Index of content:
Volume 105, Issue 1, 01 July 1996

Orientational correlation functions and polarization selectivity for nonlinear spectroscopy of isotropic media. I. Third order
View Description Hide DescriptionThe contribution of orientational relaxation to the tensor components of the third‐order nonlinear polarization is evaluated for off‐resonance Raman and dipole resonant experiments in the perturbative limit. Orientational correlation functions are calculated within the model of orientational diffusion for all third‐order tensor components relevant to isotropic media. General expressions for polarization geometries that are selective to particular components of the signal, i.e., magic angles, are derived for collinear and crossed‐beam excitation geometries. It is shown that although limited selectivity exists for Raman spectroscopies, no combination of polarizations will give complete selectivity to the isotropic, anisotropic, or nonresonant contributions to the Raman polarizabilitytensor. For resonant spectroscopies, the four‐time correlation function that describes the orientational polarization decay can be written as the product of three two‐time correlation functions. While magic angles for orientational relaxation will exist for experiments that probe population dynamics, such as pump–probe and transient grating spectroscopies, orientational relaxation cannot be removed from coherence experiments such as the photon echo.

Orientational correlation functions and polarization selectivity for nonlinear spectroscopy of isotropic media. II. Fifth order
View Description Hide DescriptionThe influence of orientational relaxation on the fifth‐order nonlinear polarization is evaluated for off‐resonant Raman and dipole resonant experiments in the perturbative limit. The symmetry properties of the χ^{(5)}tensor are discussed, and correlation functions for orientational diffusion are calculated for all fifth‐order tensor elements relevant to isotropic media. The results allow generalization of the effect of orientational motion on the nonlinear experiment of arbitrary order. The general polarization dependence of the fifth‐order experiments are obtained and used to address the selectivity of certain polarization geometries to orientational dynamics. It is shown that for χ^{(5)}Raman spectroscopies, no combination of polarizations will give complete selectivity to the isotropic, anisotropic, or nonresonant contributions to the Raman polarizabilitytensor. Similar restriction of selectivity exists for resonant experiments. Polarization conditions are suggested to facilitate the comparison of third‐ and fifth‐order spectroscopies.

Observation of the lowest ^{1}Δ_{ u } Rydberg state of acetylene by multiphoton ionization spectroscopy
View Description Hide DescriptionThe ^{1}Δ_{ u }, 3dπ component of the lowest ungerade 3d+4sRydberg supercomplex of acetylene has been observed by (3+1) photonionization spectroscopy of C_{2}H_{2} and C_{2}D_{2}. In both isotopic species the vibrationless level of this new electronic state is sufficiently long lived to support rotational structure. From the observed isotopic shift and from the rotational and vibrational parameters determined in the present analyses, this state could be unambiguously identified as the lowest Rydberg state of ^{1}Δ_{ u } symmetry, belonging to the 3d complex of acetylene. The weak intensity of this three‐photon ^{1}Δ_{ u }–^{1}Σ^{+} _{ g } electronic transition is discussed in comparison with the other Rydberg transitions within the same supercomplex. Excited vibronic bands in the same energy region allowed to determine the ν_{1} and ν_{2} frequencies for some components of this Rydberg supercomplex. The absence of the nearby H̃ ^{1}Π_{ u }, 3dδ Rydberg state in the MPI spectra is discussed in terms of predissociation.

Quantum analysis of absolute collision‐induced scattering spectra from bound, metastable and free Ar diatoms
View Description Hide DescriptionMotivated by recent experimental measurements on the low‐frequency binary (Ar)_{2} depolarized spectrum, a fully quantum frequency‐resolved analysis of spectral intensities from bound, metastable and free argon diatoms is performed in collision‐induced light scattering. The methodology is based on an analytical discrete variable representation (DVR) allowing the reliable and systematic computation of all bound and resonance state energies and wave functions as well as of the discretized low‐energy continuum associated to any rotational level.

