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Notes: In this paper we explore the energetic control of sequential and superexchange electron transfer (ET) mechanisms on the basis of quantum-mechanical simulations and calculations for long-range ET in DBA systems, where the donor (D) and the acceptor (A) are separated by a bridge (B). We studied ET dynamics in a Franck–Condon (FC) system characterized by three multi-dimensional displaced harmonic potential surfaces, where an initial single vibronic doorway state |α〉 (with energy Eα) in the DBA (≡D) electronic state is coupled to the mediating {|β〉} vibronic quasicontinuum of the D+B−A (≡B) electronic state, which in turn is coupled to the final {|γ〉} vibronic quasicontinuum of the D+BA− (≡A) electronic state. The level structure was described by the vibrational frequencies (for a four-mode harmonic system) and the energy gaps ΔGDB and ΔGDA between the origins of the corresponding electronic states (with nα=1–50, nβ=1000–2000, and nγ=1000–2000 states in the {|α〉}, {|β〉}, and {|γ〉} manifolds, respectively), while the couplings were characterized by the spectral densities and by the pair correlations (specified in terms of correlation parameters ηαα′ and ηββ′) between states belonging to the same manifold. The correlation parameters ηαα′ (α,α′=1–40) for the doorway-quasicontinuum coupling and ηββ′ (β,β′=150–190) for the interquasicontinuum coupling are considerably lower than unity (|ηαα′|≤0.4 and |ηββ′|≤0.3), obeying propensity rules with the highest values of |ηαα′| and |ηββ′| which correspond to a single vibrational quantum difference, while for multimode changes between α and α′ or between β and β′ very low values of |ηαα′| or |ηββ′| are exhibited. Radiationless transitions theory was applied for quantum-mechanical simulations based on the dynamcis of wave packets of molecular eigenstates for resonance (ΔGDB〈Eα) and for off-resonance (ΔGDB〉Eα) coupling. Resonance |α〉–{|β〉}–{|γ〉} coupling results in two-step sequential ET kinetics for all doorway states |α〉, manifesting phase erosion due to weakly correlated intercontinuum coupling, without the need of intermediate state phonon induced thermalization. Off-resonance |α〉–{|β〉} coupling in conjunction with {|β〉}–{|γ〉} resonance interactions results in unistep superexchange ET kinetics. The simulated sequential ET rates and the superexchange rate are in good agreement with the calculated quantum-mechanical rates obtained using the electronic couplings and FC densities. The energy-gap (ΔGDB) dependence of the simulated and the calculated ET rates from a single doorway state reveal a "transition" from sequential to superexchange ET with increasing ΔGDB. For a finite-temperature system, characterized by a fixed ΔGDB (〉0) small energy gap, the thermally averaged rate from a canonical ensemble of doorway states will result in the superposition of both superexchange and sequential mechanisms. © 1997 American Institute of Physics.

Notes: Ultrafast femtosecond Coulomb explosion of charged homogeneous (Xen) and heterogeneous doped (HIArn) small and medium sized clusters (n〈60) is studied resting on the picture of a vertical high-order multiphoton ionization from the ground state nuclear configuration. The final average atomic velocity (simulated at constant charge) increases with increasing the cluster size, and at constant cluster size increases linearly with the ion charge, in accord with the predictions of an analytical model. The linear dependence of the reciprocal explosion time on the charge is also in accord with the analytical prediction. From the energetics of the Coulomb explosion (reflecting a probable initial atomic distribution of the cluster size for small clusters), a nonvertical multiphoton ionization during the Coulomb explosion cannot be inferred. © 1997 American Institute of Physics.

