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Volume 79, Issue 5, 01 September 1983

Two‐dimensional analysis of the ring‐puckering and PH inversion vibrations of 3‐phospholene
View Description Hide DescriptionThe ring‐puckering energy levels for 3‐phospholene, CH_{2}CH=CHCH_{2}PH, in both the ground and excited states of the PH inversion vibration have been established from the vibrational spectra of this molecule. The availablity of such extensive data made it possible to determine a reliable two‐dimensional (with the ring‐puckering and the P–H inversion as the two coordinates) potential energy surface. For the calculations, the kinetic energy coefficients g _{4} _{4}, g _{5} _{5}, and the cross term g _{4} _{5} were accurately represented as functions of both coordinates. An initial approximation to the asymmetric two‐dimensional potential energy surface was obtained from the one‐dimensional ring‐puckering function as well as from structural data from microwave spectroscopy. Symmetry constraints established which potential terms were to be utilized. Three separate computer programs were written in order to calculate the vibrational energy levels and to adjust the potential parameters. The most efficient approach utilized a product of two prediagonalized basis sets for the basis functions. Initial attempts to fit the data with a potential surface using terms up through fourth power proved unsatisfactory in fitting data for the inversion excited state. A local solution based on Van Vleck perturbation theory was thus obtained and then expanded, using the symmetry constraints, to the entire solution. The resulting potential surface, which required the use of sixth power terms, gave excellent agreement with the observed spectra. Only five variable parameters were adjusted (for the local solution) in order to fit the 20 observed frequencies. The final potential surface has a central barrier of about 5500 cm^{−} ^{1} for the planar configuration. The more stable endo conformation lies 785 cm^{−} ^{1} in energy below that of the exo form with similar puckering angle (18°).

Quantum beating of vibrational factor group components in molecular solids^{a)}
View Description Hide DescriptionWe report the first observation of coherent Raman induced quantum beats from exciton states in molecular crystals. The paper describes the relevant crystal optics and phasematching conditions needed to ensure coherent excitation of more than one Raman transition in an anisotropicsolid. The study of the 991 cm^{−} ^{1} mode of C_{6}H_{6} at 1.6 K has allowed the identification of two nearby (0.6 cm^{−} ^{1}) factor group components and their lifetimes. The larger damping of the weaker A _{ g }→B _{2} _{ g }transition suggests that intraband scattering is operative.

NaH: Studies of the X ^{1}Σ^{+} state near dissociation and of the radiative lifetimes and collision cross sections of the A ^{1}Σ^{+} state
View Description Hide DescriptionWith a dye laser pumped by an excimer laser, the NaH A ^{1}Σ^{+} state has been excited up to v′=21. Its decay to the X ^{1}Σ^{+}ground state has been observed up to v″=19, a vibrational level close to the dissociation limit, allowing us to obtain a precise value of the X ^{1}Σ^{+}dissociation energy:D _{ e }=15 785±20 cm^{−} ^{1}. For v″≳15, the vibrational spacings and the rotational constants decrease very rapidly, as also observed recently in CsH, due to a sudden change of configuration mixing. The A ^{1}Σ^{+} radiative lifetimes do not vary appreciably from v′=3 to v′=18, τ=27±2 ns, but increase to 35±2 ns at v′=21. The quenching and rotational transfer collision cross sections of the A ^{1}Σ^{+} state with H_{2} have nearly the same values for a given v′. They increase from v′=4 to v′=21 as do the calculated electric dipole moments and the geometric extent of the levels.

Quantum vs classical calculation of nonlinear spectra‐reduced dynamics and intramolecular entropy
View Description Hide DescriptionA non‐Markovian reduced equation of motion (REM) is derived for a generating function P(a,t;a′) which allows the calculation of two‐time correlation functions in nonlinear systems. The form of the REM is identical for classical and quantum systems and it depends on an entropy function ln g(a), a velocity kernel W(a,a″), and a non‐Markovian kernel K(a,a″,t), a being the expectation value of the dynamical variable under consideration. We give exact formal expressions for these quantities for the quantum and the classical case. In the linear (harmonic) limit the REM reduces rigorously to a non‐Markovian Fokker–Planck equation. The present approach may allow a convenient and a systematic way for the calculation and the comparison of classical and quantum nonlinear spectra.

