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Volume 98, Issue 9, 01 May 1993

Molecular engineering implications of rotational invariance in quadratic nonlinear optics: From dipolar to octupolar molecules and materials
View Description Hide DescriptionMolecules and assemblies therefrom with strictly vanishing multipolar‐like tensorial susceptibilities of given orders are defined in general, following group theoretical prescriptions. This approach leads, in the case of quadratic nonlinear optical properties, to a new class of molecules with strictly vanishing dipole moments and dipolar components of the quadratic hyperpolarizability tensor β. The remaining nonvanishing irreducible β component, referred to as the octupolar component, had not been previously considered in the perspective of molecular engineering and optimization, as proposed in this work. The adequate tensorial framework for depicting such an approach is derived for the various point‐symmetry classes and a vectorial representation introduced to depict the full anisotropic nature of nonlinear polarizabilities. It permits a more general and adequate scaling of molecules and materials in terms of their efficiencies, while previous molecular classifications, strongly biased by the electric field second‐harmonic (EFISH) solution experiment, focus almost exclusively on the dipolar component of β. Various molecular engineering routes meant at enhancing the octupolar β component are proposed and illustrated by specific examples. The molecular quantum implications of the existence of octupolar nonlinearities are discussed with three‐level systems shown to replace the inadequate traditional two‐level model. Finally, identical tensorial symmetry considerations, applied consistently to molecular assemblies (χ^{(2)}susceptibility) and interacting light beam (F ^{(2)} cubic field tensor) evidence the relevance of circularly polarized beams to probe octupolar assemblies, the ellipticity of the outgoing beam in the case of second‐harmonic generation depending on the ratio of the octupolar over dipolar susceptibility components.

Vibrational and K ^{’} _{ a } dependencies of the multidimensional tunneling dynamics in the 82.6 cm^{−1} intermolecular vibration of the water dimer‐d _{4}
View Description Hide DescriptionUsing tunable far infrared laserabsorption spectroscopy, 12 vibration–rotation‐tunneling (VRT) subbands, consisting of approximately 230 transitions have been measured and analyzed for an 82.6 cm^{−1} intermolecular vibration of the water dimer‐d _{4}. Each of the VRT subbands originate from K ^{‘} _{ a } = 0 and terminate in either K ^{’} _{ a } = 0 or 1. These data provide a complete characterization of the tunneling dynamics in the vibrationally excited state as well as definitive symmetry labels for all VRT energy levels. Furthermore, an accurate value for the A’rotational constant of 122.9 GHz is found to agree well with its corresponding ground state value. All other excited staterotational constants are fitted, and discussed in terms of the corresponding ground state constants. In this vibration, the quantum tunneling motions are determined to exhibit large dependencies with both the K ^{’} _{ a } quantum number and the vibrational coordinate, as is evidenced by the measuredtunneling splittings. The generalized internal‐axis‐method (IAM) treatment, which has been developed to model the ground statetunneling dynamics, is considered for the qualitative description of each tunneling pathway, however, the variation of tunneling splittings with vibrational excitation indicate that the high barrier approximation does not appear to be applicable in the excited state. The data are consistent with a motion possessing a’ symmetry, and the vibration is assigned as the ν_{8} acceptor bending coordinate. This assignment is in agreement with the vibrational symmetry determined from the data, the results of high level ab initio calculations, and preliminary data assigned to the analogous vibration in D_{2}O–DOH.

Fourier‐transform microwave spectroscopy of the HCCN radical. Determination of the hyperfine coupling constants
View Description Hide DescriptionTwo low‐J transitions, N(J)=1(0)−0(1) and 1(2)−0(1), of the HCCN radical in its ^{3}Σ^{−} ground state have been studied by a pulsed‐discharge‐nozzle Fourier‐transform microwave spectrometer. Spectrum with well‐resolved hyperfine splittings due to hydrogen and nitrogen nuclei was observed, which enabled us to determine accurate hyperfine coupling constants for both the nuclei for the first time in the present study, as well as a much improved spin–spin coupling constant. These hyperfine coupling constants suggest that the electronic structure of the HCCN radical can be described as the one with the allenic structure to be almost twice more important than the carbenic structure. The present results seems to support a conclusion that the molecular structure of the radical is almost linear with a possibility of a large amplitude bending motion.

