Surface hopping simulation of vibrational predissociation of methanol dimer

The mixed quantum-classical surface hopping method is applied to the vibrational predissociation of methanol dimer, and the results are compared to more exact quantum calculations. Utilizing the vibrational SCF basis, the predissociation problem is cast into a curve crossing problem between dissociative and quasibound surfaces with different vibrational character. The varied features of the dissociative surfaces, arising from the large amplitude OH torsion, generate rich predissociation dynamics. The fewest switches surface hopping algorithm of Tully [J. Chem. Phys. 93, 1061 (1990)] is applied to both diabatic and adiabatic representations. The comparison affords new insight into the criterion for selecting the suitable representation. The adiabatic method's difficulty with low energy trajectories is highlighted. In the normal crossing case, the diabatic calculations yield good results, albeit showing its limitation in situations where tunneling is important. The quadratic scaling of the rates on coupling strength is confirmed. An interesting resonance behavior is identified and is dealt with using a simple decoherence scheme. For low lying dissociative surfaces that do not cross the quasibound surface, the diabatic method tends to overestimate the predissociation rate whereas the adiabatic method is qualitatively correct. Analysis reveals the major culprits involve Rabi-like oscillation, treatment of classically forbidden hops, and overcoherence. Improvements of the surface hopping results are achieved by adopting a few changes to the original surface hopping algorithms.     

A perturbative calculation of the rovibrational energy levels of methane

The rovibrational energy levels of methane are determined from a quartic ab initio potential energy force field where the expansion coordinates are the Morse coordinates for the stretches and extension coordinates for the bends. Energies are calculated using canonical Van Vleck perturbation theory. Results are obtained for both rotation-vibration Hamiltonians expressed as functions of curvilinear and rectilinear normal coordinates. Second, fourth, and sixth order curvilinear results are compared with experimental results, and fourth order results for the rectilinear and curvilinear Hamiltonian are compared to each other. The calculated rovibrational levels are in good agreement with the experimental values for low J levels. The calculated rotational level splittings are in even better agreement with the experiment. In particular, the ground state tetrahedral splittings, which are as small as 10(-4) cm(-1), are well reproduced by our calculations at sixth order.     

Entity authentication schemes using braid word reduction

Artin's braid groups currently provide a promising background for cryptographical applications, since the first cryptosystems using braids were introduced in [I. Anshel, M. Anshel, D. Goldfeld, An algebraic method for public-key cryptography, Math. Res. Lett. 6 (1999) 287-291, I. Anshel, M. Anshel, B. Fisher, D. Goldfeld, New key agreement schemes in braid group cryptography, RSA 2001, K.H. Ko, S.J. Lee, J.H. Cheon, J.W. Han, J.S. Kang, C. Park, New public-key cryptosystem using braid groups, Crypto 2000, pp. 166-184] (see also [V.M. Sidelnikov, M.A. Cherepnev, V.Y. Yashcenko, Systems of open distribution of keys on the basis of noncommutative semigroups, Ross. Acad. Nauk Dokl. 332-5 (1993); English translation: Russian Acad. Sci. Dokl. Math. 48-2 (1194) 384-386]). A variety of key agreement protocols based on braids have been described, but few authentication or signature schemes have been proposed so far. We introduce three authentication schemes based on braids, two of them being zero-knowledge interactive proofs of knowledge. Then we discuss their possible implementations, involving normal forms or an alternative braid algorithm, called handle reduction, which can achieve good efficiency under specific requirements.     

Preparation of polyetherol-appended sulfur porphyrazines and investigations of peripheral metal ion binding in polar solvents

We describe the complete synthesis and characterization of a new family of peripherally functionalized porphyrazines (pz's) with four, three, or two (in a trans conformation) bis[thioethoxy(ethoxy)ethanol] moieties appended at the pyrroles. These "polyetherol" groups serve as weak exocyclic binding sites for a number of metal ions and also provide solubility of the pz's in low molecular-weight alcohols and water. Electronic spectra of the modified porphyrazines exhibit distinct changes in the visible region (both absorbance and fluorescence) in response to treatment with Ag+, Pb2+, Cd2+, Cs+, and Ni2+ in solution. Such properties make these compounds intriguing candidates for incorporation into the transducer layers in optically based chemical sensors.