Parent-molecule rotational depolarization of photofragment angular momentum distributions: diatomic and polyatomic molecules

We extend the A(q)(k) polarization-parameter model, which describes product angular momentum polarization from one photon photodissociation of polyatomic molecules in the molecular frame [J. Chem. Phys., 2010, 132, 224310], to the case of rotating parent molecules. The depolarization of the A(q)(k) is described by a set of rotational depolarization factors that depend on the angle of rotation of the molecular axis γ. We evaluate these rotational depolarization factors for the case of dissociating diatomic molecules and demonstrate that they are in complete agreement with the results of Kuznetsov and Vasyutinskii [J. Chem. Phys., 2005, 123, 034307] obtained from a fully quantum mechanical approach of the same problem, showing the effective equivalence of the two approaches. We further evaluate the set of rotational depolarization factors for the case of dissociating polyatomic molecules that have three (near) equal moments of inertia, thus extending these calculations to polyatomic systems. This ideal case yields insights for the dissociation of polyatomic molecules of various symmetries when we compare the long lifetime limit with the results obtained for the diatomic case. In particular, in the long lifetime limit the depolarization factors of the A(0)(k) (odd k), Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) for diatomic molecules vanish; in contrast, for polyatomic molecules the depolarization factors for the A(0)(k) (odd k) reduce to a value of 1/3, whereas for the Re(A(1)(k)) (even k) and Im(A(1)(k)) (odd k) they reduce to 1/5.     

An animated visualization of orbital angular momentum and spin‐orbit coupling

This paper presents an approach toward visualizing a complex orbital based on animation using a time‐dependent phase factor. This makes orbital angular momentum clearly visible, in a way that reflects the nature of the orbital angular momentum wavefunction. Visualization of this quantity is also useful for examining the effects of spin‐orbit coupling (SOC), in which higher orbital angular momentum states are admixed into the orbital; in this case, however, scaling of one phase‐component is needed. The phase orientation of a complex orbital, which is generally not guaranteed by the SCF procedure, must be considered when doing this. The method of visualization presented here may prove useful when analyzing properties where SOC is important, such as magnetic resonance parameters. Animated visualizations are performed, and compared with the method of phase‐colored isosurfaces, first for a model p‐orbital to explain the idea, and then for the singly‐occupied molecular orbitals of two small doublet radicals.     

Influence of the coriolis coupling on angular correlation functions of rotating molecules

In this paper, the influence of the Coriolis coupling of first order on angular correlation functions of symmetric-top and spherical-top molecules in gases and liquids is studied. The theories of St. Pierre and Steele, and of McClung on molecular reorientation processes are revised to include Coriolis coupling. The theoretical angular correlation functions show drastic changes for a varying Coriolis coupling constant ξ. They are compared with experimental data obtained by Fourier transforming vibration-rotation spectra of chloroform, carbonyls and methanes, in the gaseous and the liquid state. The effect of Coriolis coupling on the angular correlation functions of linear molecules is also provided by the above theory. As an example the experimental correlation function of the perpendicular transition of OCS in a dense medium is presented     

Construction of orbital angular momentum eigenfunctions for many-particle systems by harmonic projection

Formulas are derived which allow the direct construction of total orbital angular momentum eigenfunctions for many-particle systems without the use of Clebsch–Gordan coefficients. One of the equations is closely analogous to Dirac' identity for the total spin operator. This equation describes the action of L² on a function of the particle coordinates in terms of a class operator of the symmetric group and a "contraction operator." A general projection operator for constructing symmetric eigenfunctions of L² is presented.     

Analytical solutions of Schr?dinger equation for the diatomic molecular potentials with any angular momentum

Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also considered. Algebraic method is used in the calculations.     

Formaldehyde photodissociation: dependence on total angular momentum and rotational alignment of the CO product

Quasiclassical trajectory calculations are reported to investigate the effects of rotational excitation of formaldehyde on the branching ratios of the fragmentation products, H2+CO and H+HCO. The results of tens of thousands of trajectories show that increased rotational excitation causes suppression of the radical channel and enhancement of the molecular channel. Decomposing the molecular channel into "direct" and "roaming" channels shows that increased rotation switches from suppressing to enhancing the roaming products across our chosen energy range. However, decomposition into these pathways is difficult because the difference between them does not appear to have a distinct boundary. A vector correlation investigation of the CO rotation shows different characteristics in the roaming versus direct channels and this difference is a potentially useful signature of the roaming mechanism, as first speculated by Kable and Houston in their experimental study of photodissociation of acetaldehyde [P. L. Houston and S. H. Kable, Proc. Nat. Acad. Sci. 103, 16079 (2006)].     

Role of s-p orbital mixing in the bonding and properties of second-period diatomic molecules

Qualitative molecular orbital theory is widely used as a conceptual tool to understand chemical bonding. Symmetry-allowed orbital mixing between atomic or fragment orbitals of different energies can greatly complicate such qualitative interpretations of chemical bonding. We use high-level Amsterdam Density Functional calculations to examine the issue of whether orbital mixing for some familiar second-row homonuclear and heteronuclear diatomic molecules results in net bonding or antibonding character for a given molecular orbital. Our results support the use of slopes of molecular orbital energy versus bond distance plots (designated radial orbital-energy slope: ROS) as the most useful criterion for making this determination. Calculated atomic charges and frontier orbital properties of these molecules allow their acid-base chemistry, including their reactivities as ligands in coordination chemistry, to be better understood within the context of the Klopman interpretation of hard and soft acid-base theory. Such an approach can be extended to any molecular species.     