Magnetic field induced alignment–orientation conversion: Nonlinear energy shift and predissociation in Te_{2} B1_{ u } state
View Description Hide DescriptionThe paper analyzes magnetic field induced alignment–orientation conversion (AOC) phenomenon caused by simultaneous effect of quadratic terms in Zeeman energy shift and magnetic predissociation (PD), producing asymmetry either in energy splitting ω_{ MM }±1≠ω_{−M∓1−M or in relaxation of coherence Γ MM ±1}≠Γ_{−M }∓1−M between coherently excited M, M±1 magnetic sublevels. The AOC is registered via the appearance of circular polarization (C) of fluorescence under linearly polarized excitation. The unified perturbation treatment of a molecule in external magnetic fieldB is presented, accounting for magnetic and intramolecular perturbations via interaction with bonded or continuum states, considering Hund’s (c)‐case coupling and dividing the intramolecular perturbation operator into homogeneous (ΔΩ=0) and heterogeneous (ΔΩ=±1) parts. Explicit expressions up to B ^{2} terms are given for energy shift and PD rate, adapted to 1_{ u } state in conditions relevant to the B ^{3}Σ^{−} _{ u } complex of Te_{2} molecule. Numeric simulation revealed that nonlinear magnetic energy shift and heterogeneous magnetic PD produce dispersion type fluorescence circularity signals C(B) of different sign. Fitting of experimental data on B1^{−} _{ u }, v(J)=2(96) state of ^{130}Te_{2} molecule allowed to determine the electronic matrix element of paramagnetic Hamiltonian (Ω=0Ĥ _{pm}Ω=1)≡G _{±}=2.7, as well as the natural C _{ v } ^{het}=±6 s^{−1/2} and the magnetic α_{ v } ^{het}=∓9×10^{3} s^{−1/2} T^{−1} rate constants of heterogeneous PD, supposing that the B1^{−} _{ u } state PD takes place through 0^{−} _{ u } state continuum. As a result, magnetic AOC represents a sensitive method to investigate molecular structure and intramolecular interaction between both bonded and continuum states. Additionally, it has been shown that the magnetic PD effect leads to strong amplification of nonzero field level crossing signals caused by B ^{2} terms in Zeeman energy shift.

Excited‐state absorption spectra of V ^{2+}‐doped fluoroperovskites. An ab initio model potential embedded‐cluster study
View Description Hide DescriptionIn this paper we present an ab initio model potential embedded‐cluster study of the electronic structure of the local excited states of V ^{2+}‐doped KMgF_{3}, KZnF_{3}, and CsCaF_{3} fluoroperovskites, which are more directly involved in their potential laser activity: the ^{4} T _{2g }, ^{4} T ^{ a } _{1g }, and ^{4} T ^{ b } _{1g } states of the (V F_{6})^{4−} embedded‐cluster. The ab initio model potential embedded‐cluster model used allows for the consideration of intracluster electron correlation and Jahn–Teller coupling in the excited states, as well as of lattice effects which include quantum mechanical interactions resulting from a relaxed, dipole polarized crystal lattice. The embedding potentials enable the geometry optimization of the embedded‐cluster electronic ground‐state but also of the excited states; as a consequence, the ab initio calculation of the vertical ground‐state absorption, excited‐state absorption, and emission spectra is possible and it is done in this work, without resorting to the use of experimental structural parameters of the local defect, which, in any case, are not available for the ground state and not attainable for the excited states. The agreement of the calculated ground‐state absorption, excited‐state absorption, and emission transition energies with the available experimental data is satisfactory and systematic. Our results allow for the discussion of (a) the competition between the infrared ^{4} T _{2g }→^{4} T ^{ a } _{1g } excited‐state absorption and the ^{4} T _{2g }→^{4} A _{2g } spontaneous emission, (b) the overlap between the excited‐state absorption bands and the pumping bands, and (c) the ^{4} A _{2g }→^{4} T _{2g } reabsorption, for all three V ^{2+}‐doped fluoroperovskites, as well as their host dependency. The overall conclusion is that the laser efficiency is expected to deteriorate in the investigated series, going from KMgF_{3}:V ^{2+} to CsCaF_{3}:V ^{2+}.