Notes: In this paper we explore temporal vibrational coherence effects in nonadiabatic radiationless transitions between two electronic states in a large molecule or in the condensed phase, accounting explicitly for the role of the (intramolecular and/or medium) vibrational quasicontinuum of the final states. Our treatment of the time evolution of the wave packet of states and of coherence effects in the nonradiative population probabilities of the reactants and the products rests on the diagonalization of the Hamiltonian of the entire multimode system, with supplementary information being inferred from the effective Hamiltonian formalism. New features of the vibrational Franck–Condon quasicontinuum, which originate from weak, but finite, correlations between off-diagonal coupling terms, were established. The state dependence of the off-diagonal couplings Vsα between the doorway states manifold {|s〉} and the quasicontinuum {|α〉} was quantified by the correlation parameters ηss=〈VsαVαs〉/[〈Vsα2〉〈Vsα2〉]1/2, where 〈 〉 denotes the average over the relevant energy range. Calculations were conducted for a Franck–Condon four-mode system consisting of ns=100 doorway states and nα=3000 quasicontinuum states. The correlation parameters for all pairs of doorway states are considerably lower than unity (|ηss|(approximately-less-than)0.4), obeying propensity rules with the highest values of |ηss| corresponding to a single vibrational quantum difference, while for multimode changes between |s〉 and |s〉 very low values of |ηss| are established. Quantum beats in the population probabilities of products and reactants in nonadiabatic dynamics are characterized by an upper limit for their modulation amplitudes ξ≅(Γ/ΔE)η (for ΔE/2πΓ≥1), where Γ is the decay width of the doorway states and ΔE is their energetic spacing. These low ξ values originate from a small (∼Γ/ΔE) contribution to the off-diagonal matrix elements of the nonradiative decay matrix in conjunction with low correlation parameters. The amplitudes of the quantum beats in nonradiative temporal dynamics provide dynamic information on the larger correlation parameters ηss. Our theoretical and numerical analysis was applied for temporal coherence effects in nonadiabatic electron transfer dynamics in a Franck–Condon quasicontinuum of Mulliken charge transfer complexes [K. Wynne, G. Reid, and R. M. Hochstrasser, J. Chem. Phys. 105, 2287 (1996)]. This accounts for the "preparation" (signature of coherent excitation), for the low amplitudes of coherent temporal modulation of reactants and products (ξ≅0.05–0.06 determined by the ηss parameters) and for the dominating contributions to temporal coherence (subjected to propensity rules). © 1997 American Institute of Physics.

Notes: In this article we explore the structural, dynamic, and spectroscopic implications of large local configurational changes in electronically excited Xe*ArN (N=12,54,146,199) heteroclusters, where the Xe* [≡Xe(3P1)] atom is excited to the lowest dipole-allowed extravalence Rydberg excitation. The ultrafast femtosecond and picosecond dynamics driven by the short-range repulsive interaction between the vertically excited Xe* Rydberg and the cluster Ar atoms was studied by molecular dynamics simulations. From the analysis of the time dependence of the structural parameters for site-specific Xe excitations in medium-sized (N=54) and large (N=146,199) clusters, two general configurational relaxation phenomena were established: a "bubble" formation (i.e., a large configurational dilation around Xe*) for Xe interior sites and a "spring" formation (i.e., the stretching of Xe* outside the cluster) for Xe surface sites. General Xe site-specific features of both bubble and spring formation involve ultrashort (Gaussian) energy transfer to the cluster (∼50–100 fs characteristic times τET) inducing configurational relaxation, which manifests a multimodal time solution. The initial (Gaussian) temporal mode (∼150–300 fs characteristic times τ0〉τET) is followed by an exponential mode (ps lifetime τ1), with subsequent impact induced, damped vibrational coherence effects with frequencies (ω2,ω3), and exponential decay (ps lifetimes τ2,τ3). The bubble formation for the central site of Xe*Ar146 or Xe*Ar54 is induced by energy transfer of τET≅60 fs followed by subsequent multimodal dilation with τ0≅170 fs and τ1≅2 ps, and a subsequent expansion with coherent motion of vibrational wave packets with ω2,ω3≅20, 40 cm−1 and τ2,τ3≅2, 6 ps. The bubble reaches an equilibrium configuration after ∼10 ps with asymptotic spatial expansion of ΔRb*=0.7–0.8 Å. The spring formation for an exterior surface site of Xe*Ar146 is τET≅80 fs and τ0≅210 fs, which is followed by a substantial (≅1.2 Å) Xe* stretching and a subsequent contraction accompanied by vibrational coherence effects with ω2≅10 cm−1 and τ2≅20 ps, with the asymptotic spring spatial extension ΔRs*≅0.6 Å, being accomplished after ∼30 ps. Regarding dynamic cluster size effects we established that following vertical excitation at initial temperatures Ti=10–30 K, the following phenomena are manifested: (i) Large Xe*Ar146 and Xe*Ar199 clusters exhibit short-time (10–20 ps) configurational relaxation in rigid clusters. (ii) The central site in a medium-sized Xe*Ar54 cluster undergoes a rigid–nonrigid ("melting") transition induced by the electronic excitation, with the Xe* manifesting long-time (100–200 ps) mass transport from the interior bubble to the