Potential Benefits and Barriers to Integration

The rhetoric surrounding integration of mathematics and science abounds. Professional organizations’ standards and recommendations for reform in mathematics and science education each point out the need to make connections among various disciplines. However, some remain unconvinced, citing a lack of research supporting the assertion that integration improves student achievement. This article examines the current situation, discusses the growing body of related research, and examines the implementation issues related to integrated curriculum projects. The conclusion calls for mathematics and science educators to work collaboratively to address implementation issues surrounding reform of any kind and to explore further the possibilities of integration.     

Photodissociation dynamics of methyl nitrate at 193 nm: energy disposal in methoxy and nitrogen dioxide products

The photodissociation dynamics of methyl nitrate, CH(3)ONO(2), has been investigated at 193 nm by examining the products from the primary dissociation channel, namely CH(3)O and NO(2). The CH(3)O (X (2)E) photoproducts were probed by laser-induced fluorescence (LIF) on the A (2)A(1)-X (2)E transition under both nascent and jet-cooled conditions. The 3 and 3 bands originating from the vibrationless and C-O stretch (nu(3)) levels, respectively, were characterized to obtain the internal energy distribution of the CH(3)O products. Only a small fraction of the CH(3)O products (< or =10%) were produced with one quantum of C-O stretch excitation as determined from the relative intensities of the bands in combination with transition probabilities derived from dispersed fluorescence measurements and/or calculated Franck-Condon factors. The CH(3)O products also had minimal rotational excitation: those produced in the ground vibrational state had a rotational temperature of 238 +/- 7 K, corresponding to less than 1% of the available energy. Products with C-O stretch excitation were found to have a higher rotational temperature, but still a small fraction of the total energy. Combining the CH(3)O internal energy findings with previous photofragment translational energy measurements [X. Yang, P. Felder and J. R. Huber, J. Phys. Chem., 1993, 97, 10903] indicates that most of the available energy is deposited in the NO(2) fragment. This is verified through dispersed fluorescence measurements which show that the NO(2) fragment is produced electronically excited with internal energies extending to the NO + O dissociation limit. Ab initio calculations confirm that the dominant initial excitation is strongly localized on the NO(2) moiety. The calculations are also used to reveal the forces that give rise to internal excitation of the CH(3)O fragment upon electronic excitation.     

Experimental characterization of the weakly anisotropic CN X 2Σ+ + Ne potential from IR-UV double resonance studies of the CN-Ne complex

IR-UV double resonance spectroscopy has been used to characterize hindered internal rotor states (n(K) = 0(0), 1(1), and 1(0)) of the CN-Ne complex in its ground electronic state with various degrees of CN stretch (ν(CN)) excitation. Rotationally resolved infrared overtone spectra of the CN-Ne complex exhibit perturbations arising from Coriolis coupling between the closely spaced hindered rotor states (1(1) and 1(0)) with two quanta of CN stretch (ν(CN) = 2). A deperturbation analysis is used to obtain accurate rotational constants and associated average CN center-of-mass to Ne separation distances as well as the coupling strength. The energetic ordering and spacings of the hindered internal rotor states provide a direct reflection of the weakly anisotropic intermolecular potential between CN X (2)Σ(+) and Ne, with only an 8 cm(-1) barrier to CN internal rotation, from which radially averaged anisotropy parameters (V(10) and V(20)) are extracted that are consistent for ν(CN) = 0-3. Complementary ab initio calculation of the CN X (2)Σ(+) + Ne potential using MRCI+Q extrapolated to the complete one-electron basis set limit is compared with the experimentally derived anisotropy by optimizing the radial potential at each angle. Experiment and theory are in excellent accord, both indicating a bent minimum energy configuration and nearly free rotor behavior. Analogous experimental and theoretical studies of the CN-Ne complex upon electronic excitation to the CN B (2)Σ(+) state indicate a slightly more anisotropic potential with a linear CN-Ne minimum energy configuration. The results from these IR-UV double resonance studies are compared with prior electronic spectroscopy and theoretical studies of the CN-Ne system.     

