Marcelo P. de Miranda

Quantum dynamical stereochemistry of atom–diatom reactions

We have used density matrix techniques and angular momentum algebra to obtain quantum–mechanical equations describing the dynamical stereochemistry of the atom–diatom reaction A+BC⇌AB+C. The relative motions of reagents and products are specified by four vectors: rotational angular momenta of diatomic molecules and relative velocities of reagents and products. Our equations show how the correlations between the spatial distributions of these four vectors are related to the scattering matrix determined in quantum scattering calculations. We present three different expressions for the four-vectors correlation. One of them is appropriate to the helicity representation of the scattering matrix, while the others are appropriate to the orbital angular momentum representation with either space-fixed or body-fixed reference frames. The formulation adopted allows for a rigorous comparison between theory and experiment. It takes mixed quantum–mechanical states and unobserved quantum-numbers into account, and all ve...

Antisymmetric exchange in two tricopper(II) complexes containing a [Cu3(μ3-OMe)]5+ core

Reaction of CuX2(X-=Cl- or Br-) with 2 molar equivalents of 3[5]-(2,4,6-trimethylphenyl)pyrazole (HpzMes) in MeOH in the presence of NaOH yields [Cu3X(HpzMes)2(micro-pzMes)3(micro3-OMe)]X (X-=Cl- or Br-). Crystal structures of these compounds show almost identical triangles of Cu(II) ions, centred by a triply bridging methoxide ligand and with three edge-bridging pyrazolide groups. The mesityl substituents on the bridging pyrazolide ligands are arranged in HT, HH, TT fashion. chi(M)T for both compounds decreases steadily with decreasing temperature, reaching 0.40 cm(3) mol(-1) K at 70 K before decreasing further below 40 K. This low temperature behaviour could not be interpreted using conventional superexchange Hamiltonians, but was reproduced by an alternative model that incorporated an additional antisymmetric exchange term. This interpretation was confirmed by the Q-band EPR spectra of the two compounds. NMR experiments show that the structures of these compounds are not retained in solution, in contrast to other closely related tricopper compounds. These are the first examples of triangular Cu(II) compounds bearing a [Cu3micro3-OR)]5+(R is not equal to H) core motif, and the first triangular compounds showing antisymmetric exchange to have been analysed by both susceptibility and EPR measurements.

Spatial distributions of angular momenta in quantum and quasiclassical stereodynamics

We have recently reported a derivation of the relationship between the quantum and classical descriptions of angular momentum polarization [M. P. de Miranda and F. Javier Aoiz, Phys. Rev. Lett. 93, 083201 (2004)]. This paper presents a detailed account of the derivation outlined in that paper, and discusses the implications of the new results. These include (i) a new expression of the role of the uncertainty principle in the broadening of angular momentum distributions, (ii) the attribution of azimuthal fluctuations of angular momentum distributions to spatial quantum beats, (iii) the definition of a new Fourier transform of the density matrix, distinct from those suggested in the past, that provides an alternative view of how the quantum description of angular momentum polarization approaches the classical one in the correspondence principle limit, (iv) a prescription for the determination of a quasiclassical angular momentum distribution function that does not suffer from problems encountered with its purely classical counterpart, and (v) a description of how angular momentum distributions commonly visualized with recourse to the classical vector model can be depicted with exact and well-defined quantum mechanics.