Power-gap law and the dynamical constraints on angular momentum transfer in rotationally inelastic molecular collisions

The model proposed by Dexheimer, Durand, Brunner and Pritchard has been developed and tested on CO₂H₂, CO₂He, Na₂He, Na₂Ne and N₂Ar. This model explains the rapid decrease in the rotationally inelastic integral cross sections with increase in the amount of rotational energy transfer (∣ΔE∣) in the region ∣ΔE∣ > ∣ΔE∣^*, ∣ΔE∣^* is foun to depend on the reduced mass of the system, the moment of inertia of the molecule, the initial rotational state, and the interaction potential. Data for the systems studied show quantitative agreement with the predictions of the model.     

Correlation between atomic orientation and product angular momentum alignment in the reaction of oriented Ar (3P2) with CH3OH

Atomic orientation effect for the CH(3)O(*) formation has been studied for the dissociative energy transfer reaction of oriented Ar ((3)P(2)) with CH(3)OH. The degree of polarization of CH(3)O(*) chemiluminescence was determined as a function of each magnetic M(J) (') substate in the collision frame. A drastic change of the product angular momentum alignment due to atomic orientation was recognized.     

Bond strength and bond angles for hybrid orbitals composed of arbitrary sets of orbital angular momentum quantum number

According to the formulas obtained in the preceding paper, it may be used for all types of the hybridization with any set of azimuthal quantum numbers l, l = 0 through l = 5, and a complete theoretical data of bond angles and bond strengths are shown in this paper.     

Evidence for partial quenching of orbital angular momentum upon complex formation in the infrared spectrum of OH-acetylene

The entrance channel leading to the addition reaction between the hydroxyl radical and acetylene has been examined by spectroscopic characterization of the asymmetric CH stretching band of the pi-hydrogen bonded OH-acetylene reactant complex. The infrared action spectrum observed at 3278.6 cm(-1) (origin) consists of seven peaks of various intensities and widths, and is very different from those previously reported for closed-shell HF/HCl-acetylene complexes. The unusual spectrum arises from a partial quenching of the OH orbital angular momentum in the complex, which in turn is caused by a significant splitting of the OH monomer orbital degeneracy into (2)A(') and (2)A(") electronic states. The magnitude of the (2)A(')-(2)A(") splitting as well as the A rotational constant for the OH-acetylene complex are determined from the analysis of this b-type infrared band. The most populated OH product rotational state, j(OH)=9/2, is consistent with intramolecular vibrational energy transfer to the nu2 C triple bonded C stretching mode of the departing acetylene fragment. The lifting of the OH orbital degeneracy and partial quenching of its electronic orbital angular momentum indicate that the electronic changes accompanying the evolution of reactants into products have begun to occur in the reactant complex.     

Rates of vibrational and dissociative excitation of diatomic molecules in atom-molecule collisions in a hot gas

Vibrational relaxation and dissociation in O₂-Ar at low O₂ contents are considered. The populations of the vibrational levels are found as functions of time. The vibrational relaxation time and the dissociation rate constant at 3000 to 20 000 K are calculated. The relaxation equation for the vibrational energy per unit volume in the presence of dissociation is considered.     

Coupled hartree-fock and second order polarization propagator calculations of indirect nuclear spin-spin coupling constants for diatomic molecules

We report ab initio calculation of indirect nuclear spin-spin coupling constants for the HD, FH, CO and CH⁺ molecules using the first (coupled Hart     

Beyond the spin model: exchange coupling in molecular magnets with unquenched orbital angular momenta

In this critical review we review the problem of exchange interactions in polynuclear metal complexes involving orbitally degenerate metal ions. The key feature of these systems is that, in general, they carry an unquenched orbital angular momentum that manifests itself in all their magnetic properties. Thus, interest in degenerate systems involves fundamental problems related to basic models in magnetism. In particular, the conventional Heisenberg-Dirac-Van Vleck model becomes inapplicable even as an approximation. In the first part we attempt to answer two key questions, namely which theoretical tools are to be used in the case of degeneracy, and how these tools can be employed. We demonstrate that the exchange interaction between orbitally degenerate metal ions can be described by the so-called orbitally-dependent exchange Hamiltonian. This approach has shown to reveal an anomalously strong magnetic anisotropy that can be considered as the main physical manifestation of the unquenched orbital angular momentum in magnetic systems. Along with the exchange coupling, a set of other interactions (such as crystal field effects, spin-orbit and Zeeman coupling), which are specific for the degenerate systems, need to be considered. All these features will be discussed in detail using a pseudo-spin-1/2 Hamiltonian approach. In the second part, the described theoretical background will be used to account for the magnetic properties of several magnetic metal clusters and low-dimensional systems: (i) the dinuclear face-sharing unit [Ti(2)Cl(9)](3-), which exhibits a large magnetic anisotropy; (ii) the rare-earth compounds Cs(3)Yb(2)Cl(9) and Cs(3)Yb(2)Br(9), which, surprisingly, exhibit a full magnetic isotropy; (iii) a zig-zag Co(II) chain exhibiting unusual combination of single-chain magnet behavior and antiferromagnetic exchange coupling; (iv) a trigonal bipyramidal Ni(3)Os(2) complex; (v) various Co(II) clusters encapsulated by polyoxometalate ligands. In the two last examples a pseudospin-1/2 Hamiltonian approach is applied to account for the presence of exchange anisotropy (150 references).     

