Practically Impractical: Contemplative Practices in Science

Contemplation has been described as a “long, loving look at the real,” a characterization that could equally well apply to science. In this paper, I frame a contemplative approach to the teaching and practice of science which draws strongly on the Christian monastic traditions. Students, in particular, struggle with the ever increasing information density in their course work which can cloud their understanding of the relationship of their work to broader contexts. I suggest that the monastic counsels of intentional simplicity, deep listening and constancy can provide a foundation for the design of science courses which help students engage more deeply with their work in the midst of a deluge of information, particularly visual and graphical information. I present four different contemplative practices suited for use in the scientific classroom and research lab: a simple, discreet stilling exercise for focus and attention, a ‘beholding’ approach to exploring visual data and two writing exercises designed for laboratory researchers

Distance Dependence of Nonadiabaticity in the Branching Between C–Br and C–Cl Bond Fission Following 1[n(O),π∗(C=O)] Excitation in Bromopropionyl Chloride

These experiments on bromopropionyl chloride investigate a system in which the barrier to C-Br fission on the lowest 1A\u27\u27 potential energy surface is formed from a weakly avoided electronic configuration crossing, so that nonadiabatic recrossing of the barrier to C-Br fission dramatically reduces the branching to C-Br fission. The results, when compared with earlier branching ratio measurements on bromoacetyl chloride, show that the additional intervening CH2 spacer in bromopropionyl chloride reduces the splitting between the adiabatic potential energy surfaces at the barrier to C-Br fission, further suppressing C-Br fission by over an order of magnitude. The experiment measures the photofragment velocity and angular distributions from the 248 nm photodissociation of Br (CH2)2COCl, determining the branching ratio between the competing primary C-Br and C-Cl fission pathways and detecting a minor C-C bond fission pathway. While the primary C-Cl:C-Br fission branching ratio is 1:2, the distribution of relative kinetic energies impar-ted to the C-Br fission fragments show that essentially no C-Br fission results from promoting the molecule to the lowest 1A\u27\u27 potential energy surface via the 1[n(O),pi*(C-O)] transition; C-Br fission only results from an overlapping electronic transition. The results differ markedly from the predictions of statistical transition state theories which rely on the Born-Oppenheimer approximation. While such models predict that, given comparable preexponential factors, the reaction pathway with the lowest energetic barrier on the 1A\u27\u27 surface, C-Br fission, should dominate, the experimental measurements show C-Cl bond fission dominates by a ratio of C-Cl:C-Br=1.0: \u3c0.05 upon excitation of the 1[n(O),pi*(C=O)] transition. We compare this result to earlier work on bromoacetyl chloride, which evidences a less dramatic reduction in the C-Br fission pathway (C-Cl:C-Br = 1.0:0.4) upon excitation of the same transition. We discuss a model in which increasing the distance between the C-Br and C=O chromophores decreases the electronic configuration interaction matrix elements which mix and split the 1n(O)pi*(C=O) and np(Br)sigma*(C-Br) configurations at the barrier to C-Br bond fission in bromopropionyl chloride. The smaller splitting between the adiabats at the barrier to C-Br fission increases the probability of nonadiabatic recrossing of the barrier, nearly completely suppressing C-Br bond fission in bromopropionyl chloride. Preliminary ah initio calculations of the adiabatic barrier heights and the electronic configuration interaction matrix elements which split the adiabats at the barrier to C-Br and C-Cl fission in both bromopropionyl chloride and bromoacetyl chloride support the interpretation of the experimental results. We end by identifying a class of reactions, those allowed by overall electronic symmetry but Woodward-Hoffmann forbidden, in which nonadiabatic recrossing of the reaction barrier should markedly reduce the rate constant, both for ground state and excited state surfaces

Competing C–Br and C–C Bond Fission Following 1[n(O),π∗(C=O)] Excitation in Bromoacetone: Conformation Dependence of Nonadiabaticity at a Conical Intersection

These experiments investigate the competition between C-C and C-Br bond fission in bromoacetone excited in the (1)[n(O),pi(*)(C=O)] absorption, elucidating the role of molecular conformation in influencing the probability of adiabatically traversing the conical intersection along the C-C fission reaction coordinate. In the first part of the paper, measurement of the photofragment velocity and angular distributions with a crossed laser-molecular beam time-of-flight technique identifies the primary photofragmentation channels at 308 nm. The time-of-flight spectra evidence two dissociation channels, C-Br fission and fission of one of the two C-C bonds, BrH2C-COCH3. The distribution of relative kinetic energies imparted to the C-Br fission and C-C fission fragments show dissociation is not occurring via internal conversion to the ground electronic state and allow us to identify these channels in the closely related systems of bromoacetyl- and bromopropionyl chloride. In the second part of the work we focus on the marked conformation dependence to the branching between C-C fission and C-Br fission. Photofragment angular distribution measurements show that C-Br fission occurs primarily from the minor, anti, conformer, giving a beta of 0.8, so C-C fission must dominate the competition in the gauche conformer. Noting that the dynamics of these two bond fission pathways are expected to be strongly influenced by nonadiabatic recrossing of the reaction barriers, we investigate the possible mechanisms for the conformation dependence of the nonadiabatic recrossing with low-level ab initio electronic structure calculations on the C-Br reaction coordinate and qualitative consideration of the conical intersection along the C-C reaction coordinate. The resulting model proposes that C-C bond fission,cannot compete with C-Br fission in the anti conformer because the dissociation samples regions of the phase space near the conical intersection along the CC fission reaction coordinate, where nonadiabaticity inhibits C-C fission, while from the gauche conformer C-C fission can proceed more adiabatically and dominate C-Br fission. A final experiment confirms that the branching ratio changes with the relative conformer populations in accord with this model