Two Heptacopper(II) Disk Complexes with a [Cu7(μ3-OH)4(μ-OR)2]8+ Core

The reaction of CuX(2) (X(-) ≠ F(-)) salts with 1 equiv of 3-pyridyl-5-tert-butylpyrazole (HL) in basic methanol yields blue solids, from which disk complexes of the type [Cu(7)(μ(3)-OH)(4)(μ-OR)(2)(μ-L)(6)](2+) and/or the cubane [Cu(4)(μ(3)-OH)(4)(HL)(4)](4+) can be isolated by recrystallization under the appropriate conditions. Two of the disk complexes have been prepared in crystalline form: [Cu(7)(μ(3)-OH)(4)(μ-OCH(2)CF(3))(2)(μ-L)(6)][BF(4)](2) (2) and [Cu(7)(μ(3)-OH)(4)(μ-OCH(3))(2)(μ-L)(6)]Cl(2)·xCH(2)Cl(2) (3·xCH(2)Cl(2)). The molecular structures of both compounds as solvated crystals can be described as [Cu⊂Cu(6)(μ-OH)(4)(μ-OR)(2)(μ-L)(6)](2+) (R = CH(2)CF(3) or CH(3)) adducts. The [Cu(6)(μ-OH)(4)(μ-OR)(2)(μ-L)(6)] ring is constructed of six square-pyramidal Cu ions, linked by 1,2-pyrazolido bridges from the L(-) ligands and by basal, apical-bridging hydroxy or alkoxy groups, while the central Cu ion is bound to the four metallamacrocyclic hydroxy donors in a near-regular square-planar geometry. The L(-) ligands project above and below the metal ion core, forming two bowl-shaped cavities that are fully (R = CH(2)CF(3)) or partially (R = CH(3)) occupied by the alkoxy R substituents. Variable-temperature magnetic susceptibility measurements on 2 demonstrated antiferromagnetic interactions between the Cu ions, yielding a spin-frustrated S = (1)/(2) magnetic ground state that is fully populated below around 15 K. Electrospray ionization mass spectrometry, UV/vis/near-IR, and electron paramagnetic resonance measurements imply that the heptacopper(II) disk motif is robust in organic solvents.

Photodissociation of NO2 in the (2) B22 state: The O(D12) dissociation channel

Direct current slice and crush velocity map imaging has been used to probe the photodissociation dynamics of nitrogen dioxide above the second dissociation limit. The paper is a companion to a previous publication [J. Chem. Phys. 128, 164318 (2008)] in which we reported results for the O((3)P(J)) + NO((2)Pi(Omega)) adiabatic product channel. Here we examine the O((1)D(2)) + NO((2)Pi(Omega)) diabatic product channel at similar excitation energies. Using one- and two-color imaging experiments to observe the velocity distributions of state selected NO fragments and O atoms, respectively, we are able to build a detailed picture of the dissociation dynamics. We show that by combining the information obtained from velocity map imaging studies with mass-resolved resonantly enhanced multiphoton ionization spectroscopy it is possible to interpret and fully assign the NO images. By recording two-color images of the O((1)D(2)) photofragments with different polarization combinations of the pump and probe laser fields we also measure the orbital angular momentum alignment in the atomic fragment. We find that the entire O((1)D(2)) photofragment distribution is similarly aligned with most of the population in the M(J) = +/-1 magnetic sublevels. The similarity of the fragment polarizations is interpreted as a signature of all of the O((1)D(2)) atoms being formed via the same avoided crossing. At the photolysis energy of 5.479 52 eV we find that the NO fragments are preferentially formed in v = 1 and that the vibrationally excited fragments exhibit a bimodal rotational distribution. This is in contrast to the unimodal rotational profile of the NO fragments in v = 0. We discuss these observations in terms of the calculated topology of the adiabatic potential energy surfaces and attribute the vibrational inversion and rotational bimodality of the v = 1 fragments to the symmetric stretch and bending motion generated on excitation to the (2) (2)B(2) state.

Quantum stereodynamics of four-atom reactions: theory and application to H2+OH↔H2O+H

This article presents a theoretical quantum method for the description of the stereo- dynamics of four-atom reactions of the type AB(vAB, jAB)+CD(vCD, jCD)↔ABC(v1′, v2′, v3′, j′)+D. The method is based on density matrix techniques and angular momentum algebra, and requires knowledge of the scattering matrix. Reagents and products are treated on an equal footing, and the reaction stereodynamics can be analysed either in the rotational polarisation or in the molecular polarisation representation. The formalism is applied to the H2(0, jH2)+OH(0, jOH)↔H2O(0, 0, 0, 0)+H reaction at zero total angular momentum and reveals state-specific correlations between the polarisations of the diatomic molecules, their approach or recoil directions, and the reaction probability.

