Index of content:
Volume 102, Issue 21, 01 June 1995

Sideband optical–optical double resonance Zeeman spectroscopy. I. Theory of saturation and line shape behavior
View Description Hide DescriptionSeveral variants of the one‐laser, two‐color technique of sideband optical–optical double resonance Zeeman (SOODRZ) spectroscopy, which enables Zeeman and hyperfine splittings to be measured at sub‐Doppler resolution, are described; a detailed theory of the line shape and signal‐to‐noise ratio for each variant is also presented. In the single‐frequency variant of SOODRZ spectroscopy,radio frequency sidebands are imposed onto a single‐frequency continuous wave laser beam to determine energy splittings between pairs of closely spaced levels. Each pair of closely spaced levels is coupled to a third isolated level by optical transitions and is tuned into resonance by the Zeeman effect. A theoretical treatment of the SOODRZ effect is presented here. It is shown that both the real and imaginary contributions to the complex third‐order optical susceptibility tensor χ^{(3)} can be observed and that the SOODRZ signal originates from a cross term between the amplitude of the unperturbed frequency‐modulated beam of the laser and the nonlinear signal amplitude Re{E _{ L } ^{*}⋅E _{ NL }}. The SOODRZ signal is directly proportional to ΔNμ^{4} MI^{2} _{0} (where M is the modulation index), rather than (ΔN)^{2}, μ^{8}, and I ^{3} _{0} as in degenerate four‐wave mixing and other nonlinear spectroscopies, which means the detection sensitivity of SOODRZ spectroscopy is considerably higher for low laser intensities and at lower number densities.
Moreover, the linewidth of the sub‐Doppler feature is independent of the both the Doppler width of the optical transition and the natural width of the common linked level and, hence, is immune from the effects such as upper state predissociation. Two different types of modulators, acousto‐optic and electro‐optic, can be used in the single‐frequency variant of SOODRZ spectroscopy. The unique features of SOODRZ schemes incorporating both types of modulators are described. SOODRZ spectroscopy can also be performed with a multimode broadband laser, where the adjacent cavity modes serve the same function as the sidebands in the single‐frequency version. Examples of such multimode SOODRZ spectra will be presented as well. The effect of different detection schemes (i.e., nearly crossed polarizers and/or coherent detection), laser frequency detuning relative to the center of the absorption line, and ac magnetic field modulation conditions on the intensity, phase, and functional form of the sub‐Doppler double resonance line shape will be discussed here. The simplest possible form of the SOODRZ line shape is a second derivative of a Lorentzian.

Accidental predissociation phenomena in the E ^{1}Π, v=0 and v=1 states of ^{12}C^{16}O and ^{13}C^{16}O
View Description Hide DescriptionWe have studied v=0 and v=1 levels of the E ^{1}Π state of CO in excitation from the ground state by one‐ and two‐photon transitions, thus probing e and f Λ‐doublet components. New accidental predissociations were found in the E ^{1}Π, v=0 state for high J values (J _{ e }=41, 44 for ^{12}C^{16}O and J _{ e }=41, 50 for ^{13}C^{16}O). The predissociation phenomenon in the E ^{1}Π, v=1 state at J=7 was reinvestigated and for both e and f components also J=9, 10, and 12 were found to be perturbed. Perturbations by all three spin components of a k ^{3}Π, v=5 state were deduced. Furthermore the accidental predissociation in E ^{1}Π, v=0 J _{ e }=31 was reinvestigated. Measurements of spectral line shifts were modeled assuming a spin‐orbit coupling between E ^{1}Π and the ^{3}Π_{1} component of the k ^{3}Π state. Relative predissociation lifetimes of k ^{3}Π, v=3 and 5 with respect to E ^{1}Π, v=0 and v=1 are deduced from an analysis of observed intensity effects. For the E ^{1}Π, v=1 state rotational state dependent lifetimes were determined at low‐J values. Line positions of CO lines were calibrated on an absolute frequency scale within 0.05 cm^{−1} against the tellurium and iodine standard in the visible. Accurate molecular constants for the E ^{1}Π, v=0 and v=1 states are determined for both ^{12}C^{16}O and ^{13}C^{16}O. The E ^{1}Π, v=1 state of ^{12}C^{17}O is observed for the first time.