Infrared action spectroscopy and dissociation dynamics of the HOOO radical

The HOOO radical has long been postulated to be an important intermediate in atmospherically relevant reactions and was recently deemed a significant sink for OH radicals in the tropopause region. In the present experiments, HOOO radicals are generated in a pulsed supersonic expansion by the association of O(2) and photolytically generated OH radicals, and the spectral signature and vibrational predissociation dynamics are investigated via IR action spectroscopy, an IR-UV double resonance technique. Rotationally resolved IR action spectra are obtained for trans-HOOO in the fundamental (nu(OH)) and overtone (2nu(OH)) OH stretching regions at 3569.30 and 6974.18 cm(-1), respectively. The IR spectra exhibit homogeneous line broadening, characteristic of a approximately 26-ps lifetime, which is attributed to intramolecular vibrational redistribution and/or predissociation to OH and O2 products. In addition, an unstructured feature is observed in both the OH fundamental and overtone regions of HOOO, which is likely due to cis-HOOO. The nascent OH X(2)Pi, v = 0 or v = 1, products following vibrational predissociation of HOOO, nu(OH) or 2nu(OH), respectively, have been investigated using saturated laser-induced fluorescence measurements. A distinct preference for population of Pi(A') Lambda-doublets in OH was observed and is indicative of a planar dissociation of trans-HOOO in which the symmetry of the bonding orbital is maintained.     

Communication: A new spectroscopic window on hydroxyl radicals using UV + VUV resonant ionization

A 1 + 1' multiphoton ionization (MPI) detection scheme for OH radicals is presented. The spectroscopic approach combines initial excitation on the well-characterized A(2)Σ(+)-X(2)Π band system with vacuum ultraviolet (VUV) ionization via autoionizing Rydberg states that converge on the OH(+) A(3)Π ion state. Jet-cooled MPI spectra on the (1,0) and (2,0) bands show anomalous rotational line intensities, while initial excitation on the (0,0) band does not lead to detectable OH(+) ions. The onset of ionization with the (1,0) band is attributed to an energetic threshold; the combined UV + VUV photon energies are above the first member of the autoionizing (A(3)Π)nd Rydberg series. Comparison of the OH 1 + 1' MPI signal with that from single photon VUV ionization of NO indicates that the cross section for photoionization from OH A(2)Σ(+), v' = 1 is on the order of 10(-17) cm(2).     

Infrared overtone spectroscopy and vibrational analysis of a Fermi resonance in nitric acid: Experiment and theory

High resolution infrared spectra of nitric acid have been recorded in the first OH overtone region under jet-cooled conditions using a sequential IR-UV excitation method. Vibrational bands observed at 6933.39(3), 6938.75(4), and 6951.985(3) cm(-1) (origins) with relative intensities of 0.42(1), 0.38(1), and 0.20(1) are attributed to strongly mixed states involved in a Fermi resonance. A vibrational deperturbation analysis suggests that the optically bright OH overtone stretch (2nu1) at 6939.2(1) cm(-1) is coupled directly to the nu1 + 2nu2 state at 6946.4(1) cm(-1) and indirectly to the 3nu2 + nu3 + nu7 state at 6938.5(1) cm(-1). Both the identity of the zero-order states and the indirect coupling scheme are deduced from complementary CCSD(T) calculations in conjunction with second-order vibrational perturbation theory. The deperturbation analysis also yields the experimental coupling between 2nu1 and nu1 + 2nu2 of -6.9(1) cm(-1), and that between the two dark states of +5.0(1) cm(-1). The calculated vibrational energies and couplings are in near quantitative agreement with experimentally derived values except for a predicted twofold stronger coupling of 2nu1 to nu1 + 2nu2. Weaker coupling of the strongly mixed states to a dense background of vibrational states via intramolecular vibrational energy redistribution is evident from the experimental linewidths of 0.08 and 0.25 cm(-1) for the higher energy and two overlapping lower energy bands, respectively. A comprehensive rotational analysis of the higher energy band yields spectroscopic parameters and the direction of the OH overtone transition dipole moment.     