b‐dipole transitions in trans‐HOCO observed by far infrared laser magnetic resonance
View Description Hide DescriptionFar infrared lasermagnetic resonancespectroscopy is used to measure components of 12 rotational transitions in the ground state of the HOCO radical. The transitions are all b‐dipole in character in contrast to the a‐dipole rotational spectrum previously reported [Radford, Wei, and Sears, J. Chem. Phys. 97, 3989 (1992)]. The new data determine the Arotational constant to high precision and allow the determination of several centrifugal distortion constants for the first time. The hyperfine coupling in the radical leads to observable splittings in several of the observed transitions and these are used to estimate two of the four expected nonzero hyperfine parameters in the radical.

On the use of time domain methods to study the excitation of a molecule by a strong, long laser pulse
View Description Hide DescriptionCalculations which solve the time dependent Schrödinger equation on a grid are generally useful for studying the cw excitation of a molecule by a weak laser or the excitation by a short, strong laser pulse. Here we show how time dependent methods can be applied to study excitation by strong, long pulses. Moreover, even though the molecule is driven by a time dependent field, one can identify energy eigenstates that provide the time scales on which various observables evolve. The calculations which illustrate the methodology are performed on a model of the bound‐to‐bound electronic excitation of the I_{2} molecule. We study the dependence of the excitation probability on time, power, and laser frequency. We find that the I_{2} molecule driven by a strong laser emits at many frequencies below and above the laser frequency.

Efficiency and mechanism of electronic predissociation of B state I_{2}–Ar
View Description Hide DescriptionThe isomer of the I_{2}–Ar complex which yields discrete bands in the B←X spectrum is shown, as expected, to be T shaped on the basis of rotational structure observed in the vibronic bands. Precise fluorescence quantum yields for I_{2}–Ar relative to I_{2} were measured via simultaneous acquisition of absorption and fluorescence excitation spectra in a slit nozzle expansion. These fluorescence quantum yields provide vibrational predissociation efficiencies for B state I_{2}–Ar as a function of vibrational state from v’ of 15 to 26. This is an oscillating function with local maxima at v’ of 16, 22, and 26. For v’=22 and 26, 73%±3% of the complexes undergo vibrational, rather than electronic predissociation.Fluorescence intensities of combination bands with excitation in the van der Waals modes were also found to have oscillating v’ dependencies with patterns nearly identical to that for the bands without van der Waals mode excitations. Thus, these oscillations must arise from the electronic predissociation channel, rather than the vibrational channel. Deconvolution of the lifetime of B state I_{2}–Ar into vibrational and electronic lifetimes indicates that the similar overall lifetimes at v’ of 18 and 21 result from a twofold increase in the electronic lifetime at v’=21, which compensates for a decrease in the vibrational lifetime. Assumption of a smooth v’ dependence for the vibrational lifetime leads to oscillatory predicted overall lifetimes of 35, 77, 82, 51, and 30 ps over the v’ range of 20–24, respectively. Based on symmetry arguments, as well as the observed vibrational predissociation efficiencies, the electronic predissociation of I_{2}–Ar must arise from coupling of the B state to the Π_{ g } state. This coupling may also be the dominant channel for collisional quenching of B state I_{2}.

