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Volume 104, Issue 18, 08 May 1996

Simulation of ultrafast dynamics and pump–probe spectroscopy using classical trajectories
View Description Hide DescriptionIn this paper, we develop a method for accurately modeling ultrafast molecular dynamics and pump–probe spectroscopy using classical trajectory simulations. The approach is based on a semiclassical limit of the Liouville formulation of quantum mechanics. Expressions for the nonstationary classical phase space probability density created by an ultrashort laser pulse on an excited electronic state, and the observable fluorescence signal resulting from a pump–probe experiment, are derived in the weak‐field limit using perturbation theory. By introducing additional approximations, these expressions are cast in a form that can be directly implemented using classical trajectory integration and ensemble averaging. The method is tested against multisurface time‐dependent quantum mechanical wave packet calculations for a one‐dimensional model system representing I_{2} photodissociation‐recombination in a static Ar lattice. Nearly quantitative agreement between the exact calculations and the trajectory‐based method is obtained. Although demonstrated for a one‐dimensional system, the method is easily incorporated in conventional molecular dynamics programs, allowing efficient treatment of many‐body ultrafast dynamics and spectroscopy.

Theory of magnetic circular dichroism in molecules oriented by photoselection
View Description Hide DescriptionExpressions describing the absorption of light by molecules partially aligned by photoselection in the presence of a static external magnetic field are presented in complete form as a function of the molecular moments and the polarizationproperties of excitation and probe beams. The magnetic circular dichroism(MCD) of such samples is shown to involve terms arising from the coupling of electronic transition moments for excitation and probe photons that are additional to terms present in isotropic samples. The theoretical description presented here provides a basis for understanding the nature of MCD signals in samples partially aligned by photoselection and for interpreting the time evolution of MCD measurements when photoselection‐induced alignment decays through rotational diffusion.

Lifetime measurements of selectively excited rovibrational levels of the V ^{1} B _{2} state of CS_{2}
View Description Hide DescriptionThe radiative lifetimes of selectively excited rovibrational levels of the V ^{1} B _{2} state of the CS_{2} molecule have been measured under collision‐free conditions in a cold molecular beam using a pulse‐modulated frequency‐doubled single‐mode cw dye laser. Pure exponential fluorescence decays were found for all excited levels. The lifetimes, scattering considerably in the range of 2–13 μs, give evidence of interactions of the V ^{1} B _{2} state with background states. A deperturbation analysis performed for rotational levels involved in local two‐level interactions yields detailed quantitative information on the V ^{1} B _{2} state and on the background levels. It is shown that these levels represent rovibrational levels of the B _{2}(^{3} A _{2}) state and highly excited rovibrational levels of the X ^{1}Σ_{ g } ^{+} electronic ground state. The coupling mechanisms are: (1) the spin–orbit interaction between the V ^{1} B _{2} state and the B _{2}(^{3} A _{2}) state where the latter is coupled to the X ^{1}Σ_{ g } ^{+}ground state by spin–orbit/vibronic and spin–orbit/Coriolis interaction and (2) the Coriolis coupling of the V ^{1} B _{2} state to the X ^{1}Σ_{ g } ^{+}ground state. Further sources of perturbations are the spin‐uncoupling in the ^{3} A _{2} state and the Renner–Teller coupling of the V ^{1} B _{2} state to the ^{1} A _{2} state. From the measured radiative lifetimes of the background states information on the electronic structure of the CS_{2} molecule is gained.

