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Volume 103, Issue 17, 01 November 1995

Doubly excited 1 ^{3}∑^{−} _{ g } state of Na_{2}: Observation and calculation
View Description Hide DescriptionThe v=0–57 levels of the 3p+3p doubly excited 1 ^{3}∑^{−} _{ g } state of Na_{2} have been observed by pulsed perturbation facilitated optical–optical double resonance (PFOODR) fluorescence excitation spectroscopy. The T _{ v=57}=39 943.5 cm^{−1} of the 1 ^{3}∑^{−} _{ g } state is 385 cm^{−1} above the X ^{2}∑^{+} _{ g } v ^{+}=0, J ^{+}=0 ionization threshold and 9 cm^{−1} below the Na (3p,^{2} P _{3/2})+Na(3p,^{2} P _{1/2}) dissociation limit. No significant line broadening was observed above the X ^{2}∑^{+} _{ g } v ^{+}=0, J ^{+}=0 ionization threshold with our resolution. Molecular constants and the Rydberg–Klein–Rees (RKR) potential curve have been obtained from the observed data. The major constants are T _{ e }=36 519.13(17) cm^{−1}, ω_{ e }=93.635(41) cm^{−1}, and B _{ e }=0.118 95(90) cm^{−1}. We have carried out an all‐electron ab initio calculation for the 1 ^{3}∑^{−} _{ g } state and transitiondipole moment for the 1 ^{3}∑^{−} _{ g }↔b ^{3}Π_{ u } system of Na_{2}. Molecular constants calculated from our ab initio potential curve have reasonable agreement with the experimental constants.

Fluorescence depletion spectroscopy of the CH/D–Ne B ^{2}Σ^{−}–X ^{2}Π transition
View Description Hide DescriptionFluorescence depletion techniques were used to test vibronic and rotational assignments for the B ^{2}Σ^{−}–X ^{2}Π transition of CH–Ne. Previous vibronic assignments [W. H. Basinger, U. Schnupf, and M. C. Heaven, Faraday Discuss. 97, 351 (1994)] were confirmed, and observations of transitions to dissociation continua provided accurate dissociation energies for the B and X states. Errors in the rotational assignments were discovered. Re analysis of the rotational structure yielded ground stateparity splittings and improved rotational constants. Adiabatic model calculations were used to determine approximate angular potential energy curves for the B and X states. These calculations also accounted for the prominent optical activity of internal rotation in the spectrum.

Binding energies of carbazole⋅S van der Waals complexes (S=N_{2}, CO, and CH_{4})
View Description Hide DescriptionMass‐selective ground‐state vibronic spectra of molecular van der Waals complexes carbazole⋅S, S=N_{2}, CO, and CH_{4}, were measured by stimulated emission pumping followed by resonant two‐photon ionization of the vibrationally hot complexes. S _{0}‐state vibrational modes were accessed from ≊200 cm^{−1} up to the ground‐state dissociation limit D _{0}(S _{0}) of the van der Waals bond. Above D _{0}, efficient vibrational predissociation of the complexes occurs, allowing accurate determination of the van der Waals dissociation energies as 627.2±7.9 cm^{−1} for N_{2}, 716.5±29.8 cm^{−1} for CO, and 668.6±15.1 cm^{−1} for CH_{4}. In the S _{1}excited state, the van der Waals binding energies increase to 678.5±8.0, 879.2±29.9, and 753.8±15.2 cm^{−1}, respectively. The relative increases upon electronic excitation are about 8% and 13% for N_{2} and CH_{4}, similar to the analogous rare gases Ar and Kr. For CO, the relative increase of van der Waals binding energy is 23%. The differences are primarily due to electrostatic interactions.

Determination of the long‐range potential and dissociation energy of the 1 ^{3}Δ_{ g } state of Na_{2}
View Description Hide DescriptionThe 1 ^{3}Δ_{ g } state of Na_{2} has been studied extensively by both filtered fluorescence and ionization detection and analyzed by both Dunham‐type expansion and near‐dissociation expansion (NDE) models in the analysis. Our observations have covered 99.998% of the potential well depth with the outermost Rydberg–Klein–Rees (RKR) turning point at 28.02 Å. NDE analysis gives T _{ e }=28 032.468 (±0.021) cm^{−1}, D _{ e }=7162.436 (±0.021) cm^{−1}, and R _{ e }=3.463 81 (±0.000 28) Å. Significant long‐range behavior in the near dissociation levels has been observed. Fitting of the RKR turning points gives the long‐range coefficients C _{5}=1.388 (±0.031)×10^{6} cm^{−1} Å^{5} and C _{6}=0.4008 (±0.0046)×10^{8} cm^{−1} Å^{6}. These newly observed results show reasonable agreement with recent theoretical calculations.