surface spring. (iii) Small Xe*Ar12 clusters exhibit stepwise reactive dissociation on the ps time scale. The spectroscopic implications of large configurational relaxation in Xe*ArN (N=54,146) clusters were interrogated by the simulations of the Xe site-specific time-dependent spectral shifts in emission, which decrease from the initial large values [e.g., δνe(t=0)=0.92 eV at Ti=10 K for the central site] to low values. The time evolution of the emission spectral shifts is qualitatively similar to the structural dynamics, which involves initial ultrafast (∼50–100 fs) decay, a (ps) exponential contribution, and a damped oscillatory behavior. The time-resolved Xe site-specific emission spectral shifts obey an exponential structure-spectral relationship which is isomorphous with time-independent relations for the absorption spectral shifts and for the emission asymptotic spectral shifts. Finally, predictions are provided for the spectroscopic interrogation (by energy-resolved fluorescence) of the longer time (∼150 ps) Xe* bubble mass transport in nonrigid Xe*Ar54 clusters. The long-time fluorescence spectra, which were simulated by the spectral density method, exhibit: (i) A Gaussian line shape, corresponding to the slow modulation limit. (ii) Spectral shifts (〈δνe〉=0.01–0.1 eV) exhibiting a site-specific hierarchy, i.e., 〈δνe〉(central)〉〈δνe〉(interior)〉〈δνe〉(surface)〉〈δνe〉(top). (iii) Linewidths (full width at half-maximum) which follow the order of the site-specific hierarchy of the spectral shifts. The calculated site-specific emission spectral shifts and linewidths and the calculated Stokes shifts for central and interior bubble sites and for surface spring sites in Xe*Ar146 are in reasonable agreement with the experimental results for Xe*Ar1400 clusters. Our overall picture regarding the dynamic and spectroscopic implications of large excited-state configurational relaxation provides guidance, predictions, and insight for the fate of Rydberg states in clusters and in the condensed phase. © 1997 American Institute of Physics.

Notes: In this paper we present a theoretical study of the autoionization dynamics of high 2P1/2np′[3/2]1 Rydbergs (with the principal quantum numbers n=100–280) of Ar in weak homogeneous electric fields (F=0.01–1.0 V/cm), which were experimentally interrogated by time-resolved zero-electron kinetic energy (ZEKE) spectroscopy [M. Mühlpfordt and U. Even, J. Chem. Phys. 103, 4427 (1995)], and which exhibit a marked dilution (i.e., ∼2 orders of magnitude lengthening) of the lifetimes relative to those inferred on the basis of the n3 scaling law for the spectral linewidths of the np′ (n=12–24) Rydbergs. The multichannel effective Hamiltonian (Heff) with several doorway state(s) (for excitation and decay) and pure escape states (for decay) was advanced and utilized to treat the dynamics of the mixed Stark manifold of the ZEKE Rydbergs. Heff of dimension 2n−1 is then constructed for a n Rydberg manifold using independent experimental information on the (l dependent) quantum defects δ(l) and the (l, K, J dependent) decay widths, which are of the form Γ0(lKJ)/(n−δ(l))3, with Γ0(lKJ) being the decay widths constants. Here, l, K, and J are the azimuthal, the electronic and the total electronic angular momentum quantum numbers, respectively. Two coupling ranges are distinguished according to the strength of the reduced electric field F¯(n,p′)=(F/V cm−1)n5/ 3.4×109[δ(p′)(mod1)].Range (A); The onset of the effective coupling of the doorway and escape states, i.e., 0.7≤F¯(n,p′)≤2. Range (B); The strong mixing domain F¯(n,p′)≥3. The lifetimes in range (B) can be well represented by a nearly democratic mixing of all the doorway and escape states (lKJ), with the average value 〈τ(n)〉(approximately-equal-to)〈τSM(n)〉= 2n4(h-dash-bar)/[J(lJK)Γ0(lJK)]. In range (B) 〈τ(n)〉 increases with increasing n and is only weakly F dependent. Range (A) is characterized by a hierarchy of two time scales for the decay, with a short decay component, which manifests the residue of the doorway state, and a distribution of very long lifetimes with an average value 〈τLONG(n)〉(approximately-equal-to)η(n)〈τSM(n)〉, where η(n)(approximately-equal-to)2–5. In range (A), 〈τLONG(n)〉 decreases with increasing n and decreases with increasing F, manifesting the enhancement of mixing. We identified range (B) for n=150–280, where a semiquantitative agreement between the experimental ZEKE lifetimes and spectra and our theory was obtained. A tentative identification of range (A) for lower n (=100–150) values was accomplished. We have also performed a theoretical study of the Ar autoionization dynamics via the 2P1/2nd′[3/2]1 doorway state, which was experimentally studied by Merkt [J. Chem. Phys. 100, 2623 (1994)].The onset of range (A) was identified in the region n=70–80, with the estimated lifetimes near the onset being in agreement with experiment. Our analysis explains the higher n onset for the np′ doorway state mixing (n(approximately-equal-to)100 and F(approximately-equal-to)0.1 V/cm) than for the np′ doorway state mixing (n′=70–80 for F(approximately-equal-to)0.1 V/cm). Experimental values of 〈τLONG(n)〉 (around n(approximately-equal-to)90) in range (A), excited via the 2P1/2nd′[3/2]1 doorway state, are considerably longer than those predicted by our theory for l mixing. The discrepancy may be due to (lml) mixing, which presumably originates from Rydberg–ion collisions. © 1995 American Institute of Physics.