The low‐lying electronic states of CoF
View Description Hide DescriptionThe emission spectrum of CoF has been investigated in the 820 nm–3.5 μm spectral region using a Fourier transformspectrometer. The bands were excited in a carbon tube furnace by the reaction of cobalt metal vapor and CF_{4} at a temperature of about 2300 °C. The bands observed in the 3000–9000 cm^{−1} region have been classified into three new transitions. The bands with 0‐0 R‐heads at 3458 cm^{−1}, 3759 cm^{−1}, and 4012 cm^{−1} have been assigned as the ^{3}Δ_{1}–^{3}Φ_{2}, ^{3}Δ_{2}–^{3}Φ_{3}, and ^{3}Δ_{3}–^{3}Φ_{4} subbands of the C ^{3}Δ–X ^{3}Φ_{ i } electronic transition. To higher wave numbers, two bands with R‐heads at 8396 cm^{−1} and 8565 cm^{−1} have been assigned as the ^{3}Δ_{2}–^{3}Φ_{3} and ^{3}Δ_{3}–^{3}Φ_{4} subbands of the D ^{3}Δ–X ^{3}Φ_{ i } transition. In addition, the bands with R‐heads at 6339 cm^{−1} and 6542 cm^{−1} have been assigned as the 0‐0 ^{3}Φ_{4}–^{3}Δ_{3} and ^{3}Φ_{3}–^{3}Δ_{2} subbands of the G ^{3}Φ–C ^{3}Δ transition. The G ^{3}Φ–X ^{3}Φ transition has been reported previously as the [10.3]^{3}Φ–X ^{3}Φ transition. The rotational analysis of many bands of these transitions has been obtained and the molecular constants for the two new low‐lying excited states have been extracted. Six new band involving the high vibrational levels of ground state (up to v=6) have been identified in the ^{3}Φ_{4}–^{3}Φ_{4} subband of the G ^{3}Φ–X ^{3}Φ transition. The rotational analysis of these bands provides improved constants for the ground state. We have noticed, as have previous workers, the strong correspondence that exists between the states of transition metal monofluorides and monohydrides. In addition, all of the low‐lying states of CoF and CoH are related to the low‐lying terms of the Co^{+} atom. We discuss these correlations between the energy levels of CoF, CoH, and Co^{+}.

Algebraic approach to molecular spectra: Two‐dimensional problems
View Description Hide DescriptionThe Lie algebraic approach is extended to two‐dimensional problems (rotations and vibrations in a plane). Bending vibrations of linear polyatomic molecules are discussed. The algebraic approach is particularly well suited to treat coupled bending modes. The formalism needed to treat coupled benders is introduced and a sample case, acetylene, is analyzed in terms of two coupled local benders.

Phase transitions and critical dynamics in (C_{18}H_{37}NH_{3})_{2}SnCl_{6}
View Description Hide DescriptionPhase transitions in the layer structured (C_{18}H_{37}NH_{3})_{2}SnCl_{6} were studied using ^{1}H NMR. The spin‐lattice relaxation rate reflects the critical slowing down around the order–disorder phase transition temperature, and is compatible with the three‐dimensional Ising model. A critical slowing down is also observed at the conformational transition in the second moment measurement, presumably for the first time.

Light‐induced migration of Ag in Xe films and generation of sites
View Description Hide DescriptionScattering losses and inhomogeneous broadening are reduced by an optimized cocondensation of laser evaporated Ag atoms with Xe gas allowing the determination of absolute quantum efficiencies in light‐induced processes. A jump probability per absorbed photon increasing from 10% to about unity for higher temperatures is observed for the migration of Ag atoms originating from electronic excitation. A model based on a concerted host–guest motion is proposed. A well defined metastable site with a strongly red shifted absorption band and a generation probability of 1.5% which decreases with temperature is attributed to an intermediate position in the migration process.

Vibronic effects in the photon energy‐dependent photoelectron spectra of the CH_{3}CN^{−} dipole‐bound anion
View Description Hide DescriptionPhotoelectron spectra are reported for the ‘‘dipole‐bound’’ CH_{3}CN^{−} negative ion at three photodetachmentenergies (1.165, 2.331, and 3.496 eV), where the anion is prepared by photodissociation of the I^{−}⋅CH_{3}CN ion–molecule complex. While all three spectra are dominated by a single feature centered near zero electron binding energy, as expected for a dipole‐bound anion, vibrational structure is also observed and found to depend strongly on the photodetachmentenergy. This observation indicates that the vibrational excitation is not exclusively due to distortion between the ion and neutral, but also involves non‐‘‘Franck–Condon’’ effects. The origin of the energy dependence is traced to excitation of the π_{CN} ^{*} shape resonance corresponding to the valence or ‘‘chemical’’ anion. The vibrational envelope of the nonresonant spectrum is surprisingly similar to the infrared spectrum of neutral acetonitrile, suggesting that even this excitation may not result from intramolecular distortions. We develop a simple model to illustrate that vibrational excitation can occur upon photodetachment of a dipole‐bound electron due to the perturbation of the weakly bound electron by the fluctuatingdipole moment of the vibrating neutral molecule. We treat this effect in a Herzberg–Teller interaction picture where the dipole‐bound state is mixed with the low lying electron continuum through a dipolar interaction with the neutral molecule.

