A Bernstein property of solutions to a class of prescribed affine mean curvature equations

Let \(x: M \rightarrow A^{n+1}\) be a locally strongly convex hypersurface, given as the graph of a locally strongly convex function x _n+1 = z(x ₁, ..., x _n ). In this paper we prove a Bernstein property for hypersurfaces which are complete with respect to the metric \(G^{\sharp} = \sum \left( \frac{\partial^{2}z}{\partial x_{i} \partial x_{j}} \right) dx_{i} dx_{j}\) and which satisfy a certain Monge–Ampère type equation. This generalises in some sense the earlier result of Li and Jia for affine maximal hypersurfaces of dimension n = 2 and n = 3 (Li, A.-M., Jia, F.: A Bernstein property of affine maximal hypersurfaces. Ann. Glob. Anal. Geom. 23, 359–372 (2003)), related results (Li, A.-M., Jia, F.: Locally strongly convex hypersurfaces with constant affine mean curvature. Diff. Geom. Appl. 22(2), 199–214 (2005)) and results for n = 2 of Trudinger and Wang (Trudinger, N.S., Wang, X.-J.: Bernstein-Jörgens theorem for a fourth order partial differential equation. J. Partial Diff. Equ. 15(2), 78–88 (2002)).     

Quantum/classical studies of vibrationally mediated photodissociation of Ar x H2O

Results of multiple configuration quantum/classical simulations of the dynamics of Ar x H2O photodissociation are reported. In agreement with experimental studies of Nesbitt and co-workers [J. Chem. Phys. 2000, 112, 7449], we find that the OH products emerge rotationally excited, compared to the dissociation of bare H2O. The wavelength dependence of the total cross section and the energy transfer to the argon atom are also investigated. The trends are interpreted in terms of features in the Ar x H2O A state potential surface.     

Unraveling rotation-vibration mixing in highly fluxional molecules using diffusion Monte Carlo: applications to H3+ and H3O+

A thorough examination of the use of fixed-node diffusion Monte Carlo for the study of rotation-vibration mixing in systems that undergo large amplitude vibrational motions is reported. Using H(3)(+) as a model system, the overall accuracy of the method is tested by comparing the results of these calculations with those from converged variational calculations. The effects of the presence of a large amplitude inversion mode on rotation-vibration mixing are considered by comparing the H(3)(+) results with those for H(3)O(+). Finally, analysis of the results of the fixed-node diffusion Monte Carlo calculations performed in different nodal regions is found to provide clear indications of when some of the methodology's underlying assumptions are breaking down as well as provide physical insights into the form of the rotation-vibration coupling that is most likely responsible.     

Dynamic mapping of CN rotation following photoexcitation of ICN-

In a spin: the dynamics of photoexcited ICN(-) (Ar)(0-5) are presented. Photodetachment produces quasi-thermal electron emission that leaves ICN with up to 2.85 eV of internal energy. Photodissociation at 2.5 eV leads to one-atom caging and highly solvated anion products. Calculations indicate efficient energy transfer into CN rotation upon excitation to the (2)Π(1/2) excited state. CN rotation is vital to explain the unique dynamics observed.     

Time-dependent wave packet studies on the Cl + HCl hydrogen exchange reaction

The initiation of the hydrogen exchange reaction Cl((2)P)+HCl --> ClH+Cl((2)P) by excitation of the HCl molecular stretch to v=2 is studied for total angular momentum quantum number J=(1)/(2) and both even and odd parity. The calculations were performed using a time-dependent propagation from an initial quasi-bound state and employed all three relevant potential energy surfaces and the nonadiabatic couplings between them. Coriolis and spin-orbit coupling were also taken into account. The electronic and HCl rotational distributions of the products in both dissociation channels are analyzed, and the results are interpreted using features of the potential energy surfaces.     