Fluorescence-dip infrared spectroscopy and predissociation dynamics of OH A 2Sigma+ (v = 4) radicals

Fluorescence-dip infrared spectroscopy, an UV-IR double-resonance technique, is employed to characterize the line positions, linewidths, and corresponding lifetimes of highly predissociative rovibrational levels of the excited A (2)Sigma(+) electronic state of the OH radical. Various lines of the 4 <--2 overtone transition in the excited A (2)Sigma(+) state are observed, from which the rotational, centrifugal distortion, and spin-rotation constants for the A (2)Sigma(+) (v = 4) state are determined, along with the vibrational frequency for the overtone transition. Homogeneous linewidths of 0.23-0.31 cm(-1) full width at half maximum are extracted from the line profiles, demonstrating that the N = 0 to 7 rotational levels of the OH A (2)Sigma(+) (v = 4) state undergo rapid predissociation with lifetimes of < or =23 ps. The experimental linewidths are in near quantitative agreement with first-principles theoretical predictions.     

Experimental characterization of the CN X 2Σ+ + Ar and H2 potentials via infrared-ultraviolet double resonance spectroscopy

The hindered internal rotor states (n(K) = 0(0), 1(1), and 1(0)) of the CN-Ar complex with two quanta of CN stretch (v(CN) = 2), along with its ground state (v(CN) = 0), have been characterized by IR-UV double resonance and UV spectroscopy. Analysis of rotationally structured bands enable n(K) assignments and reveal perturbations due to Coriolis coupling between two closely spaced hindered rotor states, n(K) = 1(1) and 1(0). A deperturbation analysis is carried out to derive accurate rotational constants and their associated CN center-of-mass to Ar bond lengths as well as the magnitude of the coupling. The energetic ordering and spacings of the CN-Ar hindered rotor states provide a direct experimental probe of the angular dependence of the CN X (2)Σ(+) + Ar potential and permit radially averaged anisotropy parameters (V(10) = 5.2 cm(-1) and V(20) = 3.2 cm(-1)) to be determined. This analysis indicates a relatively flat potential about a linear N≡C-Ar configuration with a barrier to CN internal rotation of only ~12 cm(-1). The angular potentials determined from experiment and ab initio theory are in good accord, although theory predicts a higher barrier to CN internal rotation. A similar approach yields the infrared spectrum of H(2)-CN in the CN overtone region, which exhibits a rotationally resolved Σ ← Σ parallel band that is consistent with theoretical predictions for ortho-H(2)-CN.     

Reactive quenching of OH A (2)Σ(+) by O(2) and CO: Experimental and nonadiabatic theoretical studies of H- and O-atom product channels

The outcomes following collisional quenching of electronically excited OH A (2)Σ(+) by O(2) and CO are examined in a combined experimental and theoretical study. The atomic products from reactive quenching are probed using two-photon laser-induced fluorescence to obtain H-atom Doppler profiles, O ((3)P(J)) atom fine structure distributions, and the relative yields of these products with H(2), O(2), and CO collision partners. The corresponding H-atom translational energy distributions are extracted for the H + O(3) and H + CO(2) product channels, in the latter case revealing that most of the available energy is funneled into internal excitation of CO(2). The experimental product branching ratios show that the O-atom producing pathways are the dominant outcomes of quenching: the OH A (2)Σ(+) + O(2) → O + HO(2) channel accounts for 48(3)% of products and the OH A (2)Σ(+) + CO → O + HCO channel yields 76(5)% of products. In addition, quenching of OH A (2)Σ(+) by O(2) generates H + O(3) products [12(3)%] and returns OH to its ground X (2)Π electronic state [40(1)%; L. P. Dempsey, T. D. Sechler, C. Murray, and M. I. Lester, J. Phys. Chem. A 113, 6851 (2009)]. Quenching of OH A (2)Σ(+) by CO also yields H + CO(2) reaction products [26(5)%]; however, OH X (2)Π (v(") = 0,1) products from nonreactive quenching are not observed. Theoretical studies characterize the properties of energy minimized conical intersections in four regions of strong nonadiabatic coupling accessible from the OH A (2)Σ(+) + CO asymptote. Three of these regions have the O-side of OH pointing toward CO, which lead to atomic H and vibrationally excited CO(2) products and∕or nonreactive quenching. In the fourth region, energy minimized points are located on a seam of conical intersection from the OH A (2)Σ(+) + CO asymptote to an energy minimized crossing with an extended OH bond length and the H-side of OH pointing toward CO in a bent configuration. This region, exoergic with respect to the reaction asymptote, is likely to be the origin of the dominant O + HCO product channel.