Vibrational numbering and potential of the c ^{3}Σ^{+} state of NaK determined from the c ^{3}Σ^{+}→a ^{3}Σ^{+} transition
View Description Hide DescriptionWe report the observation of the c ^{3}Σ^{+}→a ^{3}Σ^{+} emission in NaK following excitation of single rovibronic levels in the c ^{3}Σ^{+} state. The dispersed fluorescence displays both diffuse and discrete features. The characteristic reflection structure of the bound–free spectra permits a direct, unambiguous assignment of the vibrational numbering in the c ^{3}Σ^{+} state: The v=20 level is the first vibrational level of c ^{3}Σ^{+} lying above v=0 in the B ^{1}Π state. The c ^{3}Σ^{+} state potential curve is determined from bound–free parts of the observed spectra with the inversion procedure of LeRoy et al. [J. Chem. Phys. 89, 4564 (1988)]; its most important parameters are T _{ e }=15 857±15 cm^{−1} and R _{ e }=0.445±0.001 nm.

Infrared spectra of ice surfaces and assignment of surface‐localized modes from simulated spectra of cubic ice
View Description Hide DescriptionThe use of a new method of preparing micron‐thick deposits of nanocrystals of ice for Fourier transform infrared sampling, with the nanocrystals supported on a vertical infrared window, has greatly improved the signal‐to‐noise levels of the spectra available for large ice clusters. High quality spectra of modes of the surface molecules are reported, even for regions that underlie the intense bands of the bulk ice modes. These experimental features are most clearly displayed through the use of difference spectra. For example, the difference between spectra obtained for nanocrystals, before and after an annealing cycle that significantly increases the average cluster size, reflects the decrease in number of surface groups and the corresponding increase in number of interior molecules. Similarly, differences between spectra of bare and adsorbate‐coverednanocrystals, obtained at the same temperature for the same ice sample, show the significant shifts of ‘‘surface‐localized’’ ice modes caused by the adsorbate molecules. These difference spectra, and similar spectra for amorphous ice, are rich with information about the (three) distinct types of icesurface water molecules and their interactions with small adsorbate molecules. The extraction of that information has been initiated by comparison of the experimental difference spectra from two sizes of D_{2}O cubic icenanocrystals with simulated difference spectra for a relaxed cubic ice surface compared to bulk cubic ice.
From these comparisons specific experimental features have been assigned to modes of the three categories of surface D_{2}O(HDO) molecules: (a) three‐coordinated molecules with dangling‐D—2725 (2713) cm^{−1}; (b) three‐coordinated D_{2}O molecules with dangling‐O—2645 (∼2600) cm^{−1}; (c) relaxed four‐coordinated molecules—∼2580 (∼2550) cm^{−1}. Also, information has been obtained on the approximate positions (cm^{−1}) of other modes of surface molecules: (a) D‐bonded part of dangling‐D(H) molecules; ∼2350; (b) dangling‐O molecules; ∼2500; (c) four‐coordinated molecules; 2300–2500. The computations also indicate that, of the various modes of the surface molecules, only the higher frequency modes of the dangling‐D and dangling‐O are strongly localized; and only the dangling‐D mode is localized on individual surface molecules.