Site dependence of the 1 ^{1} A _{ g } to 2 ^{1} A _{ g } transition of all‐trans‐1,3,5,7‐octatetraene
View Description Hide DescriptionHighly resolved emission and one‐photon fluorescence excitation spectra and fluorescence lifetimes for all‐trans‐1,3,5,7‐octatetraene substituted in a series of n‐alkane crystals maintained at liquid heliumtemperatures have been measured. In the n‐octane host, the 1 ^{1} A _{ g } to 2 ^{1} A _{ g } transition is strictly symmetry forbidden: In other hosts, the spectra exhibit both allowed and symmetry forbidden components. While the relative intensity of the allowed (built on the 0–0) and the symmetry forbidden (built on odd symmetry vibrational modes) components of the spectra are sensitive to local perturbations, the energies of the excited 1 ^{1} A _{ g } and 1 ^{1} B _{ u } states and the vibrational development of the 1 ^{1} A _{ g } to 2 ^{1} A _{ g } transition are nearly the same in all of the hosts studied. The increase in the allowed component of the spectrum with increasing site perturbation correlates with a decrease in the measuredfluorescence lifetime.

On the vibrational frequency correlation in liquids: Raman study of aqueous thiocyanate solutions
View Description Hide DescriptionThe vibrational frequency correlation functions 〈ω(0) ω(t)〉 are calculated from isotropic Raman spectra for the CN stretching mode of the SCN^{−} anion in aqueous LiSCN, NaSCN, and KSCN solutions, at concentrations 1–10 M, and at temperatures of 30, 55, and 80 °C. The experimental 〈ω(0) ω(t)〉 shows rapid relaxation within a particular environment on a subpicosecond time scale, accompanied by constant positive correlation. It is concluded that the homogeneous dephasing is due to the fast relaxation of 〈ω(0) ω(t)〉, and that the inhomogeneous dephasing comes from the static positive correlation, which should be attributed to a distribution of environments persisting over the time scale of Raman probe. The analysis of 〈ω(0) ω(t)〉 confirms that the inhomogeneous broadening increases with decreasing temperature, with increasing salt concentration, and in the order KSCN<NaSCN<LiSCN.

Energy and phase relaxation of phosphorescent F centers in CaO
View Description Hide DescriptionIn this paper we study the temperature‐induced homogeneous broadening of the no‐phonon line in the emission spectrum of the F center in CaO. The linewidth can be fitted to n̄(n̄+1), where n̄ is the thermally averaged occupation number of phonons with a frequency of 90 cm^{−} ^{1}. The results are characteristic of elastic scattering of pseudolocalized phonons at the defect site. These phonons also appear to dynamically couple the Jahn–Teller components of the F center in the photoexcited^{3} T _{1u } state and thus give rise to a temperature dependence of the lifetime of this phosphorescent state. Finally, from experiments using laser‐selective excitation it is concluded that the zero‐phonon emission peaking at 571.1 nm does not originate in the F center.

Theoretical interpretation of the resonance Raman spectrum of gaseous chlorine
View Description Hide DescriptionA theoretical calculation of the Raman band profiles of gaseous chlorine excited by a 3638 Å line is performed. The resonance part of the Raman amplitude is calculated within a semiclassical approach and the nonresonant part by an ab initio calculation. The profiles of the overtones are well described by considering only the resonant scattering via the excited electronic stateC ^{1}Π(1u) and the anomalous value of the fundamental band intensity compared to the first overtone is shown to be due to virtual transitions to higher electronic states (normal Raman effect).

