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Volume 85, Issue 6, 15 September 1986
85(1986); http://dx.doi.org/10.1063/1.450981View Description Hide Description
The general problem of the polarization dependence of an orientationally averaged four‐photon process in a rigid isotropic medium is examined. The theory is then reduced to the special case of three‐photon photoselection (3PP) in which an excited state is first created by the simultaneous absorption of three identical photons and then the system is interrogated by a one‐photon probe step (absorption or emission). When the probe signal is measured as a function of both excitation and probing polarizations, five unique transition tensor invariants can be determined. These five invariants provide a characteristic signature of the symmetry of the initial three‐photon absorption (3PA). A symmetry analysis is illustrated within the hexagonal point groups where it is demonstrated how the measurement of a single photoselection polarization ratio formally allows, with one exception, a unique symmetry assignment to be made for any three‐photon allowed transition. This measurement makes use of circularly polarized excitation with variably polarized probing. The polarized probe step in a 3PP experiment provides information concerning the three‐photon transition beyond that available from a simple polarized 3PA study.
85(1986); http://dx.doi.org/10.1063/1.450982View Description Hide Description
Although group theoretically allowed, the benzene B 2u ←A 1g three-photon transition appears to derive intensity exclusively through a vibronic coupling route. The ν6 (e 2g ) vibration is dominant in providing e 1u vibronic symmetry, just as it is in the one-photon transition. Several experiments are presented that provide further insight into the lack of allowed vibronic b 2u activity in the three-photon spectrum. Pseudoparity, applicable to even alternate hydrocarbons in the PPP formalism, and offering selection rules beyond those based on symmetry alone, is examined as a possible explanation by looking for effects from the inductive perturbation in a fluorine substituted benzene. The possibility of nonresonant third harmonic generation in the condensed phase sample, which may lead to a viable one-photon absorption route to the excited B 2u state, is also explored in both a three-photon photoselection study as well as in an experiment comparing the relative three-photon to one-photon cross sections for benzene and biphenyl. The results obtained for the benzene B 2u transition and the corresponding A′2 transition in the symmetrically substituted trifluorobenzene appear to confirm the importance of pseudoparity selection rules and suggest that the third harmonic generation pathway is of minor importance.
85(1986); http://dx.doi.org/10.1063/1.450983View Description Hide Description
From measurements of the angularly dependent second order quadrupole shift of the central transition of the 2 3Na spectrum in Na β″‐alumina at 5 K, it is possible to conclude that sodium resides in two distinct sites in the conduction plane. Calculations of electric field gradients (efg) consistent with experiment indicate that these sites are located along the miror planes characterizing the conduction directions. Independent calculation of the efg’s with a point charge model reveals (1) that the Na ions in the two sites are shifted from the BR crystallographic positions in the lattice; in one case a very small amount and in the second a much larger shift and (2) the presence of vacant BR positions. The NMR results agree with the extended 2D superlattice of Boilot e t a l. [Phys. Rev. B 2 2, 5912 (1980)] used to account for x‐ray diffuse scattering and diffraction.
85(1986); http://dx.doi.org/10.1063/1.450984View Description Hide Description
From measurements of the angularly dependent second order quadrupole shift of the central transition of the 2 3Na spectrum in Na β‐alumina at 5 K, it is possible to conclude that sodium resides in three distinct kinds of sites in the conduction plane. Calculation of the electric field gradients (efg) consistent with experiment indicate that these sites are localized around a structural defect in the conduction plane that changes the local symmetry away from that of the average unit cell. Independent calculation of the efg’s with a point charge model reveals (1) that the sodiums in one of the three sites, called site 1, are closely associated with the BR position in the conduction plane, (2) sites 2 and 3 are nearby the mO positions clustered around the charge compensating oxygen, and (3) site 3 is closer to this oxygen than site 2. The NMR results agree with the Roth–Reidinger model of the conduction plane as modified by Wang.