Stimulated emission pumping spectroscopy via two‐color resonant four‐wave mixing
View Description Hide DescriptionWe present a combined theoretical and experimental study of the application of two‐color resonant four‐wave mixing (RFWM) to stimulated emission pumping (SEP) spectroscopy. The theoretical approach employs time‐independent, diagrammatic perturbation theory and a spherical tensor analysis in an extension of a recent treatment of degenerate four‐wave mixing [Williams, Zare, and Rahn, J. Chem. Phys. 101, 1072 (1994)]. The resulting signal expression for two‐color RFWM separates the molecular properties from purely laboratory‐frame factors determined by the polarizations of the input beams and the rotational branch types of the SEP PUMP and DUMP transitions. This expression is valid in the limit of weak fields and for molecules in which the total angular momentum (omitting nuclear spin) is a good quantum number. In addition, we demonstrate that the spectral response for tuning the DUMP laser is a simple Lorentzian in free‐jet experiments. We test our theoretical results and demonstrate the applicability of RFWM‐SEP to jet‐cooled, transient species in experiments on C_{3} and HCO. Using the well‐studied Ã ^{1}Π_{ u }–X̃ ^{1}Σ^{+} _{ g } system of C_{3}, we illustrate and compare the two possible schemes for RFWM‐SEP. These are defined as ω_{1}=ω_{2} (PUMP) and ω_{3}=ω_{4} (DUMP) or ω_{1}=ω_{4} (PUMP) and ω_{2}=ω_{3} (DUMP), where ω_{1}, ω_{2}, and ω_{3} are the input frequencies and ω_{4} is the signal frequency.
Using the B̃ ^{2} A’–X̃ ^{2} A’ system of HCO, we obtain RFWM‐SEP spectra that probe ground‐state vibrational resonances lying above the low threshold for dissociation to H+CO. Varying the polarization of the input beams or PUMP rotational branch produce dramatic effects in the relative intensities of rotational lines in the RFWM‐SEP spectra of HCO; these effects are well‐described by our theoretical analysis. Finally, RFWM‐SEP spectra of HCO resonances that are homogeneously broadened by dissociation are consistent with the theoretically predicted Lorentzian line shape; the full widths for these levels are in good agreement with those determined via unsaturated fluorescence depletion SEP.

Auger electron spectroscopy of molecules: Angular and spin correlation with photoelectrons from rotating linear molecules
View Description Hide DescriptionA detailed theoretical framework is developed for studying sequential emission of a photoelectron and an Auger electron from a rotating linear molecule with information on momenta and spin‐polarization of the departing particles. Identical expressions, except, of course, for different dynamical amplitudes, in both the Hund’s coupling schemes (a) and (b) are obtained for the three different correlation functions considered in this paper. The use of the parity adapted wave functions for the molecular states involved results in, among other things, the presence of only a finite number of harmonics for each of the directions included in the correlation function. Several specific photon‐propagation, electron‐detection configurations are suggested for which the general correlation functions derived herein become particularly simple. The correlation between the Auger and the photoelectrons is shown to become, under specific conditions, completely isotropic for all bound molecular orbitals, whatever may be their symmetries, from which pair of electrons comes out. This analysis is independent of any dynamical calculations which can be performed in a hierarchy of approximations beginning from semiempirical phenomenological models to sophisticated ab initio methods.

CH_{3} state distributions form the reactions of O(^{1} D) with saturated and chlorinated hydrocarbons
View Description Hide DescriptionCH_{3} product state distributions arising from the reaction of O(^{1} D) with CH_{4}, C_{2}H_{6}, C_{3}H_{8}, and i‐C_{4}H_{10} were characterized using resonantly enhanced multiphoton ionization (REMPI). The vibrational distributions in the ν_{1} symmetric stretch and in the ν_{2} ‘‘umbrella’’ mode are noninverted in all cases. The results are compared to statistical adiabatic channel‐phase space theory (SACM‐PST) calculations. The ν_{2} excitation is much less excited than statistically expected for the reactions with CH_{4} and C_{2}H_{6} but nearly statistical in the case of the heavier hydrocarbons. For all reactions but the one with C_{2}H_{6}, the ν_{1} excitation is similar to the distribution statistically expected. The CH_{3} rotational distribution from the reaction of O(^{1} D) with CH_{4} is much hotter than room temperature as comparison with simulated rotational band contours showed. From the integrated CH_{3} band intensities, we obtained approximate reaction cross sections for the CH_{3} channel with a decrease in the order CH_{3}≳C_{2}H_{6}≳C_{3}H_{8}≳i‐C_{4}H_{10}. In the reactions of O(^{1} D) with CH_{3}Cl, CH_{3}CH_{2}Cl, and CH_{3}CH_{2}CH_{2}Cl, we observed CH_{3} as a primary product. CH_{3}–ν_{1} excitation is small in all cases but ν_{2} excitation is considerable with even an inverted v=1/v=0 distribution in the case of the reaction with C_{2}H_{5}Cl. The relative reaction cross sections for the CH_{3} channel decrease in the order CH_{4}≫CH_{3}Cl≳CH_{3}CH_{2}Cl≳CH_{3}CH_{2}CH_{2}Cl.