A (1+1′)+1 multiphoton ionization study of CS_{2} in the 68 500–73 000 cm^{−1} energy region. The 3d and 5s Rydberg states
View Description Hide DescriptionThe two color (1+1′)+1 resonance enhanced multiphoton ionization spectrum of CS_{2} has been recorded in the 68 500–73 000 cm^{−1}excitation energy range. Strong bands were recorded in the 68 800–70 000 cm^{−1} region and the upper states assigned to 3d and 5s gerade Rydberg states with quantum defects of 0.0 and 2.0, respectively. The two color spectra were recorded in both parallel and crossed polarization configurations to assist in state symmetry assignments. Some weaker features in the 70 500–71 500 cm^{−1} region are most likely associated with vibronically induced transitions to a 5pRydberg state.

Calculation of the Herman–Wallis effect in Π–Σ vibrational overtone transitions in a linear molecule: Comparison with HCN experimental results
View Description Hide DescriptionThe high sensitivity of cavity ring‐down spectroscopy has allowed us to observe a few perpendicular vibrational overtone transitions of HCN in the visible. These transitions display a sizable Herman–Wallis effect, that is an asymmetry in the relative intensities of the R and P branch lines. We have developed a theory for the first‐order Herman–Wallis effect based upon using variational vibrational wave functions but treating the vibration–rotation interaction by first‐order perturbation theory. In the specific case of perpendicular transitions, the first‐order effect is dominated by Coriolis mixing of Σ and Π overtone states. We used the empirical energy surface by Carter, Mills, and Handy [J. Chem. Phys. 99, 4379 (1993)] restricted to the stretching degrees of freedom. Bending was included by multiplication of these stretching wave functions by harmonic wave functions of the bend. Vibrational transition moments were calculated using a polynomial surface fit to ab initio CCSD(T) dipole moment points by Botschwina et al. [Chem. Phys. 190, 345 (1995) and private communication]. We expected that this treatment would be accurate but the calculated Herman–Wallis effect is about one order of magnitude too large. To gain further insight into the poor agreement between theory and experiment, we have calculated the sensitivity of the Herman–Wallis coefficient and of the transition moment to the dipole and energy surface parameters. From this, it appears that the dipole surface, while producing accurate band intensities, could at the same time be inadequate to account for the Herman–Wallis effect. A similar possibility stands for the energy surface, which however is highly constrained by the requirement to fit the observed band origins.

Line‐mixing in the 106←000 overtone transition of HCN
View Description Hide DescriptionBy using cavity ring‐down spectroscopy (CRDS), we have obtained visible overtone absorption spectra of HCN which display a large collisional line‐mixing effect in the proximity of the R branch band heads, for J∼18. We consider in detail the 106←000 (1=CN, 0=bend, 6=CH) parallel transition. The R branch profile was modeled using the modified‐exponential‐gap (MEG) and energy‐corrected‐sudden approximation (ECS) population transfer rate laws. We used the rates previously determined by Pine and Looney (PL) by fitting the self broadening coefficients measured for the Q branches of Π–Σ infrared perpendicular stretch–bend combination bands of HCN [J. Chem. Phys. 96, 1704 (1992)]. Contrary to what is found by these authors, in the present case the MEG law reproduces the R branch line‐mixing satisfactorily, while the ECS model fails. This reflects an increasing propensity at higher J for collisional transitions with smaller ΔJ. Using the MEG law, we found we need to include, as had PL in their fits to the infrared Q branches, an empirical dephasing scale factor F∼0.6 for the coherence transfer rates to obtain a satisfactory simulation of the R band head. PL suggested that dephasing in the Q branch spectra are due to cross relaxation across l‐type doublet levels of the Π state, but no such mechanism would be available in the present case. However, we have found that by using a 50/50 linear combination of the ECS and MEG rate laws, it is possible to fit our data even with F=1, which would imply no dephasing of coherence. We take this as a demonstration that the dephasing factor F cannot be reliably extracted from line‐mixing studies alone but instead requires some independent source of information on the relative value for state to state inelastic collision rates.