Quantum dynamics of rovibrational transitions in H2-H2 collisions: internal energy and rotational angular momentum conservation effects

We present a full dimensional quantum mechanical treatment of collisions between two H(2) molecules over a wide range of energies. Elastic and state-to-state inelastic cross sections for ortho-H(2)?+ para-H(2) and ortho-H(2)?+ ortho-H(2) collisions have been computed for different initial rovibrational levels of the molecules. For rovibrationally excited molecules, it has been found that state-to-state transitions are highly specific. Inelastic collisions that conserve the total rotational angular momentum of the diatoms and that involve small changes in the internal energy are found to be highly efficient. The effectiveness of these quasiresonant processes increases with decreasing collision energy and they become highly state-selective at ultracold temperatures. They are found to be more dominant for rotational energy exchange than for vibrational transitions. For non-reactive collisions between ortho- and para-H(2) molecules for which rotational energy exchange is forbidden, the quasiresonant mechanism involves a purely vibrational energy transfer albeit with less efficiency. When inelastic collisions are dominated by a quasiresonant transition calculations using a reduced basis set involving only the quasiresonant channels yield nearly identical results as the full basis set calculation leading to dramatic savings in computational cost.     

Quantum theory of molecular collisions in a magnetic field: efficient calculations based on the total angular momentum representation

An efficient method is presented for rigorous quantum calculations of atom-molecule and molecule-molecule collisions in a magnetic field. The method is based on the expansion of the wave function of the collision complex in basis functions with well-defined total angular momentum in the body-fixed coordinate frame. We outline the general theory of the method for collisions of diatomic molecules in the (2)Σ and (3)Σ electronic states with structureless atoms and with unlike (2)Σ and (3)Σ molecules. The cross sections for elastic scattering and Zeeman relaxation in low-temperature collisions of CaH((2)Σ(+)) and NH((3)Σ(-)) molecules with (3)He atoms converge quickly with respect to the number of total angular momentum states included in the basis set, leading to a dramatic (>10-fold) enhancement in computational efficiency compared to the previously used methods [A. Volpi and J. L. Bohn, Phys. Rev. A 65, 052712 (2002); R. V. Krems and A. Dalgarno, J. Chem. Phys. 120, 2296 (2004)]. Our approach is thus well suited for theoretical studies of strongly anisotropic molecular collisions in the presence of external electromagnetic fields.     

Rydberg-London potential for diatomic molecules and unbonded atom pairs

We propose and test a pair potential that is accurate at all relevant distances and simple enough for use in large-scale computer simulations. A combination of the Rydberg potential from spectroscopy and the London inverse-sixth-power energy, the proposed form fits spectroscopically determined potentials better than the Morse, Varnshi, and Hulburt-Hirschfelder potentials and much better than the Lennard-Jones and harmonic potentials. At long distances, it goes smoothly to the London force appropriate for gases and preserves van der Waals's "continuity of the gas and liquid states," which is routinely violated by coefficients assigned to the Lennard-Jones 6-12 form.     

Intramolecular interactions of L‐phenylalanine: Valence ionization spectra and orbital momentum distributions of its fragment molecules

Intramolecular interactions between fragments of L ‐phenylalanine, i.e., phenyl and alaninyl, have been investigated using dual space analysis (DSA) quantum mechanically. Valence space photoelectron spectra (PES), orbital energy topology and correlation diagram, as well as orbital momentum distributions (MDs) of L ‐phenylalanine, benzene and L ‐alanine are studied using density functional theory methods. While fully resolved experimental PES of L ‐phenylalanine is not yet available, our simulated PES reproduces major features of the experimental measurement. For benzene, the simulated orbital MDs for 1e_1g and 1a_2u orbitals also agree well with those measured using electron momentum spectra. Our theoretical models are then applied to reveal intramolecular interactions of the species on an orbital base, using DSA. Valence orbitals of L ‐phenylalanine can be essentially deduced into contributions from its fragments such as phenyl and alaninyl as well as their interactions. The fragment orbitals inherit properties of their parent species in energy and shape (ie., MDs). Phenylalanine orbitals show strong bonding in the energy range of 14‐20 eV, rather than outside of this region. This study presents a competent orbital based fragments‐in‐molecules picture in the valence space, which supports the fragment molecular orbital picture and building block principle in valence space. The optimized structures of the molecules are represented using the recently developed interactive 3D‐PDF technique. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011