Rate and mechanism of intramolecular vibrational redistribution in the ν_{16} asymmetric methyl stretch band of 1‐butyne
View Description Hide DescriptionThe spectrum of the ν_{16} asymmetric methyl stretch vibration of 1‐butyne near 2991 cm^{−1} has been studied via direct absorptioninfrared spectroscopy at a resolution of 35 MHz. Analysis by ground state combination difference indicates that the ν_{16} band is extensively perturbed by dark vibrational bath states. All of the transitions appear as multiplets of about five eigenstates in a window of about 0.017 cm^{−1}. A detailed analysis is presented for the upper state levels K ^{’} _{ a } = 0–2 and J’=0–6. A lack of J’ dependence implies anharmonic coupling is dominant and that b‐ and c‐type Coriolis interactions are not important at these low J’ values. However, the average dilution factor goes from 0.72 at the K ^{’} _{ a } = 0 to 0.46 at the K ^{’} _{ a } = 2 suggesting weak a‐type Coriolis interactions. For the K ^{’} _{ a } = 0 levels, the measured average level density of 17 states/cm^{−1}/symmetry species is comparable to the value of 14 vibrational states/cm^{−1}/symmetry species obtained from a symmetry specific direct count. This is an indication that the dynamics explore all of the energetically available vibrational phase space. The nearly Gaussian distribution of matrix elements suggests that there is significant coupling among the bath states. At the K ^{’} _{ a } = 0 level, the rms anharmonic coupling matrix element is <v _{ sj } ^{2}≳^{1/2}=0.0125 cm^{−1}. From the frequency‐resolved data, a coherently prepared asymmetric methyl stretch in 1‐butyne is deduced to decay with a 276 ps time constant to the asymptotic probability of 0.6.

Random matrix treatment of intramolecular vibrational redistribution. I. Methodology and anharmonic interactions in 1‐butyne
View Description Hide DescriptionA random matrix methodology is presented which is capable of modeling sparse through intermediate case intramolecular vibrational redistribution (IVR). A class of random Hamiltonian ensembles, called the Gaussian Poisson ensembles, is defined. These ensembles deviate from the Gaussian orthogonal ensemble (GOE) in a way that allows particular molecular spectra to be modeled, yet they can retain the desirable GOE statistical properties. The principal assumption tested by this work is that the vibrational identity of the bath states in both the calculation and in 1‐butyne is sufficiently scrambled that a statistical treatment is justified. Comparison to the experimental eigenstate‐resolved infrared spectra of 1‐butyne is accomplished by means of four measures of IVR: the dilution factor, the interaction width, the counted level density, and the effective level density. Corrections to each of the four measures for limited experimental signal‐to‐noise are presented. A fit to the dilution factor and interaction width yielded the root‐mean‐square matrix elements for anharmonic coupling of the bright state to the bath. The values obtained, 0.010 and 0.014 cm^{−1}, respectively, for the ν_{1} and ν_{16} bands of 1‐butyne, are in close agreement with those obtained by direct deconvolution of the spectra.

Infrared laser spectroscopy of jet‐cooled carbon clusters: The bending dynamics of linear C_{9}
View Description Hide DescriptionWe report improved measurements for the ν_{6} antisymmetric stretch fundamental and observation of the (ν_{6}+ν_{15})−ν_{15} and (ν_{6}+2ν_{15})−2ν_{15} hot bands of the linear C_{9}carbon cluster by direct absorptiondiode laser spectroscopy of a supersonic carbon cluster beam. Analysis of these bands characterizes C_{9} as a semirigid molecule with a bending potential similar to that of C_{5} and further evidences the alternation in degree of rigidity of linear carbon clusters with the g–u symmetry of the HOMO.

Line shape of transition to the predissociative level Cs_{2} D ^{1}Σ_{ u } ^{+}(v, J) and the effects of magnetic field
View Description Hide DescriptionA collimated cesium beam is crossed at right angles by the laser beam, and the excitation spectrum of the D ^{1}Σ_{ u } ^{+}–X ^{1}Σ_{ g } ^{+} transition is measured by detecting the emission from the dissociated atom Cs(6p ^{2} P _{3/2}). Line broadening is observed for a number of transitions to the D ^{1}Σ_{ u } ^{+}(v, J) levels, and the line shapes of the isolated lines are observed to be Lorentzian. When an external magnetic fieldH is applied parallel to the electric vector of the laser light, the linewidths are observed to increase proportionally to H ^{2}, and it is attributed to the magnetic predissociation. Some lines are observed to change by the magnetic field from a Lorentzian to an asymmetric line shape accompanied by energy shift of the intensity maximum, and it is identified as originating from the M dependence of both the transition moment <D ^{1}Σ_{ u } ^{+}‖μ‖X ^{1}Σ_{ g } ^{+}≳ and the Zeeman energy of the ^{3}Π_{ u } state.