The 2345 multimode resonance in acetylene: A bifurcation analysis
View Description Hide DescriptionThis paper reports on a classical phase space bifurcationanalysis of the 2345 Fermi resonance of acetylene. The 2345 Fermi resonance is a multimode nonlinear, resonance coupling that is important to the vibrational dynamics and energy flow of highly excited acetylene. The bifurcationanalysis is performed on an integrable Hamiltonian that represents a planar five‐mode model of acetylene in which the ν_{2}, ν_{3}, ν_{4}, and ν_{5} vibrational modes are nonlinearly coupled through the 2345 Fermi resonance. The phase space structures of the 2345 Fermi resonance are shown to be analogous to but more complicated than phase space structures of the two‐mode, 1:1 and 2:1 Fermi resonance. The results are presented in terms of bifurcation diagrams and molecular catastrophe maps. The bifurcationanalysis of this multidimensional system with a complicated multimode resonance is a step beyond the simple integrable, resonantly coupled two‐mode systems that are now well understood. Analysis of this integrable system also represents a necessary step toward using a multiresonance, i.e., ‘‘chaotic’’ model to decipher the vibrational spectra of highly excited acetylene, based on knowledge of the anharmonic modes born from bifurcations of the low‐energy normal modes.

Wave‐packet dynamics in the Li_{2} E(^{1}Σ^{+} _{ g }) shelf state: Simultaneous observation of vibrational and rotational recurrences with single rovibronic control of an intermediate state
View Description Hide DescriptionA three‐step excitation sequence is used to study the wave‐packet dynamics in the E(^{1}Σ^{+} _{ g }) ‘‘shelf’’ state of lithium dimer. In the first excitation step, a continuous wave (cw) dye laser prepares a single rovibrational level (v=14, J=22) in the intermediate ^{7}Li_{2} A(^{1}Σ^{+} _{ u }) state. Ultrafast excitation of this single level with a 200 fs laser pulse centered at 803 nm creates a rovibrational wave packet (v=13–16; J=21 and 23) in the shelf region of the E(^{1}Σ^{+} _{ g }) state. The motion of this three‐dimensional wave packet is probed via ionization by a second ultrafast laser pulse of the same color. The initial cw excitation step allows precise control of the states that compose the wave packet. Fourier analysis of the pump–probe transients shows 15 frequency components that correspond to energy differences between the levels that constitute the wave packet. Because of the large rotational energy splitting, the rotational beats occur in the same frequency range as the vibrational beats. Experiments performed with parallel and perpendicular pump‐probe polarizations provide a ‘‘magic angle’’ transient in which only the pure vibrational beats are observed, thus aiding in the spectroscopic assignment. The observed beat frequencies agree well with conventional high resolution frequency‐domain spectroscopy. Applications of the intermediate‐state control of the initial wave packet are discussed.

Vibrational energy transfer in linear hydrocarbon chains: New quantum results
View Description Hide DescriptionIn this paper we report quantum calculations of the survival probability in linear hydrocarbon chains. We have performed both adiabatic gauge transform calculations and calculations that include corrections beyond the adiabatic approximation. We have managed to perform intermediate steps of the calculations analytically. We require the initial basis set expansion and final summations to be performed numerically. The corrections beyond the adiabatic approximation are shown to be small for this system for multiple time step calculations and large for single time step calculations. We have proved an identity that allows the extension of the calculations for HC_{2} to longer chains at little computational cost. In particular, we have proved that the quantum solution for any linear hydrocarbon chain can be obtained from the solution of a problem with 3 degrees of freedom. We have performed multi‐step adiabatic calculations for HC_{2} and HC_{6} that converge at up to 35–40 fs. We have devised a simple diagrammatic scheme that summarizes our method in a very compact form. Finally, we propose an alternative strategy of calculation that might lead to very fast solutions of the quantum dynamics of this system.