Rotational spectrum, H, 1 9F spin–spin and D–nuclear quadrupole coupling constants, and molecular geometry of the sulphur dioxide–hydrogen fluoride dimer85(1986); http://dx.doi.org/10.1063/1.451829View Description Hide Description
The ground state rotational spectra of three isotopic species 3 2SO2⋅⋅⋅HF, 3 2SO2⋅⋅⋅DF, and 3 4SO2⋅⋅⋅HF of a dimer formed between sulphur dioxide and hydrogen fluoride have been detected and measured using a pulsed‐nozzle, Fourier‐transform microwave spectrometer. An analysis of observed nuclear hyperfine structure leads to the H, 1 9F nuclear spin–nuclear spin coupling constants D HF a a =−190(2) kHz and (D HF b b −D HF c c ) =−57(4) kHz for 3 2SO2⋅⋅⋅HF, and to the D‐nuclear quadrupole coupling constants χ a a =227(3) kHz and (χ b b −χ c c ) =68(13) kHz for 3 2SO2⋅⋅⋅DF. Rotational and centrifugal constants have been determined for all three isotopic species, with the following values for 3 2SO2⋅⋅⋅HF: A 0=16 502.775(4) MHz, B 0=2100.308(1) MHz, C 0=1853.642(1) MHz, Δ J =18.31(2) kHz, Δ J K =−521.78(4) kHz, and δ J =4.37(3) kHz. The rotational constants for the three isotopic species are interpreted in terms of a planar geometry in which hydrogen fluoride forms a c i shydrogen bond to one of the oxygen atoms of SO2. Assuming a linear hydrogen bond and unchanged subunit geometries, it is found that r(O⋅⋅⋅F)=2.818(8) Å and θ=215.1° where θ is the S=O⋅⋅⋅H bond angle. The nuclear hyperfine coupling constants are shown to be consistent with this arrangement.
85(1986); http://dx.doi.org/10.1063/1.450985View Description Hide Description
Absorption from the lowest‐lying ion pair state of HgBr (i.e., Hg+–Br−: B 2∑+ 1/2 ) has been observed by transient absorption spectroscopy in a pulsed, transverse discharge containing a mixture of Ne, N2, and HgBr2 vapor. A highly structured band peaking at ∼447 nm is shown to be associated with charge–transfer transitions from the B 2∑+ 1/2 state to a higher‐lying, covalently bonded (Hg*–Br) state. By pumping the 447 nm transition with a pulsed dye laser while simultaneously monitoring gain on the HgBr (B 2∑+ 1/2 →X 2∑+ 1/2 ) band at 502 nm, the absorption cross section for the blue band was measured to be (3.0±1.5)×10− 1 7 cm2 and the saturation intensity for the transition at 447 nm was determined to be 710±50 kW cm− 2.
The first ionization potential of zirconium atoms determined by two laser, field‐ionization spectroscopy of high lying Rydberg series85(1986); http://dx.doi.org/10.1063/1.450986View Description Hide Description
An accurate value for the first ionization potential of zirconium of 53 506.0(3) cm− 1 has been obtained from convergence limits of high lying Rydberg series observed using two laser, field‐ ionization spectroscopy of an atomic beam of zirconium. The new value is consistent with analysis of s‐electron binding energies of other second transition series elements.
Methyl fluoride–1 3C in nematic liquid crystals: Anisotropy of the indirect 1 3C–1 9F spin–spin coupling and of the 1H, 1 3C, and 1 9F chemical shieldings85(1986); http://dx.doi.org/10.1063/1.450987View Description Hide Description
The anisotropy of the indirect 1 3C–1 9F spin–spin coupling tensor of methyl fluoride–1 3C in the liquid crystals ZLI 1167, EBBA, their mixtures, phase IV, and phase 1221 was studied by applying 1H and 1 9F NMR spectroscopy. The relative anisotropy ΔJ CF/J CF gets values between −4.3 (in ZLI 1167) and +30.7 (in EBBA) when determined in the conventional way from the experimental dipolar coupling constants taking into account only harmonic vibrational corrections. The inclusion of the deformational corrections in both the direct and indirect C–F coupling tensors leads to a constant, solvent independent relative anisotropy of −2.5±0.2. This result is also obtained when a mixture of the liquid crystals ZLI 1167 and EBBA is used which mixture gives an undistorted geometry for methyl fluoride. The chemical shielding anisotropies ΔσH, ΔσC, and ΔσF for methyl fluoride were determined by applying the method of mixing two thermotropic nematogens (ZLI 1167 and EBBA) with opposite anisotropies of diamagnetic susceptibility. The results ΔσH =+5.2±0.2 ppm, ΔσC =+87±4 ppm, and ΔσF =−90±4 ppm are in fair agreement with theoretical calculations.
