Accuracy of the cluster-approximation method in a nonequilibrium model

We examine a model in which a nonequilibrium phase transition from an active to an extinct state is observed. The order of this phase transition has been shown to be either continuous or first-order, depending on the parameter values and the dimension of the system. Using increasingly large clusters, we use the cluster approximation method to obtain estimates for the critical points in 1+1 dimensions. For the continuous phase transitions only, extrapolations of these approximations show excellent agreement with simulation results. Further, the approximations suggest that, consistent with simulation results, in 1+1 dimensions no first-order phase transitions are observed.Comment: 8 pages, 3 figures and 1 tabl

Cluster geometry and survival probability in systems driven by reaction-diffusion dynamics

We consider a reaction-diffusion model incorporating the reactions A -> 0, A -> 2A and 2A -> 3A. Depending on the relative rates for sexual and asexual reproduction of the quantity A, the model exhibits either a continuous or first-order absorbing phase transition to an extinct state. A tricritical point separates the two phase lines. As well as briefly examining this critical behavior in 2+1 dimensions, we pay particular attention to the cluster geometry. We observe the different cluster structures that form at criticality for the three different types of critical behavior and show that there exists a linear relationship for the probability of survival against initial cluster size at the tricritical point only.Comment: 4 pages, 6 figure

Constitutional Law: Another Chapter in the Collective Entity Doctrine

Braswell v. United States, 108 S.Ct. 2284 (interim ed. 1988)

Gas Phase Computational Studies on the Competition between Nitrile and Water Ligands in Uranyl Complexes

The gas phase formation of uranyl dicationic complexes containing water and nitrile (acetonitrile, propionitrile, and benzonitrile) ligands, [UO2(H2O)m(RCN)n]2+, has been studied using density functional theory with a relativistic effective core potential to account for scalar relativistic effects on uranium. It is shown that nitrile addition is favored over the addition of water ligands. Decomposition of these complexes to [UO2OH(H2O)m(RCN)n]+ by the loss of either H3O+ or (RCN + H)+ is also examined. It is found that this reaction is competitive with the ligand addition when the coordination sphere of uranyl is unsaturated. Additionally, this reaction is influenced by the size of the nitrile ligand with reactions involving acetonitrile being the most prevalent. Finally, ligand addition to the monocation shows trends similar to that of the dication with energetic differences being smaller for the addition to the monocation

The transition from the open minimum to the ring minimum on the ground state and on the lowest excited state of like symmetry in ozone: A configuration interaction study

The metastable ring structure of the ozone 11A1 ground state, which theoretical calculations have shown to exist, has so far eluded experimental detection. An accurate prediction for the energy difference between this isomer and the lower open structure is therefore of interest, as is a prediction for the isomerization barrier between them, which results from interactions between the lowest two 1A1 states. In the present work, valence correlated energies of the 11A1 state and the 21A1 state were calculated at the 11A1 open minimum, the 11A1 ring minimum, the transition state between these two minima, the minimum of the 21A1 state, and the conical intersection between the two states. The geometries were determined at the full-valence multi-configuration self-consistent-field level. Configuration interaction (CI) expansions up to quadruple excitations were calculated with triple-zeta atomic basis sets. The CI expansions based on eight different reference configuration spaces were explored. To obtain some of the quadruple excitation energies, the method of Correlation Energy Extrapolation by Intrinsic Scaling was generalized to the simultaneous extrapolation for two states. This extrapolation method was shown to be very accurate. On the other hand, none of the CI expansions were found to have converged to millihartree (mh) accuracy at the quadruple excitation level. The data suggest that convergence to mh accuracy is probably attained at the sextuple excitation level. On the 11A1 state, the present calculations yield the estimates of (ring minimum—open minimum) ∼45–50 mh and (transition state—open minimum) ∼85–90 mh. For the (21A1–1A1) excitation energy, the estimate of ∼130–170 mh is found at the open minimum and 270–310 mh at the ring minimum. At the transition state, the difference (21A1–1A1) is found to be between 1 and 10 mh. The geometry of the transition state on the 11A1 surface and that of the minimum on the 21A1 surface nearly coincide. More accurate predictions of the energydifferences also require CI expansions to at least sextuple excitations with respect to the valence space. For every wave function considered, the omission of the correlations of the 2s oxygen orbitals, which is a widely used approximation, was found to cause errors of about ±10 mh with respect to theenergy differences