Comparisons between statistics, dynamics, and experiment for the H+O_{2}→OH+O reaction
View Description Hide DescriptionThe accuracy of the variable reaction coordinate (VRC) implementation of transition state theory(TST) is investigated for the bimolecular reaction of H with O_{2} via direct comparisons with quantum scattering theory for J=0, classical trajectory simulations for a wide range of J, and experimental canonical rate constants. The DMBE IV potential energy surface of Varandas and co‐workers is employed in each of the theoretical calculations. The first two comparisons indicate that the VRC‐TST approach overestimates the cumulative reaction probability (CRP) for this reaction by a factor of 2.3, roughly independent of E and J for moderate energies. The trajectory simulations further indicate that this failure of TST is primarily the result of the rapid redissociation of a large fraction of the initially formed HO_{2}. An estimate for the quantum CRP on the basis of the combined dynamical and statistical results is seen to provide a useful alternative to the more standard quasiclassical trajectory estimates. A thermal averaging over the E and J‐dependence of the TST estimates for the CRP provides canonical rate constants,k(T), which, when corrected for the above‐mentioned overestimate, are still a factor of 1.7–2.0 times greater than the experimental data. This discrepancy is most likely the result of either (i) inaccuracies in the DMBE IV surface and/or (ii) an overestimate of the contribution to the reactive flux from the nearly degenerate first excited state in the exit channel region.

Core extraction for measuring state‐to‐state differential cross sections of bimolecular reactions
View Description Hide DescriptionWe describe a method we call core extraction for measuring the speed distributions of products from photoinitiated bimolecular reactions for the purpose of determining state‐to‐state differential cross sections. Core extraction is demonstrated by determination of the state‐to‐state differential cross section for the reaction Cl+CH_{4}(υ_{3}=1)→HCl(υ=1, J=1)+CH_{3}. The method of core extraction measures three‐dimensional projections of the velocity distribution using a time‐of‐flight mass spectrometer equipped with a mask to reject off‐axis scattered products. This three‐dimensional projection is then converted to a state‐to‐state differential cross section via simple transformations. Competition between instrumental resolution and signal in core extraction is discussed, and the behavior of our system is checked with simple velocity distributions that result from photodissociation of Cl_{2}. Core extraction is compared with other methods for the measurement of state‐resolved differential cross sections.

Reaction of Cl with vibrationally excited CH_{4} and CHD_{3}: State‐to‐state differential cross sections and steric effects for the HCl product
View Description Hide DescriptionThe mechanism for the reaction of atomic chlorine with vibrationally excited methane is investigated by measurement of correlated state and scattering distributions using the method of core extraction (see preceding paper). Laser photolysis of molecular chlorine creates monoenergetic chlorine atoms (≳98% Cl ^{2} P _{3/2}) that react with vibrationally excited methane molecules prepared by linearly polarized infrared laser excitation. The resulting HCl product population distributions are determined by (2+1) resonance‐enhanced multiphoton ionization (REMPI), and the differential cross section for each product rovibrational state is measured by core extraction. Approximately 30% of the product is formed in HCl(υ=1,J) with a cold rotational distribution; the remaining population is formed in HCl(υ=0,J) and is more rotationally excited. We observe a rich variation of the scattered flux that is dependent on the internal‐energy state of the product. The HCl(υ=1) product is sharply forward scattered for low J and becomes nearly equally forward–backward scattered for high J; the HCl(υ=0,J) product is back and side scattered. The reactions of Cl with C–H stretch‐excited methane (CH_{4}) and C–H stretch‐excited CHD_{3} are found to have similar angular and internal‐state distributions. Observation of the spatial anisotropy of the HCl(υ=0, J=3) product shows that significant vibrational excitation of the methyl fragment does not occur.
The measured spatial anisotropy is most consistent with a model in which backscattered HCl(υ=0, J=3) is formed in coincidence with slight methyl vibrational excitation and the forward‐scattered HCl(υ=0, J=3) is formed in coincidence with no methyl excitation. The approach of the attacking chlorine atom with respect to the C–H stretch direction can be varied by rotating the plane of polarization of the infrared excitation. A marked steric effect is observed in which Cl atoms approaching perpendicular to the C–H stretch preferentially yield forward‐scattered HCl(υ=1) product. On the other hand, the reaction is weakly dependent on the rotational quantum state of CH_{4}(υ_{3}=1,J), and on the rotational polarization. The data are consistent with a model that has a widely open ‘‘cone of acceptance’’ in which the impact parameter controls the internal‐state and scattering distributions of the HCl product.