The rovibrational spectrum of the ArCO complex calculated from a semiempirically extrapolated coupled pair functional potential energy surface
View Description Hide DescriptionThe rovibrational spectrum of the ArCO van der Waals complex has been calculated using a recently published ab initiopotential energy surface determined by the coupled pair functional approach. Comparison with known experimental values for some of the transitions shows that the anisotropy of this surface comes out reasonably well, although its well depth of 72 cm^{−1} is too small. Based on a comparison of coupled pair functional interaction energies for Ne_{2}, NeAr, and Ar_{2} with empirical potential energy curves an extrapolation scheme for the differential correlation energy is suggested. This semiempirical extrapolation scheme, with a slight modification to account for anisotropy, is also applied to the coupled pair functional interaction energies for ArCO, resulting in a surface which is characterized by a well depth of 109 cm^{−1} at a T‐shaped geometry and a barrier of 20 cm^{−1} for rotation of Ar around the oxygen end of CO and of 26 cm^{−1} for rotation around the carbon end. The rovibrational spectrum calculated from this potential is in very good agreement with the known experimental data, so that for the first time a realistic level scheme for the ArCO complex can be presented. Couplings between rotational levels of different van der Waals modes play an important role and are analysed in some detail. The intensities of infrared transitions have also been calculated in order to help in the experimental determination of the predicted new van der Waals modes.

Electron attachment to ClONO_{2} at 300 K
View Description Hide DescriptionA flowing–afterglow Langmuir probe apparatus with mass spectralanalysis has been used to measure the rate constant for electron attachment to ClONO_{2} at 300 K. Electron attachment is efficient with a rate constant of 1.1 (±50%)×10^{−7} cm^{3} s^{−1} and proceeds principally through dissociative channels to produce the major product ions NO^{−} _{2} (∼50%), NO^{−} _{3} (∼30%), and ClO^{−} (∼20%). The parent ion ClONO^{−} _{2} and Cl^{−} are also observed in the mass spectra but are at most minor products in the attachment process, ≤2% and ≤6%, respectively. A description of the secondary ion–molecule chemistry that takes place following electron attachment is given.

Ionization probabilities of A ^{2}Σ^{+}(v′=0,1,2) and B ^{2}Π(v′=0,2) states of NO
View Description Hide DescriptionIonization probabilities of NO molecules electronically excited in the A ^{2}Σ^{+} and B ^{2}Π states have been determined by (1+1) resonance‐enhanced, two‐photon ionization. Various vibrational levels within these states have been excited prior to ionization. Measurements of the unsaturated ionization signal yields accurate values for the relative detection probabilities of NO of 1:(0.70±0.07): (0.67±0.11) for excitation via the γ(0−0), γ(1−1), and γ(2−2) bands, respectively, and (3.7±0.36)×10^{−7} and (5.8±0.65)×10^{−4} for ionization through β(0−0) and β(2−1) bands, respectively. Applying published data for the γ‐ and β‐band transition probabilities allows the deduction of the ionization cross section of A ^{2}Σ^{+} and B ^{2}Π vibrational states. The respective ionization cross sections are (7.0±0.9)×10^{−19} cm^{2}, (8.5±0.8)×10^{−19} cm^{2}, (6.0±1.0)×10^{−19} cm^{2} for A ^{2}Σ^{+}(v′=0, 1, and 2) and (5.0±0.5)×10^{−21} cm^{2} and (1.7±0.2)×10^{−20} cm^{2} for B ^{2}Π(v′=0 and 2). These values are based on the experimentally determined cross section for A ^{2}Σ^{+}(v′=0). Using a larger theoretical cross section for this state the other cross sections scale accordingly, within the experimental uncertainties.