Notes: In this paper we explore the level structure, the optical excitation modes and the dynamics of a mixed Stark manifold of very high Rydberg states (with principal quantum numbers n=80–250) of large molecules, e.g., 1,4 diaza bicyclo [2,2,2] octane (DABCO) and bis (benzene) chromium (BBC) [U. Even, R. D. Levine, and R. Bersohn, J. Phys. Chem. 98, 3472 (1994)] and of autoionizing Rydbergs of atoms [F. Merkt, J. Chem. Phys. 100, 2623 (1994)], interrogated by time-resolved zero-electron kinetic energy (ZEKE) spectroscopy. We pursue the formal analogy between the level structure, accessibility and decay of very high Rydbergs in an external weak (F(approximately-equal-to)0.1–1 V cm−1) electric field and intramolecular (interstate and intrastate) relaxation in a bound molecular level structure. The onset n=nM of the strong mixing (in an external field F and in the field exerted by static ions) of a doorway state, which is characterized by a low azimuthal quantum number l, a finite quantum defect δ, and a total nonradiative width Γs(approximately-equal-to)Γ0/n3, with the inactive high l manifold is specified by nM(approximately-equal-to)80.6δ1/5(F/V cm−1)−1/5. At n≥nM the level structure and dynamics are characterized by the product γρ, where ρ is the density of states and γ=ΓsD(n) is the average decay width of the eigenstates, with the dilution factor D(n)≈n−2 for (lml) mixing and D(n)(approximately-equal-to)n−1 for (l) mixing, whereupon γρ=(Γ0/4δR)(nM/n)5, being independent of D(n).The sparse level structure is realized for γρ(very-much-less-than)1, while the dense level structure prevails for γρ(approximately-greater-than)1, resulting in two limiting situations; (a) a dense limit for n≥nM and a sparse limit for n(very-much-greater-than)nM, and (b) a sparse limit for all n≥nM. The experimental information currently available on the decay dynamics of molecular (DABCO and BBC) and atomic (Ar) Rydbergs for n≥nM corresponds to case (b). The time-resolved dynamics was characterized in terms of the excited state total population probability P(t) and the population probability I(t) of the doorway state. P(t), which is interrogated by time-resolved ZEKE spectroscopy, will exhibit for both the sparse and dense level structures and for all excitation conditions a superposition of exponential temporal decay terms with an average lifetime of ∼(h-dash-bar)/γ. I(t) can be used to interrogate coherence effects, which in case (b) are manifested in quantum beats, while case (a) corresponds to a giant resonance with a molecular time characterized by the reciprocal energetic spread of the Stark manifold. The experimental data for the onset of strong mixing and for the diluted lifetimes [(h-dash-bar)/ΓsD(n) with D(n)∼n−1] of the high Rydbergs (n∼100–200) of BBC and of DABCO are in accord with the predictions of the theory for the limit of strong (l) mixing. While strong mixing is realized for F¯=Fn5/3.4×109δ(approximately-greater-than)1, we expect that for the weak mixing regime (F¯〈1) the dynamics of ultrahigh Rydbergs will be characterized by two distinct (∼ns and ∼μs) time scales. Finally, we emphasize the universality of the model, which provides a unified description of the level structure and dynamics of high Rydbergs of molecules and of autoionizing atoms. © 1995 American Institute of Physics.