Collisional electronic quenching of OH A ^{2}Σ (v’=0) measured at high temperature in a shock tube
View Description Hide DescriptionRate coefficients are reported for electronic quenching of OH A ^{2}Σ v’=0 by N_{2}, O_{2}, CO, CO_{2}, NO, Ar, Kr, and Xe measured at high temperatures behind reproducible shock waves. The cross section for quenching by Ar was found to be less than 0.06 Å^{2}. The cross sections for quenching by N_{2} and Kr were found to be 0.5 and 1.0 Å^{2}, respectively. The cross sections for the remaining species were found to be of order gas kinetic. For all of the species the cross sections were found to be very weak functions of temperature from 1900 to 2300 K. The measured cross sections are compared with previous measurements at lower temperatures. The observed variation with species and with temperature is observed to be consistent with a charge‐transfer model for the process.

Ab initio potential energy surface and near‐infrared spectrum of the He–C_{2}H_{2} complex
View Description Hide DescriptionSymmetry‐adapted perturbation theory has been applied to compute the intermolecular potential energy surface of the He–C_{2}H_{2} complex. The interaction energy is found to be dominated by the first‐order exchange contribution and the dispersion energy. In both contributions it was necessary to include high‐level intramolecular correlation effects. Our potential has a global minimum of ε_{ m }=−22.292 cm^{−1} near the linear He–HCCH geometry at R _{ m }=8.20 bohr and ϑ_{ m }=14.16°, and a local minimum at a skew geometry (R _{ m }=7.39 bohr, ϑ_{ m }=48.82°, and ε_{ m }=−21.983 cm^{−1}). The computed potential energy surface has been analytically fitted and used in converged variational calculations to generate bound rovibrational states of the He–C_{2}H_{2} molecule and the near‐infrared spectrum, which corresponds to the simultaneous excitation of the vibration and hindered rotation of the C_{2}H_{2}monomer within the complex. The nature of the bound states and of the spectrum predicted from the ab initio potential are discussed.

On the role of solvent electronic polarization in charge transfer reactions
View Description Hide DescriptionThe effect of a solvent’s electronic polarization on the rate of a charge transferreaction is studied in both continuum and discrete solvent models. An effective system Hamiltonian that contains the equilibrium solvation from the solvent electronic polarization is obtained, and leads to an effective matrix element V _{eff} coupling the charge transfer states that is smaller than the gas phase value. Both the effective Hamiltonian and V _{eff} are dependent on the solvent’s instantaneous nuclear configuration, and liquid state theory is used to carry out the configuration average. The solvent electronic polarization reduces the transition rate for both adiabatic and nonadiabaticreactions. A standard relation between the equilibrium solvation energy of the reactants and the solvent reorganization energy is established that permits evaluation of the effect of a molecular solvent (using a Drude model for the electronic degrees of freedom) on the rate by evaluating a partition function. This permits use of a path integral formulation for the mixed quantum (electronic polarization) classical (slow nuclear configuration) solvent that leads to the information required for the rate constant. In a strong coupling regime, where the coupling between the charge‐transfer species would be so large as to preclude reactant and product species, we show that a new mechanism for charge localization arising from the solvating effect of the electronic polarization may occur, and formulate a rate constant expression for this regime. It has the form of a quantum Kramers rate and shows that the solvent provides a friction effect that will reduce the rate relative to the no‐friction rate.

Detection of neutral metastable fragments from electron‐impact on argon clusters
View Description Hide DescriptionWe have studied the production of neutral metastable fragments in electron collisions with neutral argon clusters. The fragments are detected using a time‐of‐flight technique. The time‐of‐flight spectra show that the metastable fragments appear in two velocity ranges. Kinetic energy distributions are obtained, showing that the faster fragments are ejected with energies from 0.2 to 1.5 eV and that the slower fragments have energies less than 0.2 eV. It is argued that the fragmentation of the clusters involves the excitation and decay of excitons in the clusters.The faster fragments are produced by n=2 excitons, which localize on an excimer or an excited trimer within the cluster and upon dissociation cause the ejection of a metastable atom. The slower fragments are produced by n=1 excitons, which tend to localize on the periphery of the cluster, leading to the ejection of a metastable atom due to weak repulsive forces with neighboring atoms. Four different production mechanisms for neutral metastable fragments are observed.