A high level ab initio map and direct statistical treatment of the fragmentation of singlet ketene
View Description Hide DescriptionState‐of‐the‐art ab initio quantum chemical techniques have been employed to ascertain the reaction path and associated energetics for the dissociation of CH_{2}CO into ^{1}CH_{2}+CO and thereby to investigate the kinetics of this dissociation via variational Rice–Ramsperger–Kassel–Marcus (RRKM) theory. The quantum chemical computations focused on the determination of geometric structures, energies, and force fields for four constrained C–C distances (2.2, 2.5, 2.8, and 3.1 Å) spanning the inner transition‐state region. Optimized structures were obtained with the coupled‐cluster singles and doubles method including a perturbative triples term [CCSD(T)], as implemented with a contracted [C/O, H] basis set of [5s4p2d1f, 4s2p1d] quality. The resulting energetics were corrected for basis set incompleteness and higher‐order electron correlation with the aid of second‐order Mo/ller–Plesset perturbation theory (MP2) predictions given by an immense [13s8p6d4f, 8s6p4d] basis combined with 6–31G* Brueckner doubles results augmented with perturbative contributions from both connected triple and quadruple excitations. Quadratic force fields along the reaction path were determined at the CCSD/[5s4p2d, 4s2p] level of theory. Anharmonic effects in the enumeration of accessible states for the transition state were accounted for by a direct statistics approach involving repeated MP2/6‐31G* energy evaluations. Two separate reaction coordinates defined by the C–C bond length or alternatively the center‐of‐mass separation between the ^{1}CH_{2} and CO fragments were explicitly considered in these direct statistical analyses. A spectroscopic quality quartic force field for ketene derived in a companion ab initio study was employed in the evaluation of the anharmonic reactant density of states. The final statistical predictions for the energy dependence of the dissociation rate constant are found to be in quantitative agreement with experiment (i.e., generally within 30%), thereby providing strong evidence for the quantitative validity of variational RRKM theory.

A time‐dependent calculation of the alignment and orientation of the CN fragment of the photodissociation of ICN
View Description Hide DescriptionWe calculate the alignment and orientation of the CN fragment of the photodissociation of ICN using a time‐dependent method and the diabatic potentials and transition moments of Morokuma and co‐workers [J. Chem. Phys. 100, 4894 (1994)]. The time‐dependent Schrödinger equation is solved using a Chebyshev method evaluating sums required to do the matrix‐vector products sequentially. To prevent the wave packet from drifting off the edge of our grid we propagate in successive steps. The ground statewave function, from which the molecule is dissociated, is computed using a three‐dimensional variational method. We calculate alignment and orientation for a J _{ i }=0→J _{ f }=1 transition. We use parity‐adapted angular basis functions. Our calculated alignment and orientation are qualitatively close to experimental results.

Correlation effects and vibronic coupling features in the interaction of H^{−} ions with N_{2} molecules
View Description Hide DescriptionThis paper discusses the calculation of the potential energy surfaces (PES) for the electronic singlet states of C _{2v } and C _{∞v } symmetries of a nitrogen molecule interacting with the atomic hydrogen negative ion. The behavior of such surfaces is analyzed as a function of relative orientations and also of the molecular internal coordinate. The PES’s have been obtained using an ab initio, multireference configuration interaction method (MRDCI) and the effects of correlation forces and of basis set size are analyzed in order to understand the role of electron transfer(ET) processes which are likely to take place during closer collisions between partners and which are suggested to be responsible for the vibronic coupling effects which occur during low‐energy scattering. The general features of the orientational anisotropy of this interaction, of its dependence on the molecular coordinate, and of the strength of its coupling with the impinging negative ion are also analyzed and discussed.

Two‐electron transfer reactions in polar solvents
View Description Hide DescriptionChemical, biological, and electrode based electron transfer(ET) processes involve multielectron events. However, an adequate framework in which to describe these complex reactions does not yet exist. A theory for two‐electron transfer reactions in Debye solvents is developed. The theory is formulated by generalizing Zusman’s model of ETreactions [L. D. Zusman, Chem. Phys. 49, 295 (1980)] to those involving three parabolic wells: One for the doubly reduced donor, one for the singly reduced donor/singly reduced acceptor, and one for the doubly reduced acceptor. The ET processes are described in terms of diffusional motion along a one‐dimensional reaction coordinate with tunneling transitions at the intersection points of the parabolas. Two competing mechanisms of two‐electron transfer arise. One is a process with two sequential single electron steps D ^{=} A→D ^{−} A ^{−}→DA ^{=}. The other involves ET in one concerted two‐electron step (D ^{=} A→DA ^{=}). The general rate expressions for two‐electron transfer are obtained. When the stepwise mechanism dominates, the free energy of activation is predicted to depend upon the driving forces of the two sequential steps but is independent of the overall driving force of the reaction. When concerted two‐electron transfer dominates, the Marcus relation is obtained with a reorganization energy associated with the shift of two electrons. The dynamical solvent effect in two‐electron ET processes is predicted to be unusual. Two distinct regimes exist, each with essentially linear 1/τ_{ L } dependence (with τ_{ L } the solvent longitudinal relaxation time): one for slow solvents and one for fast solvents. A combination of solvent and free energy studies could be used to elucidate the mechanism of multielectron processes in chemical and biological systems.