Radiative and radiationless decay of resonances resulting from electronically nonadiabatic interactions: A computational approach valid for both narrow and broad linewidths and large energy shifts
View Description Hide DescriptionThe description of resonances originating from several coupled electronic states in a diabatic or approximate diabatic basis can offer both conceptual insights and computational challenges. In a three‐state problem, two bound electronic states strongly coupled to a single dissociative continuum, large resonance energy shifts (thousands of cm^{−1}), and linewidths varying over 4 orders of magnitude can be encountered. In this work a nonperturbative computational approach is developed to treat this class of resonances. Expressions for both the radiative and radiationless decay rates are developed. Although the approach is nonperturbative, the linewidth is expressed in a Golden‐Rule‐type formula. The resonance energy is obtained from the iterative solution of an eigenvalue problem in the bound state space. These attributes enable efficient determination both narrow and broad linewidths and large resonance energy shifts. The approach is used to characterize both radiative and radiationless decay of the 2,3 ^{3}Π_{ g } states of Al_{2} using a rigorous three‐state diabatic basis. Lifetimes ranging from tenths of picoseconds to nanoseconds are determined. The corresponding resonance energy shifts are on the order of 4000 cm^{−1}.

Magnetic field effects on recombination fluorescence in liquid iso‐octane
View Description Hide DescriptionThe 123.6 nm photoionization of deuterated isooctane at −10 °C in the presence of hexafluorobenzene has been studied by examining the effect of a magnetic field to alter the quantum yield of recombination fluorescence. This fluorescence results from geminate recombination of hexafluorobenzene anions with isooctane positive ions. The use of a deuterated as contrasted to a protonated alkane makes the intensity of the recombination fluorescence much more sensitive to the magnetic field and permits observation of two maxima in the fluorescence yield at field strengths of 0 and 411 G and a possible third maximum at 822 G. The theory of the hyperfine induced spin evolution predicts these resonances at selected multiples of the C_{6}F^{−} _{6} hyperfine constant of 137 G. Utilizing the diffusion theory of geminate recombination in a Coulomb field, the experimental magnetic fieldspectrum is found to be well predicted over most of the range of magnetic field strengths studied (up to 2.5 kG) by a simple, one parameter, exponential radial probability density of initial scavenged geminate pair separation distances.

Coherent control of photodissociation in intense laser fields
View Description Hide DescriptionThe fragmentation dynamics of the hydrogen molecular ion H_{2} ^{+} and of its isotopic derivate HD^{+}subjected to an intense pulsed laserradiation are studied using quantum wave packet propagations. It is shown that bichromatic optical excitations are subject to a high degree of control through the variation of the relative phase between the two fields. A phase‐locked (ω,2ω) laser pulse is used to induce asymmetry in the angular distribution of the emitted fragments. In addition, an appreciable isotope separation in the fragmentation of HD^{+} is predicted. The critical role of quantum molecular interferences in such phase‐controllable processes is demonstrated.

On the effectiveness of monomer‐, dimer‐, and bond‐centered basis functions in calculations of intermolecular interaction energies
View Description Hide DescriptionA range of basis sets differing in the location of basis functions has been explored from the point of view of the effectiveness of calculating the electrostatic, induction, dispersion, and exchange components of intermolecular interaction energies. Possible location strategies range from monomer‐centered basis sets, through the dimer‐centered ones, to sets with functions centered at the intermolecular bond. It is shown that the most effective approach is to use the so‐called ‘‘monomer plus’’ basis sets containing, in addition to monomer‐centered functions and bond functions, a small number of functions centered on the interacting partner. Using such basis sets for He_{2} and (H_{2}O)_{2} the best values to date have been obtained for several interaction energy components. The conclusions from this work are relevant also for supermolecular calculations of interaction energies.

Structure and vibrations of phenol(H_{2}O)_{2}
View Description Hide DescriptionExtensive ab initio calculations at the Hartree–Fock (HF) level using different basis sets have been performed in order to obtain the minimum energy structure of the phenol(H_{2}O)_{2}‐cluster. Several hydrogen bonding arrangements and a van der Waals structure are discussed. The most stable structure turns out to be cyclic with nonlinear hydrogen bonds. This structure is similar to the one calculated for the water trimer. In contrast with the water trimer the average binding energy of a hydrogen bond decreases with increasing cluster size of Ph(H_{2}O)_{ n } (n=1,2). This is a result of non equal hydrogen bonds. A normal coordinate analysis has been carried out for the fully optimized minimum energy structure of phenol(H_{2}O)_{2} and its deuterated isotopomer d‐phenol(D_{2}O)_{2}. The calculated harmonic intramolecular vibrational modes are compared with experimental values and the intermolecular stretching vibrations are assigned.