Angle‐resolved photoelectron spectroscopy of HCl from a photon energy of 16 to 80 eV
View Description Hide DescriptionAngle‐resolved photoelectron spectroscopy was performed on HCl using synchrotron radiation over a photon energy from 16 to 80 eV. The partial cross sections and angular distribution parameters β were obtained for photoionization of both the 2π and 5σ orbitals. Multiple scatteringXα calculations were also carried out for the cross sections and β values. The calculations, together with previously published results on the cross section using a Hartree–Fock model, were compared with experiment and gave reasonable qualitative agreement. Both experimental and theoretical results were examined with particular regard to the nature of the Cooper minimum, and the differences between the behavior of the minima for the two orbitals are discussed in detail.

Fluorescence excitation spectrum of triptycene in a supersonic jet
View Description Hide DescriptionThe laser‐induced fluorescence excitation spectrum of triptycene in pulsed supersonic expansions of He reveals the electronic origin of the S _{0}→S _{1}(^{1} A ^{′} _{1}→^{1} E′) transition at 2750.85 Å (36 352 cm^{−} ^{1}), followed by 19 vibrational excitations in the energy range 350 cm^{−} ^{1} above it. This vibrational structure corresponds to the excitations of four torsional modes of the phenyl rings. Mechanical models for these torsional modes indicate the existence of three doubly degenerate vibrations, exhibiting Jahn–Teller coupling with the ^{1} E′ state, together with double excitations of a nondegenerate vibration. At excess vibrational energies of 350–1000 cm^{−} ^{1} above the S _{1} origin the laser‐induced fluorescencespectrum is extremely weak and devoid of any structure, implying the onset of a new effective intramolecular decay channel, which may result in isomerization in the isolated molecule.

EXAFS study of Ni–Cl bonding in Ni(II) aqueous solutions at increasing Cl^{−}/Ni^{2} ^{+} ratios
View Description Hide DescriptionThree aqueous solutions of NiCl_{2} with a constant concentration in Ni^{2} ^{+} and increasing Cl^{−}/Ni^{2} ^{+} ratios were examined by EXAFS spectroscopy.Fourier transforms of the experimental data give evidence of the increasing complex formation between Ni^{2} ^{+} and Cl^{−} ions. A quantitative analysis of this phenomenon is also attempted, based on the interpretation of Fourier filtered EXAFS spectra.

Temperature dependence of the spin Hamiltonian parameters in KCl:Eu^{2} ^{+} crystals
View Description Hide DescriptionThe temperature dependence of the spin Hamiltonian parameters of Eu^{2} ^{+} in orthorhombic sites of KCl crystals has been measured in the range 87–573 K using EPR techniques. In this work, we fit an analytical expression for the predominant parameter b ^{0} _{2} as a function of temperature, b ^{0} _{2}=a _{0}+a _{1} T+a _{2} coth θ/2T. With eight experimental points the equation for b ^{0} _{2} was fitted and the following values were obtained a _{0}=364.54×10^{−} ^{4} cm^{−} ^{1}, a _{1}=−0.03 ×10^{−} ^{4} cm^{−} ^{1} K^{−} ^{1}, and a _{2}=−5.72× 10^{4} cm^{−} ^{1}. The root of the mean squared deviation between calculated and reported values is σ=2.03×10^{−} ^{4} cm^{−} ^{1}.

Frequency modulation coherent anti‐Stokes Raman spectroscopy (FM‐CARS): A novel sensitive nonlinear optical method
View Description Hide DescriptionA frequency modulation coherent anti‐Stokes Raman spectroscopy (FM‐CARS) is proposed. Using phase‐modulated Stokes input field, a frequency modulated CARS output is generated. Raman resonances are detected by a CARSheterodyne signal generated in a square‐law photodetector.Theoretical estimations show that a high signal‐to‐noise ratio which is shot‐noise limited and effective background suppression are expected with the proposed method independent of the lasers polarization. In typical solvents the sensitivity estimated is χ^{(3)} _{ R }=4–8×10^{−18} esu, which corresponds to the detection of 1–2×10^{−} ^{4} M benzene in cyclohexane.