Uncontracted Rys Quadrature Implementation of up to G Functions on Graphical Processing Units

An implementation is presented of an uncontracted Rys quadrature algorithm for electron repulsion integrals, including up to g functions on graphical processing units (GPUs). The general GPU programming model, the challenges associated with implementing the Rys quadrature on these highly parallel emerging architectures, and a new approach to implementing the quadrature are outlined. The performance of the implementation is evaluated for single and double precision on two different types of GPU devices. The performance obtained is on par with the matrix−vector routine from the CUDA basic linear algebra subroutines (CUBLAS) library

Direct Dynamics Simulation of Dioxetane Formation and Decomposition Via the Singlet ·O–O–CH2–CH2· Biradical: Non-RRKM Dynamics

Electronic structure calculations and direct chemical dynamics simulations are used to study the formation and decomposition of dioxetane on its ground state singlet potential energy surface. The stationary points for 1O2 + C2H4, the singlet ·O–O–CH2–CH2· biradical, the transition state (TS) connecting this biradical with dioxetane, and the two transition states and gauche ·O–CH2–CH2–O· biradical connecting dioxetane with the formaldehyde product molecules are investigated at different levels of electronic structuretheory including UB3LYP, UMP2, MRMP2, and CASSCF and a range of basis sets. The UB3LYP/6-31G* method was found to give representative energies for the reactive system and was used as a model for the simulations. UB3LYP/6-31G* direct dynamics trajectories were initiated at the TS connecting the ·O–O–CH2–CH2· biradical and dioxetane by sampling the TS\u27s vibrational energy levels, and rotational and reaction coordinate energies, with Boltzmann distributions at 300, 1000, and 1500 K. This corresponds to the transition state theorymodel for trajectories that pass the TS. The trajectories were directed randomly towards both the biradical and dioxetane. A small fraction of the trajectories directed towards the biradical recrossed the TS and formed dioxetane. The remainder formed 1O2 + C2H4 and of these ∼ 40% went directly from the TS to 1O2 + C2H4without getting trapped and forming an intermediate in the ·O–O–CH2–CH2· biradical potential energy minimum, a non-statistical result. The dioxetane molecules which are formed dissociate to two formaldehyde molecules with a rate constant two orders of magnitude smaller than that predicted by Rice–Ramsperger–Kassel–Marcus theory. The reaction dynamics from dioxetane to the formaldehyde molecules do not follow the intrinsic reaction coordinate or involve trapping in the gauche ·O–CH2–CH2–O· biradical potential energy minimum. Important non-statistical dynamics are exhibited for this reactive system

Singlet and Triplet Potential Surfaces for the O 2 + C 2 H 4 Reaction

Electronic structure calculations at the CASSCF and UB3LYP levels of theory with the aug-cc-pVDZ basis set were used to characterize structures, vibrational frequencies, and energies for stationary points on the ground state triplet and singlet O2+C2H4potential energy surfaces (PESs). Spin-orbit couplings between the PESs were calculated using state averaged CASSCF wave functions. More accurate energies were obtained for the CASSCF structures with the MRMP2/aug-cc-pVDZ method. An important and necessary aspect of the calculations was the need to use different CASSCF active spaces for the different reaction paths on the investigated PESs. The CASSCF calculations focused on O2+C2H4 addition to form the C2H4O2biradical on the triplet and singlet surfaces, and isomerization reaction paths ensuing from this biradical. The triplet and singlet C2H4O2 biradicals are very similar in structure, primarily differing in their C−C−O−O dihedral angles. The MRMP2 values for the O2+C2H4→C2H4O2 barrier to form the biradical are 33.8 and 6.1 kcal/mol, respectively, for the triplet and singlet surfaces. On the singlet surface,C2H4O2 isomerizes to dioxetane and ethane-peroxide with MRMP2 barriers of 7.8 and 21.3 kcal/mol. A more exhaustive search of reaction paths was made for the singlet surface using the UB3LYP/aug-cc-pVDZ theory. The triplet and singlet surfaces cross between the structures for the O2+C2H4 addition transition states and the biradical intermediates. Trapping in the triplet biradical intermediate, following O32+C2H4 addition, is expected to enhance triplet→singlet intersystem crossing