Stereodynamics of the F + HD(v = 0, j = 1) reaction: direct vs. resonant mechanisms

The stereodynamics and mechanism of the F + HD(v = 0, j = 1) → HF (DF) + D (H) reactions have been thoroughly analysed at collision energies in the 0-160 meV range. Specifically, this study is focused on (i) the comparison between the stereodynamics of the collisions leading to HF and DF formation, and (ii) the stereodynamical fingerprints of the resonance that occurs at low collision energies in the HF channel and whose manifestation in the total cross section is greatly diminished for initial j > 0. While previous studies were limited to the analysis of integral cross sections (ICS), differential cross sections (DCS) and reaction probabilities, in the present work we have included the analysis of vectorial quantities such as the direction of the initial rotational angular momentum and internuclear axis, and their effect on reactivity. In particular, polarisation parameters (PP) and polarisation dependent differential cross sections (PDDCS), quantities that describe how the intrinsic HD rotational angular momentum and molecular axis polarisations contribute to reaction, are calculated and examined. The evolution of the PPs with the collision energy differs markedly between the two reaction channels. For the DF channel, the PP values are small and change very little in the energy range in which DF formation is appreciable. In contrast, rapid fluctuations in the magnitude and sign of the PPs are observed in the HF channel at low collision energies in and around the resonance. As the collision energy increases, direct (non-resonant) scattering prevails, and the various quantities are reasonably well accounted for by the QCT calculations, as in the case of the DF channel. The intrinsic directional information has been used to access the extent of control that can be achieved through polarisation of the HD molecule prior to collision. It was found that the same extrinsic preparation leads to very different outcomes on the HF channel DCS when the collision energy is close to the resonance. It is also shown that polarisation of the HD internuclear axis along the initial relative velocity enhances the effect of the resonance and allows its clear identification. Finally, the effect of different extrinsic preparations on the angle-velocity DCS is found to be strong, thus allowing considerable control of product angular distributions.

Single-parameter quantification of the sensitivity of a molecular collision to molecular polarization.

This article introduces the concept of intrinsic entropy, S, of a molecular collision. Defined in rigorously quantum mechanical terms as the von Neumann entropy of the intrinsic density matrices of reagents and products, the intrinsic entropy is a dimensionless number in the 0 < or = S < or = 1 range. Its limits are associated with situations where the collision cross section is due to a single combination of reagent and product polarizations (S = 0) or where there is absolutely no selectivity with respect to the molecular polarizations (S = 1). The usefulness of the intrinsic entropy as a quantifier of the sensitivity of a molecular collision to molecular polarizations is demonstrated with examples for the benchmark H + D(2) reaction.

The influence of antieigenvalues and antieigenvectors on the correlation between the polarizations of reagents and products of molecular collisions

This article raises and answers a question regarding the extent to which correlation between the angular momentum polarizations of reagents and products of a bimolecular collision is or is not uniform. The question is this: how markedly does product (j′) polarization change when reagent (j) polarization is changed? Using canonical collision mechanisms theory, and the operator-trigonometric concepts of maximal turning angle, antieigenvalue, and antieigenvector, the authors arrive at the following answer: barring complete or nearly complete insensitivity of the collision to steric effects, one should expect a high degree of nonuniformity in two-, three- or four-vector correlations involving j and j′.

A cyclic hexacopper(II) fluoro complex that encapsulates two fluoride anions

The complex [[Cu3(HpztBu)4(mu-pztBu)2(mu-F)2(mu 3-F)]2]F2 (HpztBu = 3[5]-tert-butylpyrazole) has a cyclic, C2v-symmetric hexacopper core. The two non-coordinated F- anions are encapsulated within cavities formed by three HpztBu ligands.