Symmetry induced kinetic isotope effects in the formation of Ar⋅CO^{+} _{2}
View Description Hide DescriptionSymmetry induced kinetic isotope effects (SIKIE) have been observed mass spectrometrically in the termolecular association reaction of Ar and CO^{+} _{2} to produce Ar⋅CO^{+} _{2} making this the first example of SIKIE in a system where the reactants have no atoms in common. The ^{18}O SIKIE shows a pronounced dependence on whether the CO^{+} _{2} are produced directly by electron ionization or indirectly by charge transfer from Ar^{+}. The results can be understood generally in terms of reaction restrictions based on a symmetry correlation scheme recently developed by one of the authors. This scheme indicates that CO^{+} _{2} ions can have very different clusteringreactivity with Ar depending on whether the ion is in an e (restricted) or an f (allowed) parity label state. Kinetic modeling of the ^{18}O SIKIE indicates that CO^{+} _{2}(e)/CO^{+} _{2}(f )≊60 for CO^{+} _{2} produced by 21 eV electron ionization.

Ab initio finite oligomer method for nonlinear optical properties of conjugated polymers: Nonresonant frequency dispersion in polyacetylene
View Description Hide DescriptionNonlinear optical properties of the linear polyenes C_{4}H_{6} through C_{30}H_{32} are calculated at frequencies below the first resonance using ab initio time‐dependent Hartree–Fock theory. The results are used to determine accurate values for the infinite polymer, polyacetylene, by means of a new extrapolation method. Dispersion coefficients describing the low frequency behavior are obtained for the largest oligomer.

The generation and use of delocalized internal coordinates in geometry optimization
View Description Hide DescriptionFollowing on from the earlier work of Pulay and Fogarasi [J. Chem. Phys. 96, 2856 (1992)] we present an alternative definition of natural internal coordinates. This set of delocalized internal coordinates can be generated for any molecular topology, no matter how complicated, and is fully nonredundant. Using an appropriate Schmidt‐orthogonalization procedure, all standard bond length, bond angle, and dihedral angle constraints can be imposed within our internal coordinate scheme. Combinatorial constraints (in which sums or differences of stretches, bends, and torsions remain constant) can also be imposed. Optimizations on some fairly large systems (50–100 atoms) show that delocalized internal coordinates are far superior to Cartesians even with reliable Hessian information available at the starting geometry.

Multiconfiguration wave functions for quantum Monte Carlo calculations of first‐row diatomic molecules
View Description Hide DescriptionWe use the variance minimization method to determine accurate wave functions for first‐row homonuclear diatomic molecules. The form of the wave function is a product of a sum of determinants and a generalized Jastrow factor. One of the important features of the calculation is that we are including low‐lying determinants corresponding to single and double excitations from the Hartree–Fock configuration within the space of orbitals whose atomic principal quantum numbers do not exceed those occurring in the Hartree–Fock configuration. The idea is that near‐degeneracy correlation is most effectively described by a linear combination of low‐lying determinants whereas dynamic correlation is well described by the generalized Jastrow factor. All the parameters occurring in both the determinantal and the Jastrow parts of the wave function are optimized. The optimized wave functions recover 79%–94% of the correlation energy in variational Monte Carlo and 93%–99% of the correlation energy in diffusion Monte Carlo.