85(1986); http://dx.doi.org/10.1063/1.450988View Description Hide Description
High resolution infrared absorption spectra have been recorded for the ν4 vibrational mode of CH4 trapped in rare gas solids. In argon, krypton, and xenon hosts two dominant sites are observed which we call site R and site A,B. For both sites we believe that the CH4 molecule replaces one host atom. The fine structure of site R at a temperature of 5 K is that predicted for a tetrahedral molecule rotating in an octahedral field; singlet peaks for P(1), Q(1), R(0), and a doublet for the R(1) transitions. The barrier for this rotation is not clearly defined. Site A,B shows site symmetry splitting and orientational ordering suggestive of C 3v symmetry. Rotational structure is also associated with site A,B; it is not clear whether the hindered rotation for this site takes place about only the C 3 axis or about axes perpendicular to C 3 as well. From annealing studies and the effects of deposition temperature we conclude that site R is for CH4 molecules trapped in the normal cubic‐close‐packed environment while site A,B is for CH4 trapped in hexagonal‐close‐packed pockets induced by stacking faults formed during deposition. Temporal changes of peak intensities while the matrices stand at 5 K are indicative of a slow relaxation of nuclear spin from a triplet state (J=1) to a quintet state (J=0). For site A,B the triplet to quintet spin relaxation is considerably faster than for site R; for example, for a matrix of CH4 in krypton (1/10 000) at 5 K the spin relaxation half‐lives are 87 minutes and 26 minutes for sites R and A,B, respectively.
Nitrogen‐broadened linewidths and strengths of nitric oxide utilizing tunable diode laser spectroscopy85(1986); http://dx.doi.org/10.1063/1.450989View Description Hide Description
Nitrogen‐broadened linewidths and line strengths of NO fundamental band lines were measured utilizing tunable diode laser spectroscopy. The spectral lines measured were the P(4.5), P(5.5), and P(6.5) line of the 1/2 subband. Spectra were taken on a 1.75% NO/N2 mixture in the temperature range of 300 to 900 K and for pressures of 200, 400, and 600 Torr. The line strengths obtained in this work were found to be lower than those determined by an earlier work, and linewidths were close to those of previously published nitrogen‐broadened half‐widths for NO.
85(1986); http://dx.doi.org/10.1063/1.450990View Description Hide Description
Line splittings observed in the 1 0B and 1 1B NMRspectra of o r t h o‐carborane‐d 2, when a solution of the compound is exposed to a very strong electric field, have been used to derive the components of the boronquadrupole coupling tensors along the molecular dipole moment direction. Furthermore, the magnitudes of the boronquadrupole coupling constants were measured from the spin‐lattice relaxation times (T 1). The boronlinewidths observed indicate the presence of a substantial scalar coupling contribution to T 2 for both boronisotopes. The direction of the axis to be associated with the quadrupole coupling constant has been derived for some of the borons in o‐carborane by combing the EFNMR results with those of the T 1 study.
Trapping site geometry of N2H+ 4 radical ion in x‐irradiated single crystals of N2H5HC2O4: An ENDOR study85(1986); http://dx.doi.org/10.1063/1.450991View Description Hide Description
The radical ion N2H+ 4 has been produced by x irradiatingsingle crystals of hydrazinium hydrogen oxalate (N2H5HC2O4) and studied by ESR and ENDORspectroscopy. The structure of the trapping site has been elucidated by observing 1H ENDOR transitions not only from the radical but also from distant protons. One of the latter originates from the proton lost by N2H+ 5 upon radical formation. Evidence that proton transfer occurs through a hydrogen bond is presented.
