ALBERT

Notes: To gain insight into the mechanism of Na(3p)2P3/2→2P1/2 fine-structure transitions induced by collision with He, we monitor the expectation values of the orbital- and spin-angular momentum vectors, l and s, as a function of time along the trajectory, using a semiclassical formalism. In a typical collision, 〈s〉 remains nearly space-fixed while 〈l〉 precesses about the rotating internuclear axis. Thus, in the interaction region, the projection of 〈l〉 onto the internuclear axis, 〈λ〉, remains nearly constant, and the molecular alignment of the orbital is preserved. We show how equations of motion for the classical analogues of these expectation values agree qualitatively with the quantum equations of motion. A qualitative comparison is also made with the Cs–He system for which the spin–orbit coupling is much stronger. We calculate cross sections for Na(2P3/2)+He→Na(2P1/2)+He as a function of the alignment of the excitation laser polarization with respect to the asymptotic relative velocity vector. For stationary pumping of the excited F=3 hyperfine level, this calculation predicts that the perpendicular alignment gives a cross section which is larger by a factor of 1.8 than that obtained by parallel alignment.

Notes: The Ca(4p2 1D2) state is prepared in a two-step excitation with linearly polarized lasers. Two different angular wave functions are selected, Y2,0 or (Y2,−1−Y2,1)/, by using parallel or perpendicular laser polarizations, respectively. Subsequent collision with a rare gas atom (He, Ne, Ar, Kr, or Xe) populates the near-resonant Ca(3d4p 1F3) state. The dependence of the collisional energy transfer process is measured as a function of the alignment of the initial 1D2 state wave function with respect to the average relative velocity vector. The laser-selected Y2,0 and (Y2,−1−Y2,1)/ angular wave functions display dramatically different alignment dependences, which are understood by an analysis of the rotation properties of these wave functions. The relative contributions to the cross section of the individual 1D2 sublevels, ML=0, ±1, and ±2, are extracted, and these vary considerably depending on the rare gas. For He, the ML=±2 sublevel (asymptotic Δ molecular state) contributes the most to the total cross section, while for all the other rare gases, the ML=0, ±1 sublevels (asymptotic Σ and Π molecular states, respectively) are more important. The contribution of the ML=0 sublevel increases smoothly with increasing mass of the rare gas collision partner, becoming the largest contributor for Xe.

Notes: In this paper we present results of coupled channel quantum scattering calculations of the alignment selected j=3/2→ j=1/2 fine structure changing integral cross section for Na(2P)+He. This cross section has in the past been written in terms of a coherent sum of partial wave amplitudes, but we have found that it can be expressed in terms of an incoherent sum of partial cross sections, each labeled by the total angular momentum J and by parity. It is also possible to define an alignment selected wave function for each J such that the azimuthal average of the square of this wave function projected onto each final state is proportional to the magnitude of the partial cross section into that state. This J labeled wave function is thus clearly related to the physical measurables, and we have used it to determine propensities for preservation of asymptotically prepared alignment during collisions. Using a potential surface based on Pascale's ab initio calculations, we find that the alignment ratio σ⊥/σ(parallel) is an increasing function of energy, with a value less than unity at low energy (〈0.01 eV), but increasing quickly to a value of about 2.0 at 0.04 eV and then more slowly at higher energy, up to a value of 2.7 at 0.2 eV (the highest energy considered). Above 0.02 eV, both the alignment ratio and the alignment selected integral cross sections are in good agreement with values calculated in an accompanying semiclassical study (Kovalenko, Leone, and Delos).An examination of the J labeled alignment selected scattering wave functions and of the expectation values of 〈Ω〉, 〈Λ〉, and 〈Σ〉 indicates that at low J when the initial state is prepared with (parallel) polarization, the dominant state at short range is Σ while with ⊥ polarization the dominant state is Π (i.e., asymptotic alignment is preserved). By way of contrast, this propensity for alignment preservation is not seen if fluxes or probability densities associated with alignment selected wave functions labeled by the initial orbital quantum number l (rather than J) are considered. This l labeled result is in accord with recent work by Pouilly and Alexander, but the lack of alignment preservation in this case has no relationship with the alignment cross sections, or with the alignment selected plane wave scattering wave function, since the l labeled wave functions must be coherently combined to generate this information. The orbital scrambling found for the l labeled solutions thus is not related to measurable properties, and instead the correct picture is provided by the J labeled solutions, which do show preservation of alignment. We find that even in the J labeled picture, alignment preservation does not by itself guarantee any specific trend in the alignment ratio for the fine structure transition.