A detailed study of conformations in the ground state of CH^{+} _{4}
View Description Hide DescriptionThe results of Coulomb explosion imaging for cold CH^{+} _{4} molecular ions are converted to the molecular conformationprobability density. This is the first complete conversion of such data for a relatively complex molecule. The results are compared with the corresponding predicted potential energy surfaces which manifest a Jahn–Teller symmetry breaking. The density of conformations along a nuclear rearrangement path is deduced and the comparison with the theory is satisfactory in almost every respect, except for the density near the minimum of the theoretical potential

On the role of conical intersections in photodissociation. III. The case of hydroxylamine
View Description Hide DescriptionConical intersections of two states of the same symmetry are usually considered rare and are frequently ignored in the treatment of nonadiabatic processes. This work addresses the veracity of this assumption. The existence of conical intersections of two states of the same symmetry is considered for the four lowest electronically excited states of hydroxylamine NH_{2}OH using configuration interactionwave functions. The existence of ‘‘same symmetry’’ conical intersections is demonstrated and their role in the photodissociation process NH_{2}OH→NH_{2}+OH investigated. Although the ground electronic state has C _{ s } symmetry (with two equivalent hydrogens) it is argued that conical intersections corresponding to nuclear configurations far removed from C _{ s } symmetry play a role in the photodissociation.

Vibrational state controlled bond cleavage in the photodissociation of isocyanic acid (HNCO)
View Description Hide DescriptionWe report the bond selected photodissociation of isocyanic acid (HNCO). This molecule dissociates from its first excited singlet state, breaking either the N–H bond to form H+NCO (X ^{2}Π) or the C–N bond to form NH (a ^{1}Δ)+CO (^{1}∑^{+}). The threshold for production of NH lies about 3900 cm^{−1} above that of NCO, and we detect both of these channels by laser induced fluorescence on either the NH or the NCO fragment. Dissociating the molecule out of a vibrationally excited state on its ground electronic surface containing four quanta of N–H stretch (4ν_{1}) enhances the efficiency of the NCO channel over the NH channel by a factor of at least 20. We reach this conclusion by comparing the results of such a vibrationally mediated photodissociation experiment to those from a conventional single photondissociation at the same total energy (about 1000 cm^{−1} above the threshold for the NH channel). Our estimate of the branching ratio in the one photondissociation at this energy is roughly Φ_{NCO}/Φ_{NH}≊20, and it grows to Φ_{NCO}/Φ_{NH}≥400 in the vibrationally mediated photodissociation.

A quantitative study of the scaling properties of the Hartree–Fock method
View Description Hide DescriptionAlthough it is usually stated that the Hartree–Fock method formally scales as N ^{4}, where N is the number of basis functions employed in the calculation, it is also well known that mathematical bounds computed with the Schwarz inequality can be used to screen and eliminate four‐center two‐electron integrals smaller than a certain threshold. In this work, quantitative data is presented to illustrate the effects of this integral screening on the scaling properties of the Hartree–Fock (HF) method. Calculations are performed on a range of carbon–hydrogen model systems, two‐dimensional graphitic sheets, and three‐dimensional diamond pieces, to determine the effective scaling exponent α of the computational expense. The data obtained in this paper for calculations including over 250 carbon atoms and 1500 basis functions shows two significant trends: (1) in the asymptotic limit of large molecules, α is found to be approximately 2.2–2.3, and (2) for molecules of modest size, α is still very much less than 4. Therefore, integral screening is quantitatively shown to substantially reduce the Hartree–Fock scaling from its formal value of N ^{4}.

Direct calculation of overtones: Application to the CD_{3}H molecule
View Description Hide DescriptionWe report a comparison of two methods designed for directly determining high lying energy levels in a polyatomic molecule. The Bloch operator, in the distorted wave version proposed by Jolicard [Chem. Phys. 115, 57 (1987)], allows one to compute a few specific eigenstates, as specified by some zero‐order description. The second method makes use of a spectral transform, in order to open up an energy window in a very dense spectrum. Test calculations have been carried out on the nine‐dimensional CD_{3}H molecular system, for different C–H stretch overtone levels. They show that the Bloch formulation rapidly converges the target eigenstate, provided that the intramolecular coupling is not too strong. In the strong coupling regime, the spectral transform has been shown to successfully display all the eigenstates located in the energy window of interest, but requires more computational effort.