Reactions of energetic tritium atoms with ethyl fluoride over an extensive pressure range
View Description Hide DescriptionRecoil tritiumreactions with ethyl fluoride have been studied over a pressure range of six orders of magnitude. The results show that subsequent to T‐for‐H substitution, the fraction of collisionally stabilized C_{2}H_{4}TF ranges from 0.05 at 10^{−} ^{2} Torr to 0.91 in the liquid. The low pressure results indicate that 95% of the C_{2}H_{4}TF molecules being formed possess an excitation energy of 65 kcal mol^{−} ^{1} or higher. The high pressure and liquid phase studies suggest that about 15% of the excited molecules have energies distributed in a very long and narrow tail at the high energy end.

Three‐body association reactions of NO^{+} and O^{+} _{2} with N_{2}
View Description Hide DescriptionThe cluster ions NO^{+} (N_{2})_{ n }, n≤5, and O^{+} _{2} (N_{2})_{ n }, n≤6, were observed in a N_{2}–O_{2} gas mixture irradiated by α particles. The temperature dependence of equilibrium constantsK for association reactions X^{+}(N_{2})_{ n−1}+2N_{2}⇄X^{+} (N_{2})_{ n }+N_{2}, X=NO, O_{2}, was determined using high‐pressure mass spectrometry. With X=NO, the enthalpies and entropies of clustering (−ΔH°, kcal/mol;−ΔS°, cal/mol K) are found to be (4.4; 13.3) and (3.9; 12.6) for n=1 and 2, respectively. Estimation of K at 204 K yields 1.1×10^{−} ^{2} (±30%) Torr^{−} ^{1} for n=3 and ∼4×10^{−} ^{3} Torr^{−} ^{1} for n=4. For X=O_{2}, the (−ΔH°;−ΔS°) values, for n=1, 2, 3 are (5.20; 15.8), (4.3; 13.8), and (3.46; 12.1), respectively. The value of K (n=4) is estimated to be ∼ 4×10^{−} ^{2} Torr^{−} ^{1} at 184 K, and ∼7×10^{−} ^{3} Torr^{−} ^{1} at 204 K; for n=5, K is ∼1×10^{−} ^{2} Torr^{−} ^{1} at 184 K. The results for n=1 are compared with previously reported measurements.

Conversion of bound states to resonances with changing internuclear distance in molecular anions
View Description Hide DescriptionThe complex self‐consistent field (CSCF) method has been used to compute the complex potential‐energy curves of the lowest ^{2}Σ^{+} _{ u } autodetaching resonance state of F^{−} _{2} and the ^{2}Π_{ g } resonance state of N^{−} _{2}. The calculated width of the ^{2}Π_{ g } resonance of N^{−} _{2} as a function of internuclear distance is in excellent agreement with the results of previous calculations by other methods. The SCF energies of the anion and the neutral molecule in these examples cross at an internuclear distance different from that at which the SCF energy of the anion becomes complex. We find this to be a general feature of the SCF description of shape resonance states. Correlation effects appear to be of critical importance in determining the behavior of the resonance states in the crossing region.

Application of scaling theory to vibrational relaxation in linear anharmonic triatomic molecules
View Description Hide DescriptionThe energy‐corrected‐sudden (ECS) scaling theory is extended to vibrational relaxation in the collisions of anharmonic linear triatomic molecules with atoms. Application is made to the collisions of He atoms with ^{1} ^{2}C ^{1} ^{6}O_{2}, ^{1} ^{4}C ^{1} ^{6}O_{2}, and ^{1} ^{2}C ^{1} ^{8}O_{2}. By combining the rate constants for the (01^{1}0 → 00^{0}0) transitions, calculated using the vibrational close‐coupling rotational infinite‐order‐sudden (VCC‐IOS) method, with the ECS scaling theory, we predict rate constants for the transitions (10^{0}0 → 01^{1}0), (02^{2}0 → 01^{1}0) and (02^{0}0 → 01^{1}0). These agree very well with the rate constants computed directly using the VCC‐IOS technique. This comparison presents a particularly severe test of the accuracy of the ECS scaling theory for anharmonic polyatomics since Fermi resonance effects are large for the 10^{0}0 and 02^{0}0 levels in CO_{2}.