The low‐lying bending vibrational levels of the CCH (X̃ ^{2}Σ^{+}) radical studied by laser‐induced fluorescence
View Description Hide DescriptionThe uv spectrum of the CCH radical was recorded using the laser‐induced fluorescence technique on the 193 nm photolysis product of acetylene. Four ^{2}Π–^{2}Π bands at 38 805, 37 946, 37 010, and 36 075 cm^{−1} of CCH were rotationally analyzed and assigned as transitions from the (0,v _{2} ^{1},0) (v _{2}=1, 3, 5, 7) vibrational levels of the X̃ ^{2}Σ^{+} state to a common upper vibronic state (denoted as U), which possibly belongs to the 2 ^{2}Π state. A simultaneous nonlinear least squares fit of the uv bands, in combination with the infrared transitions previously observed in the X̃ ^{2}Σ^{+} state, provided improved spectroscopic parameters for the U state and the (0,3^{1},0), (0,5^{1},0), and (0,7^{1},0) levels of the X̃ state.

A high‐resolution analysis of the Ã ^{2} A’–X̃ ^{2} A’ transition of CaSH by laser excitation spectroscopy
View Description Hide DescriptionThe high resolution spectrum of the Ã ^{2} A’–X̃ ^{2} A’ transition of CaSH has been recorded near 650 nm using laser excitation spectroscopy with selected fluorescence detection. While both a‐type and b‐type rotational transitions have been observed, extensive measurements have been made for the b‐type transitions up to K ^{’} _{ a } = 4 and K ^{‘} _{ a } = 5. Altogether over 3000 rotational lines have been measured and fitted with an A‐reduced Hamiltonian. The X̃ ^{2} A’ state has rotational constantsA=9.693 322(46) cm^{−1}, B=0.141 864 7(33) cm^{−1}, and C=0.139 581 0(33) cm^{−1}. The Ã ^{2} A’ state has a band origin at 15 380.284 7(2) cm^{−1}, and effective values for the rotational constantsA=9.090 808(78) cm^{−1}, B=0.147 459 8(34) cm^{−1}, and C=0.144 804 2(34) cm^{−1}. An approximate r _{0} structure for CaSH is discussed. The Ã ^{2} A’ state is the lower energy Renner–Teller component of the ‘‘Ã ^{2}Π’’ state of the hypothetical linear CaSH molecule, and consequently was found to have a relatively large positive value for the spin–rotation parameter ε_{ aa } at 3.445 69(26) cm^{−1}. The upper asymmetry component of the F _{1} spin component of the K _{ a }=1 stack and the F _{2} spin component of the K _{ a }=0 stack in the Ã ^{2} A’ state perturb each other with an avoided crossing between J=37.5 and J=38.5. These two spin components interact through the off‐diagonal ‖ε_{ ab }+ε_{ ba }‖/2 element of the spin–rotation tensor. For CaSH, the Ã ^{2} A’ state has ‖ε_{ ab }+ε_{ ba }‖/2=0.065 915(46) cm^{−1}.

A geometric representation of nuclear modulation effects: The effects of high electron spin multiplicity on the electron spin echo envelope modulation spectra of Mn^{2+} complexes of N‐ras p21
View Description Hide DescriptionA theoretical treatment is presented for the analysis of ESEEM spectra of I=1/2 nuclei coupled to an electron spin of high multiplicity, with specific attention to the case of S=5/2. This treatment is shown to account for the observed spectral behavior of ^{15}N and ^{31}P nuclei coupled to Mn^{2+} in a GDP complex with the protein N‐ras p21. The treatment involves the decomposition of the multilevel electron spin system into a set of noninteracting two level systems, an approximation that is valid when the dispersed EPRspectral width is large compared to the microwave excitation bandwidth. The consequent spectral selectivity of the microwave excitation is accounted for, in ESEEM simulations, by attaching a weight to the ESEEM subspectra associated with each EPR transition, and calculating the total ESEEM spectrum as a weighted superposition of the subspectra. The simplest means of estimating the appropriate weight factors—identifying them with the cw EPR intensity of each transition, as deduced by simulation of the EPR spectra—leads to ESEEM simulations that account for the key features of the observed spectra, in particular, features that are peculiar to high multiplicity spin systems. In the studied Mn^{2+} system, no clear indication of orientation selective effects were found. A simple geometric representation is presented which enables the facile understanding of ESEEM spectra of nuclear spinI=1/2 coupled to an electron spin of high spin multiplicity in orientationally disordered solids. Analytical expressions are derived for the ESEEM frequencies, frequency dispersions and amplitudes. It is shown that in these systems external field variation can lead to an array of spectral line‐narrowing and amplitude resonance phenomena analogous to those observed in S=1/2 systems.