Notes: We develop a replica generalization of the reference interaction site model (replica RISM) integral equation theory to describe the structure and thermodynamics of quenched-annealed systems comprising polar molecular species. It provides a successful approach to realistic models of molecular liquids, and properly allows for the effect of a quenched disordered matrix on the sorbed liquid. The description can be extended to an electrolyte solution in a disordered material containing charged chemical functionalities that determine its adsorption character. The replica reference interaction site model (RISM) equations are complemented with the hypernetted chain (HNC) closure and its partial linearization (PLHNC), adequate to ionic and polar molecular liquids. In these approximations, the excess chemical potentials are derived in a closed analytical form. We extend the description to a quenched-annealed system with soft-core interaction potentials between all species, in which the liquid and matrix equilibrium distributions are characterized in general by two different temperatures. The replica RISM/PLHNC-HNC theory is applied to water sorbed in a quenched disordered microporous network of atoms associated into interconnected branched chains, with activating polar groups grafted to matrix chains. The results are in qualitative agreement with experiment for water confined in disordered materials. © 2001 American Institute of Physics.

Notes: We modify the site–site as well as three-dimensional (3D) versions of the reference interaction site model (RISM) integral equations with the hypernetted chain (HNC) closures by adding a repulsive bridge correction (RBC). The RBC treats the overestimation of water ordering around a hydrophobic solute in the RISM/HNC approximation, and thus refines the entropic component in the hydration free energy. We build up the bridge functions on r−12 repulsive core potentials, and propose RBC expressions for both the site–site and 3D-RISM approaches. To provide fast calculation, we obtain the excess chemical potential of hydration by using the thermodynamic perturbation theory (TPT). The site–site RISM/HNC+RBC as well as 3D-RISM/HNC+RBC approaches are applied to calculate the structure and thermodynamics of hydration of rare gases and alkanes in ambient water. For both approaches, the RBC drastically improves the agreement of the hydration chemical potential with simulation data and provides its correct dependence on the solute size. For solutes of a nonspherical form, the 3D treatment yields the hydration structure in detail and better fits simulation results, whereas the site–site approach is essentially faster. The TPT approximation gives the hydration thermodynamics in good qualitative agreement with the exact results of the thermodynamic integration, and substantially reduces computational burden. The RBC–TPT approximation can improve the predictive capability of the hybrid algorithm of a generalized-ensemble Monte Carlo simulation combined with the site–site RISM theory, used to describe protein folding with due account for the water effect at the microscopic level. The RBC can be optimized for better fit to reference simulation data, and can be generalized for solute molecules with charged groups. © 2000 American Institute of Physics.

Notes: We adapt the three-dimensional reference interaction site model (3D-RISM) to calculate the potentials of mean force for ion–molecular solution as a difference between the chemical potential of solvation of a cluster of solutes and of individual ones. The method yields the solvation structure around the cluster of solutes in detail. The solvation chemical potential is obtained for the three-dimensional hypernetted chain (3D-HNC) closure as well as for its partial linearization (3D-PLHNC approximation). The solvation chemical potential is obtained in a closed analytical form for both the 3D-HNC and 3D-PLHNC closures. The 3D-RISM integral equations are solved by using the supercell technique. A straightforward supercell treatment of ionic solute in polar molecular solvent leads to a big error in the potential of mean force as well as the solvation chemical potential, which for simple ions in water amounts to about 35 kcal/mol. We elaborated corrections to the 3D-RISM integral equations, alleviating the artifact of the supercell periodicity with an accuracy of 0.05 kcal/mol or better and restoring the long-range asymptotics of the solute–solvent correlation functions. The dielectrically consistent site–site RISM/HNC theory (DRISM/HNC) is employed for the solvent correlations to provide a proper description of the dielectric properties of solution. This allowed us to extend the description to solution at a finite salt concentration. We converge both the 3D-RISM and site–site DRISM integral equations by using the method of modified direct inversion in the iterative subspace. Owing to the proper initial guess of the correlation functions, iteration begins at once for a given temperature and full molecular charge, avoiding a gradual decrease of the temperature and increase of the site charges, which greatly reduces the computation time. We calculate and discuss the potentials of mean force for sodium chloride in ambient water at infinite dilution as well as at a finite concentration. © 2000 American Institute of Physics.