Rotational analysis of some vibronic bands in the 3 A u ←1 A g transition of glyoxal. Spin splittings in the lowest triplet state of the isolated molecule85(1986); http://dx.doi.org/10.1063/1.450992View Description Hide Description
A rotational analysis of three vibronic bands (00 0, 72 0, and 51 0) in the phosphorescence excitation spectrum of glyoxal (CHO–CHO) has been performed. From this analysis we deduce the rotational, spin‐rotation, and spin–spin (plus spin‐orbit) constants of the lowest triplet state of the isolated molecule. 3 A u glyoxal has been shown to exist in nearly the same t r a n s‐planar (C 2h ) configuration as the lowest excited singlet state. Both geometries are very similar to that of the ground state. The dynamic implications of these structural findings are discussed. We also compare the spin splittings determined in this work with those previously measured in the condensed phase, using optically detected magnetic resonance methods.
85(1986); http://dx.doi.org/10.1063/1.450993View Description Hide Description
Mn atoms and MnH molecules, the latter formed by reaction between metal and hydrogen atoms, were trapped in solid argon and their ESR/ENDOR spectra measured at 4 K. At each pumping magnetic field two ENDOR lines were observed for 5 5Mn(I=5/2) atoms, corresponding to hyperfine transitions within the M S =±1/2 levels. Values of the hyperfine interaction constant and nuclear moment of 5 5Mn were derived from the six sets of data. For MnH, three sets of signals were detected: a proton ‘‘matrix ENDOR’’ line, transitions in the M S =0,±1 levels involving M I (5 5Mn)=1/2, 3/2, 5/2 levels, and proton transitions corresponding to νH and νH±a H. Analysis yielded the hyperfine constant a H =6.8(1) MHz and the nuclear quadrupole coupling constant Q′(5 5Mn)=−11.81(2) MHz. The latter compared favorably with a theoretical value derived earlier by Bagus and Schaefer. A higher term in the spin Hamiltonian appeared to be necessary to fit the proton hyperfine data.
85(1986); http://dx.doi.org/10.1063/1.450994View Description Hide Description
Spectra of the pyrazine‐d 4, pyrazine‐h 4–pyrazine‐d 4, and pyrazine‐d 4–pyrimidine dimer are obtained and analyzed with the help of Lennard‐Jones–hydrogen‐bonding (LJ–HB) potential energy calculations. The pyrazine isotopic hetero and homo dimers possess nearly identical spectra with the exception that the perpendicular dimer features are displaced to the red by ∼11 cm− 1. Exchange or excitoninteractions in this system are vanishingly small (less than 1 cm− 1). The geometries suggested by the isotopically substituted pyrazine dimer spectra are the same as those found for the pyrazine‐h 4 homo dimer: a parallel planar hydrogen bonded and a perpendicular dimer. The pyrazine‐d 4– and pyrazine‐h 4–pyrimidine dimer spectra are quite complicated. These spectra can be assigned as arising from one parallel stacked head‐to‐tail displaced dimer, one parallel planar dimer, and three perpendicular dimers based on comparisons with spectra of the pyrazine and pyrimidine dimers.
85(1986); http://dx.doi.org/10.1063/1.450995View Description Hide Description
When a chemical reaction is carried out in a continuously stirred tank reactor, the behavior may be significantly affected by the efficiency with which the entering chemicals are mixed with the main contents of the reactor. We have developed a model for this effect which assumes that a feed of premixed chemicals remains for a while in totally segregated packets before they are rapidly and perfectly mixed with the rest of the system. The time of this initial segregation is affected by the efficiency of stirring in the reactor. The model has been tested by computations on a mechanism developed by Roelofs e t a l. for a reaction which would oscillate even in a closed system. It has also been tested by computations on the rapid autocatalytic oxidation of cerous ion by bromate in the presence of a small amount of bromide. The results are qualitatively consistent with effects observed experimentally and in computations with other models including a somewhat similar one by Kumpinsky and Epstein. More quantitative tests should recognize the difference whether two streams of chemicals enter the reactor independently or are premixed before they do so.