Wave operator and artificial intelligence contraction algorithms in quantum dynamics: Application to CD_{3}H and C_{6}H_{6}
View Description Hide DescriptionWe have established in this study the capabilities of the wave operator (WO) algorithm to extract from a huge primitive space a smaller subspace (the active space) containing all of the zero order states which play an active role during the intramolecular vibrational energy redistribution (IVR) from an initial state ‖i≳^{0}. While exact methods such as the recursive residue generation method (RRGM) or the Chebychev algorithms can only be applied in a primitive space containing less than about 200 000 states, the WO algorithm can be used efficiently in ultralarge basis sets containing billions of states. The recursive residue generation method (RRGM) or Chebychev methods can then be applied in this active space which typically contains less than 10 000 states. In order to draw general conclusions on the efficiency of such a method and on the main features of IVR phenomena, we have concurrently studied IVR from the fifth CH overtone in the nine mode CD_{3}H molecule and from the second CH overtone in the 16 mode C_{6}H_{6} system. We have analyzed the main features of the active space and have shown that the WO algorithm selects the important states. A very broad energy distribution of states in the active space has been obtained for these two systems. We have also shown that C_{6}H_{6} is a very complex system to study; while only a few hundred states are effectively populated during the IVR from the fifth CH overtone in CD_{3}H, about 8000 states have to be considered in order to accurately study IVR from the second CH overtone in C_{6}H_{6}. However, we have shown that the WO method is able to reproduce correctly both the survival probability of the initial state and the intricate energy flow through the molecule during the first picosecond. Finally, we have shown that the WO algorithm builds a far more efficient active space than a more traditional artificial intelligence (Al) tree pruning procedure.

C 1s photoionization of H_{2}CO and C_{2}H_{4}: An angle‐resolved photoelectron study
View Description Hide DescriptionWe have measured partial photoionization cross sections σ and asymmetry parameters β of the C 1s main line and the π→π* shake‐up satellites of the isoelectronic molecules formaldehyde and ethylene in the near threshold region. In all channels we observe a strong cross section enhancement and a decrease in the β parameter due to a shape resonance in the continuum. For each molecule the variation of σ and β with photoelectron kinetic energy is nearly identical for main line and satellites indicating only relatively small modifications of the effective molecular potential induced by the additional π→π* excitation. There are no indications of conjugate shake‐up processes in either molecule.

Broad band dipolar recoupling in the nuclear magnetic resonance of rotating solids
View Description Hide DescriptionThe effects of homonuclear dipole couplings may be reintroduced into magic angle spinning nuclear magnetic resonance(NMR) spectra by judiciously spaced π pulse trains. This recoupling phenomenon occurs over a wide range of chemical shift differences and sample rotation speeds. We present results of magnetization exchange experiments exploiting the broad band recoupling effect, and propose a theoretical description in which pulse‐assisted dipolar recoupling may be understood as a form of compensated rotational resonance.