Notes: We applied the three-dimensional reference interaction site model (3D-RISM) integral equation theory with the 3D hypernetted chain (3D-HNC) closure or its partial linearization (3D-PLHNC) to obtain the potentials of mean force (PMFs) and the solvation structure of sodium chloride in ambient water. The bulk solvent correlations are treated by the dielectrically consistent site–site RISM/HNC theory (DRISM/HNC) to provide a proper description of the dielectric properties of solution and to include the case of a finite salt concentration. The PMF is calculated as a difference in the solvation free energy of an ion pair and of individual ions. We obtained and analyzed in detail the PMFs and solvation structure for ion pairs of NaCl at infinite dilution and a concentration of 1 M. The results are in reasonably good agreement with molecular dynamics simulations for the same model of the solution species. Positions and orientations of water molecules in the first solvation shell around the ion pair are deduced. The short-range hydration structure of the ion pairs at infinite dilution and at moderate concentration is very similar. Ionic ordering and clustering is found in 1 M solution. © 2000 American Institute of Physics.

Notes: The cooling of p-nitroaniline (PNA), dimethylamino-p-nitroaniline (DPNA) and trans-stilbene (t-stilbene) in solution is studied experimentally and theoretically. Using the pump–supercontinuum probe (PSCP) technique we observed the complete spectral evolution of hot absorption induced by femtosecond optical pumping. In t-stilbene the hot S1 state results from Sn→S1 internal conversion with 50 fs characteristic time. The time constant of intramolecular thermalization or intramolecular vibrational redistribution (IVR) in S1 is estimated as τIVR(very-much-less-than)100 fs. In PNA and DPNA the hot ground state is prepared by S1→S0 relaxation with characteristic time 0.3–1.0 ps. The initial molecular temperature is 1300 K for PNA and 860 K for t-stilbene. The subsequent cooling dynamics (vibrational cooling) is deduced from the transient spectra by assuming: (i) a Gaussian shape for the hot absorption band, (ii) a linear dependence of its peak frequency νm and width square Γ2 on molecular temperature T. Within this framework we derive analytic expressions for the differential absorption signal ΔOD(T(t),ν). After calibration with stationary absorption spectra in a low temperature range, the solute temperature T(t) may be evaluated from a transient absorption experiment. For highly polar PNA and DPNA, T(t) is well described by a biexponential decay which reflects local heating effects, while for nonpolar t-stilbene the local heating is negligible and the cooling proceeds monoexponentially. To rationalize this behavior, an analytic model is developed, which considers energy flow from the hot solute to a first solvent shell and then to the bulk solvent. Fastest cooling is found for PNA in water: a time constant of 0.64 ps (68%) corresponds to solute–solvent energy transfer while 2.0 ps (32%) characterizes the cooling of the first shell. In aprotic solvents cooling is slower than in alcohols and slows down further with decreasing solvent polarity. This contrasts with nonpolar t-stilbene which cools down with 8.5 ps both in acetonitrile and cyclohexane. Comparison of the cooling kinetics for PNA in water with those for DPNA in water-acetonitrile mixtures suggests that the solute–solvent energy transfer proceeds mainly through hydrogen bonds. © 2001 American Institute of Physics.