Experimental and theoretical investigations of the He...I2 rovibronic spectra in the I2 B-X, 20-0 region

The laser-induced fluorescence and action spectra of I2 in a helium supersonic expansion have been recorded in the I2 B-X, 20-0 region. Two features are identified within the spectra. The lower-energy feature arises from transitions between states that are localized in a T-shaped conformation on both the X- and B-state potentials. The higher-energy feature reflects transitions from states that are localized in a linear conformation on the X state to states that have energies that are larger than the barrier for free rotation of the rare gas atom about the I2 molecule on the B-state potential. Ground-state binding energies of 16.6(6) and 16.3(6) cm-1 were determined for the T-shaped and linear conformers, respectively. These spectra are compared to those calculated using the experimentally determined rotational temperatures. Based on the agreement between the experimental and calculated spectra, the binding energies of the J'=0 states with 0 and 2-6 quanta of excitation in the He...I2 bending mode on the B state were determined. Several models for the B-state potential were used to investigate the origins of the shape of the contour of the higher-energy feature in the spectra for He...I2 and He...Br2. The shape of the contours was found to be relatively insensitive to the choice of potential. This leads us to believe that the spectra of these systems are relatively insensitive to the parameters of the B-state potential energy surface and are more sensitive to properties of the halogen molecule.     

Femtosecond dynamics of Cu(H(2)O)(2)

The ultrafast relaxation dynamics of Cu(H(2)O)(2) is investigated using femtosecond photodetachment-photoionization spectroscopy. In addition, stationary points on the Cu(H(2)O)(2) anion, neutral, and cation potential energy surfaces are characterized by ab initio electronic structure calculations. Electron photodetachment from Cu(-)(H(2)O)(2) initiates the dynamics on the ground-state potential energy surface of neutral Cu(H(2)O)(2). The resulting Cu(H(2)O)(2) complexes experience large-amplitude H(2)O reorientation and dissociation. The time evolution of the Cu(H(2)O)(2) fragmentation products is monitored by time-resolved resonant multiphoton ionization. The parent ion, Cu(+)(H(2)O)(2), is not detected above background levels. The rise to a maximum of the Cu(+) signal from Cu(-)(H(2)O)(2), and the decay of the Cu(+)(H(2)O) signal from Cu(-)(H(2)O)(2) have similar tau approximately 10 ps time dependences to the corresponding signals from Cu(-)(H(2)O), but display clear differences at very short and long times. The experimental observations can be understood in terms of the following picture. Prompt dissociation of H(2)O from nascent Cu(H(2)O)(2) gives rise to a vibrationally excited Cu(H(2)O) complex, which dissociates to Cu+H(2)O due to coupling of H(2)O internal rotation to the dissociation coordinate. This prompt dissociation removes all intra-H(2)O vibrational excitation from the intermediate Cu(H(2)O) fragment, which quenches the long time vibrational predissociation to Cu+H(2)O previously observed in analogous experiments on Cu(-)(H(2)O).     

Towards the development of Eu(III) luminescent switching/sensing in water-permeable hydrogels

The synthesis of the Eu(III) complex 1.Eu and photophysical studies of this complex in solution are described. In water, the Eu(III) luminescence was ‘switched on’ in the presence of H⁺, with large enhancements in the Eu(III) luminescence. The complex was then incorporated into poly[methylmethacrylate-co-2-(hydroxyethylmethacrylate)]-based hydrogels and the luminescent properties of the resulting polymeric films were investigated using confocal laser-scanning microscopy as well as using steady-state luminescence. The luminescence was shown to be ‘switched on’ in the soft material after adjusting the pH of the solution in which the 1.Eu-incorporated film was immersed from alkaline to acid.     

Full-dimensional vibrational calculations for H5O2+ using an ab initio potential energy surface

We report quantum diffusion Monte Carlo (DMC) and variational calculations in full dimensionality for selected vibrational states of H(5)O(2) (+) using a new ab initio potential energy surface [X. Huang, B. Braams, and J. M. Bowman, J. Chem. Phys. 122, 044308 (2005)]. The energy and properties of the zero-point state are focused on in the rigorous DMC calculations. OH-stretch fundamentals are also calculated using "fixed-node" DMC calculations and variationally using two versions of the code MULTIMODE. These results are compared with infrared multiphoton dissociation measurements of Yeh et al. [L. I. Yeh, M. Okumura, J. D. Myers, J. M. Price, and Y. T. Lee, J. Chem. Phys. 91, 7319 (1989)]. Some preliminary results for the energies of several modes of the shared hydrogen are also reported.