Electronic spectroscopy and quenching dynamics of OH–H_{2}/D_{2} pre‐reactive complexes
View Description Hide DescriptionBinary complexes of OH X ^{2}Π and H_{2}/D_{2} have been stabilized in the entrance valley to the hydrogen abstraction reaction and identified in the OH A ^{2}Σ^{+}–X ^{2}Π 0–0 spectra region. Nearly all of the intermolecular vibrational levels supported by the OH A ^{2}Σ^{+} (v′=0)+H_{2}/D_{2}potential energy surface have been observed in fluorescence depletion experiments. Rapid electronic quenching precludes the observation of OH–H_{2}/D_{2} prepared in these levels by laser‐induced fluorescence. A sharp onset of laser‐induced fluorescence occurs at the OH A ^{2}Σ^{+} (v′=0)+H_{2}/D_{2}dissociation limit. The binding energies for OH–H_{2}/D_{2} in the ground state correlating with OH X ^{2}Π (v″=0)+H_{2}/D_{2} have been determined to be 54 cm^{−1} and more than 66 cm^{−1}, respectively. The OH A ^{2}Σ^{+} (v′=0)+H_{2}/D_{2}excited state is found to be at least 577 cm^{−1} (H_{2}) and 639 cm^{−1} (D_{2}) more strongly bound than the ground state. The positions of observed features are compared with the corresponding intermolecular levels observed by laser‐induced fluorescence in the OH A–X 1–0 region as well as theoretical predictions of the transition energies based on ab initio potentials for the ground and excited electronic states. The OH–H_{2}/D_{2} intermolecular levels correlating with OH A ^{2}Σ^{+} (v′=0)+H_{2}/D_{2} have lifetimes of 3.2–4.5 ps, deduced from homogeneous linewidths, due to quenching and/or chemical reaction.

Ab initio collision‐induced polarizability, polarized and depolarized Raman spectra, and second dielectric virial coefficient of the helium diatom
View Description Hide DescriptionSymmetry‐adapted perturbation theory has been applied to compute the interaction‐induced polarizability for the helium diatom. The computed polarizability invariants have been analytically fitted, and used in quantum‐dynamical calculations of the binary collision‐induced Raman spectra. The predicted intensities of the depolarized spectrum are in good agreement with the experimental data [M.H. Proffitt et al., Can. J. Phys. 59, 1459 (1981)]. The computed polarized spectrum shows agreement with the experiment within the large experimental uncertainties. The calculated trace polarizability was also checked by comparison of computed second dielectric virial coefficients with the experimental data. The ab initiodielectric virial coefficients, including first and second quantum corrections, agree well with the experimental data from indirect measurements.

On the direct complex scaling of matrix elements expressed in a discrete variable representation: Application to molecular resonances
View Description Hide DescriptionWe present an extension of a method initially proposed by Moiseyev and Corcoran [Phys. Rev. A 20, 814 (1978)] to a direct continuation of the matrix elements of a real Hamiltonian operator expressed in a contracted, discrete variable representation type basis set. It is based on the identity which relates the matrix elements of a complex scaled potential between real basis set functions to those of the unscaled potential between backward scaled basis functions. The method is first applied to the study of the resonances of a one dimensional model by means of complex scaling. It is shown that the resulting matrix elements of the scaled potential are no longer diagonal in the DVR. This paradox is discussed and shown to be of no practical consequence in the formulation. The scheme is then extended to the direct complex scaling of a two dimensional Hamiltonian operator expressed in a contracted basis set built through the successive adiabatic reduction method of Bac̆ić and Light. Results show that, due to the use of a numerical continuation, slightly larger grids have to be used as compared to the case of an analytic continuation where the potential is available.

Comparison of positive flux operators for transition state theory using a solvable model
View Description Hide DescriptionSeveral quantum operators representing ‘‘positive flux’’ are compared for the square barrier by examining their ability to reproduce the exact transmittance when traced with the exact microcanonical density operator. They are obtained by means of the ‘‘Weyl rule,’’ the ‘‘Rivier rule,’’ by symmetrizing the product of ‘‘flux’’ and ‘‘positive momentum projection’’ operators, and by a variational technique. Explicit expressions are given for all cases.

