanosecond laser at 532 and 1064 nm: wavelength dependence of the multicharged nitrogen ions

The Coulomb explosion of ammonia clusters induced by nanosecond laser field with intensity in the range of 10(10)-10(12) W cm(-2) and wavelength of 532 and 1064 nm has been studied. N2+ and N3+ ions are the main multicharged ions at 532 nm, while He-like N5+ ion is the domain multicharged ion at 1064 nm.     

Fragmentation of the tryptophan cluster [Trp9-2H]2- induced by different activation methods

Electrospray ionization (ESI) of tryptophan gives rise to multiply charged, non‐covalent tryptophan cluster anions, [Trp_n–xH]^x?, in a linear ion trap mass spectrometer, as confirmed by high‐resolution experiments performed on a Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometer. The smallest multiply charged clusters that can be formed in the linear ion trap as a function of charge state are: x = 2, n = 7; x = 3, n = 16; x = 4, n = 31. The fragmentation of the dianionic cluster [Trp₉–2H]^2? was examined via low‐energy collision‐induced dissociation (CID), ultraviolet photodissociation (UVPD) at 266 nm and electron‐induced dissociation (EID) at electron energies ranging from >0 to 30 eV. CID proceeds mostly via charge separation and evaporation of neutral tryptophan. The smallest doubly charged cluster that can be formed via evaporation of neutral tryptophans is [Trp₇–2H]^2?, consistent with the observation of this cluster in the ESI mass spectrum. UVPD gives singly charged tryptophan clusters ranging from n = 2 to n = 9. The latter ion arises from ejection of an electron to give the radical anion cluster, [Trp₉–2H]^?.. The types of gas‐phase EID reactions observed are dependent on the energy of the electrons. Loss of neutral tryptophan is an important channel at lower energies, with the smallest doubly charged ion, [Trp₇–2H]^2?, being observed at 19.8 eV. Coulomb explosion starts to occur at 19.8 eV to form the singly charged cluster ions [Trp_x–H]^? (x = 1–8) via highly asymmetric fission. At 21.8 eV a small amount of [Trp₂–H–NH₃]^? is observed. Thus CID, UVPD and EID are complementary techniques for the study of the fragmentation reactions of cluster ions. Copyright © 2010 John Wiley & Sons, Ltd.     

Photon energy dependence of fragmentation of small argon clusters

Photofragmentation of small argon clusters with size below ten atoms is reported. In this size range significant modifications from the electronic properties and geometry take place. When tuning the photon energy through the argon 2p edge, the fragmentation pattern is changed. Specifically, cation dimer production is enhanced at the 2p(32)-->4s resonance, while above the 2p edge almost complete atomization is observed. In both cases, the widths of the peaks in the mass spectra indicate that a large amount of kinetic energy is imparted to the fragment due to the formation of multiply charged clusters. A model based on "Coulomb explosion"-charge separation, simply resulting in a complete atomization of the cluster with no dependence on the photon energy-is insufficient to explain the observed photofragmentation of small clusters.     

Predicting stability limits for pure and doped dicationic noble gas clusters undergoing coulomb explosion: A parallel tempering based study

We have used a replica exchange Monte‐Carlo procedure, popularly known as Parallel Tempering, to study the problem of Coulomb explosion in homogeneous Ar and Xe dicationic clusters as well as mixed Ar–Xe dicationic clusters of varying sizes with different degrees of relative composition. All the clusters studied have two units of positive charges. The simulations reveal that in all the cases there is a cutoff size below which the clusters fragment. It is seen that for the case of pure Ar, the value is around 95 while that for Xe it is 55. For the mixed clusters with increasing Xe content, the cutoff limit for suppression of Coulomb explosion gradually decreases from 95 for a pure Ar to 55 for a pure Xe cluster. The hallmark of this study is this smooth progression. All the clusters are simulated using the reliable potential energy surface developed by Gay and Berne (Gay and Berne, Phys. Rev. Lett. 1982, 49, 194). For the hetero clusters, we have also discussed two different ways of charge distribution, that is one in which both positive charges are on two Xe atoms and the other where the two charges are at a Xe atom and at an Ar atom. The fragmentation patterns observed by us are such that single ionic ejections are the favored dissociating pattern. © 2017 Wiley Periodicals, Inc.     

Study of coulomb explosion and dissociation channels in dicationic argon clusters: a study based on stochastic optimization

In this article, we explore the use of stochastic optimization technique, namely simulated annealing, in elucidating the correct cut-off limit for suppression of Coulomb explosion in dicationic argon gas clusters. We also do a detail study of cluster sizes where the clusters are not stable as one single entity, and try to find out the dissociation channels for these, namely fission or non-fission type. We compare our results with available literature results, both theoretical and experimental.     

Fragmentation dynamics of methane by few-cycle femtosecond laser pulses

The fragmentation pattern of CH4 was experimentally studied at an intensity of approximately 10(14) W/cm2 with laser durations varying from 8 to 110 fs. When the laser duration was 8 fs, only the primarily fragmental CH3+ ion was observed in addition to the parent CH4+ ion. When the laser duration was 30 fs, small fragmental CH2+ and H+ ions appeared. When the laser duration was 110 fs, some doubly charged ions were also observed in addition to the abundant singly charged ions. The large mass spectra difference demonstrated that the pulse duration had a strong effect on the fragmentation of the parent ion produced in the single ionization. The effect of laser intensity on the fragmentation of CH4+ was also studied for few-cycle femtosecond laser pulses. The results demonstrated that the first-return recollision between the rescattered electron and the parent ion played a significant role in the fragmentation dynamics of the parent ion. Depending on the ion-electron impact energy, the recollision excited the parent ion to a dissociated state or doubly charged state. The experimentally observed singly charged fragmental ions resulted from the recollision-induced dissociation of CH4+ or the Coulomb explosion of CH(4)2+.     