85(1986); http://dx.doi.org/10.1063/1.450996View Description Hide Description
A general model of cluster formation in the laser vaporization source starting from the atomic vapor is developed and applied to carbon clusters. Two limiting cases of cluster growth exist: the diffusion‐limited regime, in which the cluster distribution is essentially featureless, and the reaction‐limited regime, in which the most stable clusters show as magic numbers in the cluster distribution. An approximate theory of the aggregation kernel allows for calculation of the cluster distribution in the reaction‐limited regime from the formation energies of the reacting clusters. Heat released in cluster fusion allows small and medium size clusters to attain their lowest or almost lowest energy configurations in both the diffusion‐ and reaction‐limited regimes. For larger clusters, crystalline structures are expected for transition metals, while network‐forming materials are likely to exibit a multitude of structures. An application to carbon clusters in the n=1–25 range reproduce the experimentally observed cluster distributions and the magic numbers in the n=10–25 regime. The equilibrium structures of the small carbon clusters formed in the nozzle are found to be chains and monocyclic rings. At the reaction temperature, the transition between the chain and ring structures occurs around n=10 for the neutral and the positively charged clusters.
85(1986); http://dx.doi.org/10.1063/1.450997View Description Hide Description
We have examined the classical limits to the orbital and energy sudden approximations. It is shown that at large orbital and rotational quantum numbers the transformations which diagonalize the coupling matrix in the sudden limit also diagonalize the coupling matrix in the classical limit. The eigenvalues are no longer a delta function fixed in position during the collision but become a narrow wave packet moving with the classical velocity. The result is a uniform approximation valid in both the sudden and classical limits. A key feature of the theory is the use of the discrete‐variable representation which allows an accurate counting of quantum states in the sudden representation. The theory should improve the accuracy of the sudden approximation while requiring little additional computer time.
85(1986); http://dx.doi.org/10.1063/1.450998View Description Hide Description
This paper considers the response of various rotational energy transfer processes to functional variations about an assumed modelintermolecular potential. Attention is focused on the scattering of an atom and a linear rigid rotor. The collision dynamics are approximated by employing both the infinite order sudden (IOS) and exponential distorted wave (EDW) methods to describe Ar–N2 and He–H2, respectively. The following cross sections are considered: state‐to‐state differential and integral, final state summed differential and integral, and effective diffusion and viscosity cross sections. Attention is first given to the forward sensitivity densities δ0/δV(R,r) where 0 denotes any of the aforementioned cross sections, R is the intermolecular distance, and r is the internal coordinates. These forward sensitivity densities (functional derivatives) offer a quantitative measure of the importance of different regions of the potential surface to a chosen cross section. Via knowledge of the forward sensitivities
and a particular variation δV(R,r) the concomitant response δ0 is generated. It was found that locally a variation in the potential can give rise to a large response in the cross sections as measured by these forward densities. In contrast, a unit percent change in the o v e r a l l potential produced a 1%–10% change in the cross sections studied indicating that the large + and − responses to local variations tend to cancel. In addition, inverse sensitivity densities δV(R,r)/δ0 are obtained. These inverse densities are of interest since they are the e x a c t solution to the infinitesimal inverse scattering problem. Although the inverse sensitivity densities do not in themselves form an inversion algorithm, they do offer a quantitative measure of the importance of performing particular measurements for the ultimate purpose of inversion. Using a set of state‐to‐state integral cross sections we found that
the resultant responses from the infinitesimal inversion were typically small such that ‖δV(R,r)‖≪‖V(R,r)‖. From the viewpoint of an actual inversion, these results indicate that only through an extensive effort will significant knowledge of the potential be gained from the cross sections. All of these calculations serve to illustrate the methodology, and other observables as well as dynamical schemes could be explored as desired.
85(1986); http://dx.doi.org/10.1063/1.450999View Description Hide Description
A physical/chemical model is presented for the reaction kinetics for methane formation from carbon, due to bombardment by energetic (∼100’s eV) H+ ions and thermal (∼1 eV) H0 atoms. While the model was developed for H+ and H0, it can be readily applied to nonhydrogenic energetic particles (ions or atoms, e.g., Ar+, He+, He) in combination with thermal (∼1 eV) hydrogen (again ions or atoms) impacting on carbon. Both collisional (in the case of the energetic particles) and chemical reaction processes are included. Special cases of sub‐eV H0 alone, energetic H+ alone, and combined H0 plus H+ were considered and fitted to experimental data. Generally good agreement was found between theoretical predictions and experimental results over the experimental flux and H+ energy ranges studied (H0 flux: 6×101 4–7×101 5 H0/cm2 s, H+ flux: 6×101 2–5×101 5 H+/cm2 s, H+ energy: 300 eV/H+ and 1 keV/H+).