Notes: In this paper we report on the ground and excited electronic states of localized excess electron surface states of (Ne)−N (N=1.1×104–6×1023) and (H2)−N (N=4.6×103–6×1023) clusters. We used an electron-cluster model potential, which consists of a short-range repulsive interaction with a strength V¯0 [with a lower limit V¯0 ((approximately-greater-than)0) corresponding to the energy of the quasifree electron in the macroscopic condensed material], and a long-range attractive polarization potential, to explore cluster size effects on the energetics and on the charge distribution of these excess electron clusters. The onset of the cluster size for excess electron localization in the ground (n=1, l=0) electronic state was inferred from a near-threshold scaling analysis, being characterized by a "critical'' cluster radius R(1,0)c(approximately-equal-to)2(1−Q)a0/Q, where Q=(ε−1)/4(ε+1) is the effective cluster charge (for the cluster dielectric constant ε), R(1,0)c=39 A(ring) for Ne(s), R(1,0)c=46 A(ring) for Ne(l), R(1,0)c=35 A(ring) for H2(s) and R(1,0)c=41 A(ring) for H2(l), where (s) and (l) denote rigid and nonrigid cluster structures, respectively. With a further increase in the cluster radius R(approximately-greater-than)R(1,0)c, higher nl electronic states become localized.Moving up in the cluster size above the localization threshold, the energy levels Enl can be expressed (for low values of ε≤1.5) in terms of a "universal'' scaling relation Enl/Ef=Φnl(rf/R), where Ef=(e2/2a0)Q2, rf=a0/Q and the scaling function Φnl is independent of ε. This scaling relation allows for the determination of isotope effects and the state of aggregation of the cluster on the energetics of electron localization. In order to make contact with experiment, we have studied electric field-induced ionization and the electronic spectroscopy of these excess electron clusters. The threshold dc electric field F(nl)c for field-induced ionization from the n,l state (over a broad range of R, i.e., R〈320 A(ring) for the 1s and 1p states and R〈900 A(ring) for the 2p state) is of the form F(nl)c∝||Enl||5/4 (ε−1)−1/4R−3. Information on electronic spectroscopy was inferred from the cluster size dependence of the transition energies and oscillator strengths for the 1s(n=1,l=0)→n'p(n'=1,2,...,l=1) transitions. The cluster size dependence of the spectroscopic data for the 1s→1p transition reveals that both the transition energy ΔE(1s→1p) and the oscillator strength f(1s→1p) are proportional to (1/R)2, with ΔE(1s→1p)→0 and f(1s→1p)→0 for R→∞, exhibiting the l degeneracy of the flat surface. On the other hand, for the 1s→2p transition, the energy ΔE(1s→2p) and the oscillator strength f(1s→2p) increase with increasing R, reaching the flat macrosurface value for R→∞.

Notes: In this paper we report on quantum mechanical calculations for the ground and the excited electronic surface states of an excess electron on (He)N clusters (N=3.5×105–6×1023), exploring the cluster size dependence of the excess electron localization and the bridging between the properties of the electron on cluster microsurfaces and on flat macrosurfaces. Representing the e-(He)N potential by a short-range repulsive model potential or by a pseudopotential, together with a long-range attractive dielectric image potential, we have shown that the electronic energies are relatively insensitive (i.e., within 20% for N=106 and within 6% for N≥107) to the details of the short-range repulsive interactions. The model potential results in a "critical'' radius R(1,0)c=148 A(ring) with a number of constituents N(1,0)c=3.0×105 for electron localization in the ground n=1, l=0 electronic state, while with a further increase of the cluster radius R above R(1,0)c, higher n,l states become localized at cluster radii R(n,l)c, with Rc(n,l') (approximately-greater-than) Rc(n,l) for l'(approximately-greater-than)l and Rc(n',l') (approximately-greater-than) Rc(n,l) for n'(approximately-greater-than)n and for all values of l and l'.The energies En,l of the n,l electronic states above the localization threshold are characterized by the scaling relations En,l(R)∝(R−R(n,l)c)η(l) with η(l)=2 for l=0 and η(l)=1 for l≠0. The charge distribution in this size domain for l=0 is characterized by the moments 〈rJ〉∝(R−R(n,0)c)−J, while for l=1, 〈r〉∝(R−R(n,1)c)−1/2. The "critical'' cluster radii for localization obey algebraic relations, which result in the cluster size dependence of the number of bound electronic states. Cluster surface size equations were obtained for R→∞ providing a quantitative description of the convergence of the electronic energies to those for a flat surface. Information on electronic spectroscopy was inferred from the cluster size dependence of the transition energies and oscillator strengths for the 1,0(1s)→n,1(np) electronic excitations. The 1s→1p electronic transition is characterized by a transition energy and an oscillator strength which both decrease as R−2, manifesting the onset of l degeneracy for macrosurfaces. Finally, electric field effects provide information on field-induced ionization and huge polarizabilities αc(approximately-equal-to) (109–1011)αH (where αH is the polarizability of the hydrogen atom) of these giant excess electron states. © 1994 American Institute of Physics.