An experimental study of HF photodissociation: Spin–orbit branching ratio and infrared alignment
View Description Hide DescriptionSingle rotational levels of HF (v=3) were prepared by using overtone excitation and these molecules were then photodissociated by ultraviolet (UV)radiation at 193.3 nm. Time‐of‐flight spectra of the hydrogen atom fragment provided the spin–orbit state distribution of the fluorine fragment. Changing the UVphotolysis laser polarization confirmed an A ^{1}Π←X ^{1}Σ^{+} electronic transition in the photodissociation step. Photodissociation of HF at 121.6 nm is also reported. Infrared (IR) induced alignment of the diatom was studied by monitoring the IR laser polarization dependence of the H‐atom product angular distribution. Depolarization due to hyperfine interaction was studied by using the R(0) transition. Agreement with theory is excellent.

Translational relaxation and electronic quenching of hot O(^{1} D) by collisions with N_{2}
View Description Hide DescriptionTranslational relaxation and electronic quenching processes of translationally hot O(^{1} D) atoms by collisions with N_{2} in a gas cell at room temperature are studied using a vacuum ultraviolet laser induced fluorescence technique. The initial hot O(^{1} D) atoms which have translational energies of 18.2 and 9.8 kcal mol^{−1} are produced by the photodissociation of N_{2}O at 193 nm and O_{2} at 157 nm, respectively. The translational relaxation processes are investigated by time resolvedmeasurements of the Doppler profiles for the O(^{1} D) atoms, while the quenching processes are studied by measuring both the decrease of the O(^{1} D) concentration and the increase of the product O(^{3} P) concentration after the photochemical formation of the hot O(^{1} D) atoms. When the initial translational energy of O(^{1} D) is 9.8 kcal mol^{−1}, about 40% of the O(^{1} D) atoms are electronically quenched before the entire thermalization of the hot O(^{1} D) atoms takes place in a gaseous mixture with N_{2}. This indicates that the translational relaxation rate of O(^{1} D) by collisions with N_{2} is not fast enough compared with the electronic quenching by N_{2}. It is found that the steady state distribution of the O(^{1} D) translational energy in the upper stratosphere is superthermal and that the populations at high translational energies are higher than that estimated from an equilibrated condition with the ambient air. The cross section of the electronic quenching by N_{2} at the high collision energy of (8±6) kcal mol^{−1} is found to be (0.7±0.1) Å^{2}, which is about 5 times smaller than that at thermal collision energy at 298 K.

Initial state laser control of curve‐crossing reactions using the Rayleigh–Ritz variational procedure
View Description Hide DescriptionA new two‐step procedure for laser control of photodissociation is presented. In the first step of the procedure, we show that control of photodissociation product yields can be exerted through preparation of the initial wave function prior to application of the photodissociation field in contrast to previous laser control studies where attention has focused on the design of the field which induces dissociation. Specifically, for a chosen channel from which maximum product yield is desired and a given photodissociation field, the optimal linear combination of vibrational eigenstates which comprise the initial wave function is found using a straightforward variational calculation. Any photodissociation pulse shape and amplitude can be assumed since the Schrödinger equation is solved directly. Application of this method to control of product yields in the photodissociation of hydrogen iodide is demonstrated. The second step of the control procedure involves the preparation of the coherent superposition of discrete levels obtained from the previous step; design of the preparatory field can be done analytically for two or three level systems as demonstrated here or with other well‐studied iterative field design methods.

Spin–orbit relaxation kinetics of Br(4 ^{2} P _{1/2})
View Description Hide DescriptionPulsed and steady‐state photolysis techniques have been employed to measure the rate coefficients for collisional deactivation of the spin–orbit excited state of atomic bromine, Br(4 ^{2} P _{1/2}). Pulsed lifetime studies for quenching by Br_{2} and CO_{2} yielded absolute rate coefficients at room temperature of k _{Br2 }=1.2±0.1×10^{−12} and k _{CO2 }=1.5±0.3×10^{−11} cm^{3}/molecule s. The rate coefficients for quenching by rare gases, N_{2}, O_{2}, NO, NO_{2}, N_{2}O, CO, CO_{2}, COS, SO_{2}, SF_{6}, CF_{4}, CH_{4}, H_{2}S, H_{2}, D_{2}, HBr, HCl, and HI, relative to that for Br_{2} were determined in a steady‐state photolysis experiment. Correlation of the deactivation probabilities with energy defect for the case of electronic‐to‐vibrational energy transfer is demonstrated.