Temperature dependence of near‐resonant vibrational energy transfer between CO_{2} and deuterated methanes
View Description Hide DescriptionVibrational deactivation of CO_{2}(00°1) by CD_{4}, CHD_{3}, CH_{2}D_{2}, and CH_{3}D has been studied using the laser fluorescence method. Rates are determined as a function of temperature in the range 220–300 K. The rate constants increase as the temperature decreases for all the systems studied. The deactivation of CO_{2}(00°1) correlates linearly with the number of stretching modes between the 2109 and 2263 cm^{−} ^{1} region of CH_{ n }D_{4−n }(n=0–4) molecules which, in turn, correlates with the number of deuterium atoms in the collision partner. The linear correlation occurs at all the temperatures studied. This result is interpreted as a near‐resonant vibrational‐rotational energy transfer process in which two vibrational quantum numbers change as the energy is shared between the collision partners. The rotational distribution of population of each CH_{ n }D_{4−n } molecule is calculated and compared with the rotational distribution of the initially excited CO_{2} molecule. Sharma–Brau probabilities are calculated and compared with experimental probabilities. These calculated probabilities include average over the distribution of velocities, impact parameter, and rotational distributions. Experimental and calculated results indicate the effect of attractive forces in the energy transfer process and the importance of the rotational transitions decreasing the ΔE released to translational motion of the collision pair.

Nitric oxide vibrational excitation from the N(^{4} S)+O_{2} reaction
View Description Hide DescriptionMeasurements of the vibrational distribution of NO produced in a room temperature flowtube study of N(^{4} S) + O_{2}→NO(0≤v≤7) + O are reported. Ultraviolet laser induced fluorescence detection of NO(v) in levels v=0–7 was employed to study NO production under conditions where O_{2} vibrational quenching was insignificant. The results indicate that 42% of the NO molecules are produced in infrared‐active states, 38% of them in levels ≥2. This is considerably more NO vibrational excitation than had been inferred from infrared chemiluminescence studies. Moreover, production of infrared active states of NO by the N(^{4} S)+O_{2}reaction may be even more efficient than these numbers indicate owing to possible vibrational relaxation of the nascent NO(v) distribution by nitrogen atoms in the flowtube.

Nascent NO vibrational distribution from 2485 Å NO_{2} photodissociation
View Description Hide DescriptionThe initial NO vibrational level distribution has been determined for NO_{2}photodissociation at 2485 Å. Excitation spectra of the NO vibrational levels were measured by using both the NO A ^{2}Σ^{+}←X ^{2}Π and B ^{2}Π←X ^{2}Π transitions, the latter being somewhat stronger due to saturation effects. It was determined that the NO population was strongly inverted, with most of the nascent NO being in v=6–8; the thermodynamic limit is v=8. Injection locking of the KrF laser output permitted study of the 2491 Å NO_{2} band, and it was evident that the increased absorption in this region gave greatly enhanced signal levels in the excitation spectra, at those wavelengths where NO_{2} and NO absorption lines coincide. It was demonstrated that in the 2640–2850 Å wavelength region, NO_{2} can be detected by use of a single dye laser, simultaneously dissociating NO_{2} and electronically exciting the resultant vibrationally hot NO. Deactivation of NO(v=8) by NO_{2} was found to proceed with a rate coefficient of 1.1×10^{−} ^{1} ^{1} cm^{3} molecule^{−} ^{1} s^{−} ^{1}, whereas the coefficient for quenching by N_{2} and He was ≤2×10^{−} ^{1} ^{5} cm^{3} molecule^{−} ^{1} s^{−} ^{1}. The peculiar NO rotational distributions noted by Zacharias et al. in their study of NO_{2}dissociation at 3371 Å were also observed in the present work.