Use of relativistic effective core potentials in calculating the electronic spectrum of the antimony dimer
View Description Hide DescriptionA relativistic configuration interaction study including the spin–orbit coupling has been carried out for a large number of electronic states for the antimony dimer and comparisons with analogous results for the isovalent Bi_{2} molecule have been made. Bond lengths r _{ e }, vibrational frequencies ω_{ e }, excitation energiesT _{ e }, and dissociation energiesD _{ e } have been computed for all bound states up to 40 000 cm^{−1}, as well as transition probabilities and radiative lifetimes based on electric–dipole matrix elements. The calculations confirm that the A1_{ u } state derives mainly from the π→π* ^{3}Δ_{ u } λ–s state and not from the lower‐lying ^{3}Σ^{+} _{ u }. The lifetime of this state (0.3 ms) is computed to be 50 times shorter than for the B0^{+} _{ u } state, suggesting that emissions from either of these states will be quite difficult to observe in gas‐phase studies. By contrast the lifetime of the D0^{+} _{ u } state is relatively short (35.6 ns), consistent with the fact that the D–X band system is quite intense. No suitable candidate is indicated for the K–X transition observed by Sontag and Weber, however, and thus it is suggested that the corresponding spectrum is a part of the D–X system.

Theoretical study of the vibrational spectra of the transition metal carbonyls M(CO)_{6} [M=Cr, Mo, W], M(CO)_{5} [M=Fe, Ru, Os], and M(CO)_{4} [M=Ni, Pd, Pt]
View Description Hide DescriptionThe harmonic force fields of the title compounds have been calculated at the level of Hartree–Fock (HF) theory, Mo/ller–Plesset second‐order perturbation theory (MP2), and gradient‐corrected density functional theory(DFT) using all‐electron and effective core potential wave functions in conjunction with polarized double‐ and triple‐zeta basis sets. The DFT results are in very good agreement with the available experimental data, whereas the HF results are inadequate and the MP2 results are satisfactory only for the 5d and (partly) the 4dtransition metal complexes, but not for the 3dtransition metal complexes. The calculated DFT frequencies are accurate enough to suggest reassignments in the vibrational spectrum of Fe(CO)_{5}. In the case of Ru(CO)_{5}, Os(CO)_{5}, Pd(CO)_{4}, and Pt(CO)_{4} where experimental data are scarce, the DFT predictions may guide future experimental work.

Monte Carlo study of the optical properties of the KXe_{ N } polyatomic exciplexes
View Description Hide DescriptionThe geometrical structures and optical properties of the K(5S)Xe_{ N } polyatomic exciplexes are studied by using the Metropolis Monte Carlo method. The many‐body potentials between an electronically excited potassium atom and xenon atoms are calculated by using the improved Baylis potential model, in which the Hamiltonian is diagonalized at every Monte Carlo step. At low temperature, the exciplex has a closed structure at the number of xenons N=8. The shifts and the linewidths of the transition energy of the calculated fluorescence spectra of individual exciplexes reflect the structures and thermal properties of each polyatomic exciplex.

A graphical unitary group approach to study multiplet specific multichannel electron correlation effects in the photoionization of O_{2}
View Description Hide DescriptionWe have implemented an efficient multichannel configuration–interaction complete‐active‐space (MCCI‐CAS) approximation to study electron–correlation effects in molecular photoionization. This approach is based on the graphical unitary group approach (GUGA) for computing matrix elements of the Hamiltonian and includes target relaxation, correlation, and polarization as well as correlation due to coupling between different asymptotic scattering channels. The statistical rule, which partitions the total cross section into multiplets by simple spin statistics, is easily derived in this formalism. The scattering equations are solved using the Schwinger variational method. We present multiplet specific results of a detailed MCCI‐CAS Schwinger study of the photoionization of molecular oxygen in the photon energy region of 12.3–20.4 eV, including up to four coupled electronic channels. Our results show the importance of using correlated target states. We have obtained all of the autoionization structure near threshold that has been assigned experimentally. In addition, we predict structure not yet resolved by experiment.