Semiclassical analysis of resonance states induced by a conical intersection
View Description Hide DescriptionThe resonance states induced by nonadiabatic coupling in the conical intersection problem are analyzed semiclassically. Not only the general framework but also the explicit analytical expressions of resonance positions and widths are presented. Interestingly, the nonadiabatic transition schemes are found to be quite different in the two representations employed, i.e., the adiabatic and generalized adiabatic (or dynamical state, or postadiabatic) representations. In the former case the transition is assigned to be of the Landau–Zener (LZ) type, and the latter case is analyzed by a mixture of LZ‐ and Rosen–Zener (RZ)‐type in the case of m≥3/2 and by the nonadiabatictunneling (NT) type in the case of m=1/2, where m is the angular momentum quantum number. Both of these semiclassical results agree well not only with each other in spite of the very different schemes, but also with the exact numerical results in a wide range of energy and angular momentum.

Coherent population transfer and dark resonances in SO_{2}
View Description Hide DescriptionHighly efficient population transfer between the (0,0,0) and the (9,1,0) vibrational levels of the electronic ground state X̃ ^{1} A _{1} of SO_{2} is demonstrated. The process relies on stimulated Raman scattering with adiabatic passage induced by two suitably delayed ultraviolet laser pulses with nearly transform‐limited bandwidth. A transfer efficiency of 100% is achieved. The associated dark resonance is observed. Properties of the latter are compared for delayed and fully overlapping pulses.

A coupled cluster study of the spectroscopic properties and electric dipole moment functions of nitrous sulfide
View Description Hide DescriptionThree‐dimensional near‐equilibrium potential energy surfaces and dipole moment functions have been calculated for the ground state of nitrous sulfide (NNS), using a large basis set and the coupled cluster method with single and double substitutions, augmented by a perturbative estimate of triple excitations [CCSD(T)]. The CCSD(T) equilibrium bond lengths with a correlation consistent polarized valence quadruple zeta (cc‐pVQZ) basis set are r _{ e }(NN)=1.1284 Å and R _{ e }(NS)=1.5904 Å, which have been corrected to 1.126 and 1.581 Å, respectively, based on the results of the corresponding calculations on the NN and NS diatomics. Rotational–vibrational energy levels and the corresponding infrared intensities for NNS have been determined using variational methods with the CCSD(T)/cc‐pVQZ potential energy and dipole moment functions. The calculated band origins (cm^{−1}) ν_{1}, ν_{2}, and ν_{3} and their intensities (km/mol) at the CCSD(T)/cc‐pVQZ level are 740.7/38.6, 463.1/0.01, and 2061.4/385.8, respectively. A complete set of second‐order spectroscopic constants have been obtained from the ab initiopotential energy surface using both the standard perturbation theory formulas and the variationally determined rovibrational energies. Comparison of the theoretical vibration–rotation interaction constants (α_{ i }) with those obtained from the published high resolution Fourier transform infrared (FTIR) spectra clearly demonstrate that the rotational quantum number (J) assignments must be revised in all the observed hot bands. A new set of spectroscopic constants for NNS, derived from a reanalysis of the published FTIR frequencies, is presented. These are in excellent agreement with our CCSD(T) predictions. Values of the quadrupole coupling constants at each nucleus are predicted using multireference configuration interaction (MRCI) with the same cc‐pVQZ basis.

A theoretical study of the ionic dissociation of HF, HCl, and H_{2}S in water clusters
View Description Hide DescriptionThe ionic dissociation of HF, HCl, and H_{2}S in water is examined using density functional theory(DFT), Hartree–Fock (HF), and Mo/ller–Plesset theory to second order (MP2). The calculations show that HF, HCl, and H_{2}S form fully dissociated stable clusters with four water molecules. Each cluster appears to be stabilized by the formation of six hydrogen bonds. These calculations also indicate that a minimum of four water molecules are required to form stable structures in which positive and negative ions coexist in the cluster. The hydrogen transfer between the acid and water molecules is very similar to the mechanism proposed for hydrogen transfer in water solutions. The binding energies of the hydrated hydrofluoric acid, hydrated hydrochloric acid, and hydrated hydrogen disulfide estimated with B‐LYP are 37.51, 41.17, and 20.68 kcal/mol, respectively.