An ab initio treatment of the electronic absorption spectra of excess‐electron alkali halide clusters Na_{ n+1}Cl_{ n } up to Na_{18}Cl_{17}
View Description Hide DescriptionElectronic excitation energies of alkali‐excess clusters Na_{2}Cl, Na_{3}Cl_{2}, Na_{4}Cl_{3}, Na_{6}Cl_{5}, Na_{14}Cl_{13}, and Na_{18}Cl_{17} are investigated using CIS(configuration interaction singles) and RPA (random phase approximation). The accuracy of these approximations is established for Na_{2}Cl by equation‐of‐motion coupled‐cluster singles and doubles calculations and by comparison to experimental results. The mode of localization of the excess electron is decisive for the electronic excitation energy. No cluster‐size dependence of the excitation energy is found. The direct UHF‐CIS (unrestricted Hartree–Fock‐CIS) and UHF‐RPA implementation within the program package TURBOMOLE is briefly described in the appendix.

A density functional study of borane and alane monoammoniate (BH_{3}NH_{3},AlH_{3}NH_{3})
View Description Hide DescriptionMolecular structures, harmonic vibrational frequencies, dissociation energies, and barriers to internal rotation have been determined using a Gaussian density functional method. Both local and nonlocal levels of theory have been employed. The calculated equilibrium geometry and harmonic vibrational frequencies for BH_{3}NH_{3} compare well with those determined by microwave and infrared experiments. The rotational barrier is found to be 2.09 kcal/mol in very good agreement with the experimental data. The calculated properties for ammonia‐alane (AlH_{3}NH_{3}) are compared with those obtained previously from high level correlated methods.

Modification of the gaussian−2 theoretical model: The use of coupled‐cluster energies, density‐functional geometries, and frequencies
View Description Hide DescriptionA family of modified GAUSSIAN−2 (G2M) calculational schemes have been proposed, based on geometry optimization and vibrational frequency calculations using the hybrid density‐functional approach, and electron correlation evaluation using the coupled‐cluster methods. The most accurate model, called G2M(RCC), gives the average absolute deviation of calculated atomization energies from experiment for 32 first‐row compounds of 0.88 kcal/mol. The other two methods, called G2M(RCC,MP2) and G2M(rcc,MP2), exhibit the average absolute deviations of 1.15 and 1.28 kcal/mol, respectively, and can be used for the calculations of molecules and radicals of larger sizes containing up to six to seven heavy atoms. The G2M(rcc,MP2) model demonstrates an accuracy comparable to that of G2(MP2) and requires less intensive computations than the latter. The preference of the G2M(RCC) methods over the original G2 is expected to be particularly significant for the open shell systems with large spin contamination.

Electrostatic decoupling of periodic images of plane‐wave‐expanded densities and derived atomic point charges
View Description Hide DescriptionThe density of a molecule expanded in plane waves is decoupled from its periodic images using a fit to atom‐centered Gaussians, which reproduces the long‐range electrostatic potential of the original density. The interaction energy between the cluster and its periodic images is calculated by an Ewald summation. The method has been applied to self‐consistent ab initiomolecular dynamics calculations of charged and polar molecules. An atomic point charge model of the charge density is obtained, which can be used for classical molecular dynamics models and to couple classical and quantum mechanical simulations.

Response functions in the CC3 iterative triple excitation model
View Description Hide DescriptionThe derivation of response functions for coupled cluster models is discussed in a context where approximations can be introduced in the coupled clusterequations. The linear response function is derived for the approximate coupled cluster singles, doubles, and triples model CC3. The linear response functions for the approximate triples models, CCSDT‐1a and CCSDT‐1b, are obtained as simplifications to the CC3 linear response function. The consequences of these simplifications are discussed for the evaluation of molecular properties, in particular, for excitation energies.Excitation energies obtained from the linear response eigenvalueequation are analyzed in orders of the fluctuation potential. Double replacement dominated excitations are correct through second order in all the triples models mentioned, whereas they are only correct to first order in the coupled cluster singles and doubles model (CCSD). Single replacement dominated excitation energies are correct through third order in CC3, while in CCSDT‐1a, CCSDT‐1b, and CCSD they are only correct through second order. Calculations of excitation energies are reported for CH^{+}, N_{2}, and C_{2}H_{4} to illustrate the accuracy that can be obtained in the various triples models. The CH^{+} results are compared to full configuration interaction results, the C_{2}H_{4} results are compared with complete active space second order perturbation theory (CASPT2) and experiment, and the N_{2} results are compared to experiment. Double replacement dominated excitations are improved significantly relative to CCSD in all the triples models mentioned, and is of the same quality in CC3 and CCSDT‐1a. The single replacement dominated excitation are close to full configuration interaction results for the CC3 model and significantly improved relative to CCSD. The CCSDT‐1 results for the single replacement dominated excitations are not improved compared to CCSD.