Laser vaporization generation of the SiB and SiAl radicals for matrix isolation electron spin resonance studies; comparison with theoretical calculations and assignment of their electronic ground states as X ^{4}Σ
View Description Hide DescriptionThe first experimental spectroscopic study of the SiB and SiAl diatomic radicals is reported. Electron spin resonance results indicate that both molecules have X ^{4}Σ ground electronic states, in agreement with earlier theoretical calculations. The SiB and SiAl radicals were generated in neon matrices at 4 K by trapping the products produced from the pulsed laservaporization of their alloys. Electronic structure information for these radicals is especially interesting given the utilization of silicon doped materials in semiconductor applications. The observed nuclear hyperfineinteractions (A tensors) for ^{10}B, ^{11}B, and ^{27}Al in these molecular radicals were compared with the results of ab initio configuration‐interaction theoretical calculations which were conducted as part of this experimental study. The neon matrix magnetic parameters (MHz) for Si ^{11}B are D=800(2), g _{∥}=2.0014(8), g _{⊥}=2.0005(4), A _{⊥}=92.4(5), and A _{∥}=111(2). For Si ^{27}Al the results (MHz) are D=9710(2), g _{∥}=1.9994(8), and g _{⊥}=1.9978(4), ‖A _{⊥}‖=10.3(6), and ‖A _{∥}‖=43.5(8).

Quantum dynamics of overtone relaxation in benzene. V. CH(v=3) dynamics computed with a new ab initio force field
View Description Hide DescriptionLarge‐scale quantum mechanical calculations of the CH(v=3) overtone spectrum and survival probability are reported for 21‐mode planar benzene. A valence coordinate hybrid force field built from the following two sets of ab initioinformation was used: (1) the quartic DZP/SCF force field recently reported by Maslen et al.; (2) a force field computed at the 6‐311G/MP2 level for the overtone excited CH chromophore. Comparisons are made between these results and the overtone spectrum and survival probability computed using the older Pulay et al. 4‐21P/SCF scaled quadratic plus cubic force field. In addition, comparisons are made with experimental spectra from two research groups. These comparisons provide information about the sensitivity of the computed results to alterations in the input force field.

The effect of nonpolar solvents on Rydberg states: van der Waals complexes of azabicyclooctanes
View Description Hide DescriptionThe effect of solvation by nonpolar solvents on the (n,3s) Rydberg states of 1,4‐diazabicyclo[2.2.2]octane (DABCO) and azabicyclo[2.2.2]octane (ABCO) is investigated through mass resolved excitation spectroscopy of their van der Waals complexes. The solute/solvent clusters formed in a supersonic expansion include DABCO and ABCO with Ar, n‐C_{ m }H_{2m+2} (m=1–7), and CF_{4} and C_{2}F_{6}. The resulting spectra are analyzed with the help of empirical potential energy calculations of the cluster binding energies, minimum energy structures, van der Waals modes, and potential barriers between the various cluster minimum energy structures. Good agreement is found between the calculated and experimental results for DABCO and ABCO clustered with argon and methane. The spectra of clusters with all other hydrocarbons can be ascribed to only one major geometry for each cluster stoichiometry, despite the fact that calculations yield many stable geometries for each cluster. This apparent lack of agreement between calculations and experiments can be rationalized based on cluster binding energy, zero point energy, and the potential energy barriers between the cluster minima. The observed blue shift of the cluster 0_{0} ^{0} transition energy as a function of the n‐alkane chain length can be qualitatively modeled by a Lennard‐Jones potential for the solute–solvent interaction for both the ground and excited states. The model reveals a strong repulsive interaction between the Rydberg state electronic distribution and the solvent molecule. This repulsion depends on the distance between the solvent molecule and the solute molecule nitrogen atom.

Intermolecular multiple‐quantum coherences and cross correlations in solution nuclear magnetic resonance
View Description Hide DescriptionIt was recently reported that multiple‐quantum NMR coherences could apparently be observed in water and other concentrated samples, in direct violation of established theory. These results were previously explained in a dressed‐state framework as manifestations of the coupling between the spins and the coil (quantized radiation damping). Here we provide details of previously communicated experimental explorations of these effects [J. Chem. Phys. 96, 1659 (1992)], and we extend these results to multicomponent samples. We observe cross peaks between independent molecules in solution in two‐dimensional experiments, including spectra with multiple‐quantum coherence transfer echoes; we also demonstrate coherence transfer between solvent and (dilute) solute molecules. However, we show that these intermolecular cross peaks are induced by a mechanism which is local in nature, and thus radiation damping (either classical or quantized) cannot provide the bulk of the explanation for their occurrence. Simulations and analytical results show that the dipolar demagnetizing field can account for many of these surprising effects, although a complete picture must be more complex.