Explosive photodissociation of methane induced by ultrafast intense laser

A new type of molecular fragmentation induced by femtosecond intense laser at the intensity of 2 x 10(14) W/cm2 is reported. For the parent molecule of methane, ethylene, n-butane, and 1-butene, fluorescence from H (n = 3-->2), CH (A 2Delta, B 2Sigma-, and C 2Sigma+-->X 2Pi), or C2 (d 3Pi g-->a 3Pi u) is observed in the spectrum. It shows that the fragmentation is a universal property of neutral molecule in the intense laser field. Unlike breaking only one or two chemical bonds in conventional UV photodissociation, the fragmentation caused by the intense laser undergoes vigorous changes, breaking most of the bonds in the molecule, like an explosion. The fragments are neutral species and cannot be produced through Coulomb explosion of multiply charged ion. The laser power dependence of CH (A-->X) emission of methane on a log-log scale has a slope of 10 +/- 1. The fragmentation is thus explained as multiple channel dissociation of the superexcited state of parent molecule, which is created by multiphoton excitation.     

Electron‐induced dissociation of doubly protonated betaine clusters: controlling fragmentation chemistry through electron energy

The [M₂₁+2H]²⁺ cluster of the zwitterion betaine, M = (CH₃)₃NCH₂CO₂, formed via electrospray ionisation (ESI), has been allowed to interact with electrons with energies ranging from >0 to 50 eV in a Fourier transform ion cyclotron resonance (FT‐ICR) mass spectrometer. The types of gas‐phase electron‐induced dissociation (EID) reactions observed are dependent on the energy of the electrons. In the low‐energy region up to 10 eV, electrons are mainly captured, forming the charge‐reduced species, {[M₂₁+2H]^{+ .} }*, in an excited state, which stabilises via the ejection of an H atom and one or more neutral betaines. In the higher energy region, above 12 eV, a Coulomb explosion of the multiply charged clusters is observed in highly asymmetric fission with singly charged fragments carrying away more than 70% of the parent mass. Neutral betaine evaporation is also observed in this energy region. In addition, a series of singly charged fragments appears which arise from C? X bond cleavage reactions, including decarboxylation and CH₃ group transfer. These latter reactions may arise from access of electronic excited states of the precursor ions. Copyright © 2009 John Wiley & Sons, Ltd.     

Unimolecular chemistry of doubly protonated zwitterionic clusters

Electrospray ionization and tandem mass spectrometry experiments have been used to study the fragmentation and electron-ion interactions of doubly charged zwitterionic clusters, [M(15) + 2H](2+) (where M = Glycine Betaine (GB), (CH(3))(3)N(+)CH(2)CO(2)(-), and Dimethylsulfonioacetate (DMSA), (CH(3))(2)S(+)CH(2)CO(2)(-)) which are close to the stability limit, i.e., the Coulomb repulsion of the charge within the cluster competes with attractive forces. The intercluster chemistry was studied using collision-induced dissociation (CID) and electron-induced dissociation (EID) in which the energy of the electrons has been varied from >0 to 30 eV. Experimental results suggest that the zwitterionic binding energy in the clusters follow the order GB > DMSA, which is consistent with theoretical calculations that highlight that the lower dipole moment of DMSA leads to a binding energy of DMSA that is 0.86 times smaller than that for GB. Multiply protonated clusters of both GB and DMSA dissociate through Coulomb explosion, which is in competition with neutral evaporation for DMSA. Electronic excitation of the cluster under EID conditions at higher electron energies >12 eV can lead to new intercluster reactions associated with bond cleavages where differences between the sulfur and nitrogen betaines are minor.     

Double ionization and Coulomb explosion of the formic acid dimer by intense near-infrared femtosecond laser pulses

Ionization and fragmentation of formic acid dimers (HCOOH)(2) and (DCOOD)(2) by irradiation of femtosecond laser pulses (100 fs, 800 nm, ~1 × 10(14) W/cm(2)) were investigated by time-of-flight (TOF) mass spectrometry. In the TOF spectra, we observed fragment ions (HCOOH)H(+), (HCOOH)HCOO(+), and H(3)O(+), which were produced via the dissociative ionization of (HCOOH)(2). In addition, we found that the TOF signals of COO(+), HCOO(+), and HCOOH(+) have small but clear side peaks, indicating fragmentation with large kinetic energy release caused by Coulomb explosion. On the basis of the momentum matching among pairs of the side peaks, a Coulomb explosion pathway of the dimer dication, (HCOOH)(2)(2+) → HCOOH(+) + HCOOH(+), was identified with the total kinetic energy release of 3.6 eV. Quantum chemical calculations for energies of (HCOOH)(2)(2+) were also performed, and the kinetic energy release of the metastable dication was estimated to be 3.40 eV, showing good agreement with the observation. COO(+) and HCOO(+) signals with kinetic energies of 1.4 eV were tentatively assigned to be fragment ions through Coulomb explosion occurring after the elimination of a hydrogen atom or molecule from (HCOOH)(2)(2+). The present observation demonstrated that the formic acid dimer could be doubly ionized prior to hydrogen bond breaking by intense femtosecond laser fields.