CF3 Rotation in 3-(Trifluoromethyl)phenanthrene. X-ray Diffraction and ab Initio Electronic Structure Calculations

The molecular and crystal structure of 3-(trifluoromethyl)phenanthrene has been determined by X-ray diffraction. The structure of the isolated molecule has been calculated using electronic structure methods at the HF/3-21G, HF/6-31G*, MP2/6-31G* and B3LYP/6-31G* levels. The potential energy surfaces for the rotation of the CF3 group in both the isolated molecule and cluster models for the crystal were computed using electronic structure methods. The barrier height for CF3 rotation in the isolated molecule was calculated to be 0.40 kcal mol-1 at B3LYP/6-311+G**//B3LYP/6-311+G**. The B3LYP/6-31G* calculated CF3 rotational barrier in a 13-molecule cluster based on the X-ray data was found to be 2.6 kcal mol-1. The latter is in excellent agreement with experimental results from the NMR relaxation experiments reported in the companion paper (Beckmann, P. A.; Rosenberg, J.; Nordstrom, K.; Mallory, C. W.; Mallory, F. B. J. Phys. Chem. A 2006, 110, 3947). The computational results on the models for the solid state suggest that the intermolecular interaction between nearest neighbor pairs of CF3 groups in the crystal accounts for roughly 75% of the barrier to rotation in the solid state. This pair is found to undergo cooperative reorientation. We attribute the CF3 reorientational disorder in the crystal as observed by X-ray diffraction to the presence of a pair of minima on the potential energy surface and the effects of librational motion

Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements

The 6‐31G* and 6‐31G** basis sets previously introduced for first‐row atoms have been extended through the second‐row of the periodic table. Equilibrium geometries for one‐heavy‐atom hydrides calculated for the two‐basis sets and using Hartree–Fock wave functions are in good agreement both with each other and with the experimental data. HF/6‐31G* structures, obtained for two‐heavy‐atom hydrides and for a variety of hypervalent second‐row molecules, are also in excellent accord with experimental equilibrium geometries. No large deviations between calculated and experimental single bond lengths have been noted, in contrast to previous work on analogous first‐row compounds, where limiting Hartree–Fock distances were in error by up to a tenth of an angstrom. Equilibrium geometries calculated at the HF/6‐31G level are consistently in better agreement with the experimental data than are those previously obtained using the simple split‐valance 3‐21G basis set for both normal‐ and hypervalent compounds. Normal‐mode vibrational frequencies derived from 6‐31G* level calculations are consistently larger than the corresponding experimental values, typically by 10%–15%; they are of much more uniform quality than those obtained from the 3‐21G basis set. Hydrogenation energies calculated for normal‐ and hypervalent compounds are in moderate accord with experimental data, although in some instances large errors appear. Calculated energies relating to the stabilities of single and multiple bonds are in much better accord with the experimental energy differences

Self‐consistent molecular orbital methods. XXIII. A polarization‐type basis set for second‐row elements

The 6‐31G* and 6‐31G** basis sets previously introduced for first‐row atoms have been extended through the second‐row of the periodic table. Equilibrium geometries for one‐heavy‐atom hydrides calculated for the two‐basis sets and using Hartree–Fock wave functions are in good agreement both with each other and with the experimental data. HF/6‐31G* structures, obtained for two‐heavy‐atom hydrides and for a variety of hypervalent second‐row molecules, are also in excellent accord with experimental equilibrium geometries. No large deviations between calculated and experimental single bond lengths have been noted, in contrast to previous work on analogous first‐row compounds, where limiting Hartree–Fock distances were in error by up to a tenth of an angstrom. Equilibrium geometries calculated at the HF/6‐31G level are consistently in better agreement with the experimental data than are those previously obtained using the simple split‐valance 3‐21G basis set for both normal‐ and hypervalent compounds. Normal‐mode vibrational frequencies derived from 6‐31G* level calculations are consistently larger than the corresponding experimental values, typically by 10%–15%; they are of much more uniform quality than those obtained from the 3‐21G basis set. Hydrogenation energies calculated for normal‐ and hypervalent compounds are in moderate accord with experimental data, although in some instances large errors appear. Calculated energies relating to the stabilities of single and multiple bonds are in much better accord with the experimental energy differences