No abstract

The B2‐Eirene code package was developed to give better insight into the physics in the scrape‐off layer (SOL), which is defined as the region of open field‐lines intersecting walls. The SOL is characterised by the competition of parallel and perpendicular transport defining by this a 2D system. The description of the plasma‐wall interaction due to the existence of walls and atomic processes are necessary ingredients for an understanding of the scrape‐off layer. This paper concentrates on understanding the basic physics by combining the results of the code with experiments and analytical models or estimates. This work will mainly focus on divertor tokamaks, but most of the arguments and principles can be easily adapted also to other concepts like island divertors in stellarators or limiter devices. The paper presents the basic equations for the plasma transport and the basic models for the neutral transport. This defines the basic ingredients for the SOLPS (Scrape‐Off Layer Plasma Simulator) code package. A first level of understanding is approached for pure hydrogenic plasmas based both on simple models and simulations with B2‐Eirene neglecting drifts and currents. The influence of neutral transport on the different operation regimes is here the main topic. This will finish with time‐dependent phenomena for the pure plasma, so‐called Edge Localised Modes (ELMs). Then, the influence of impurities on the SOL plasma is discussed. For the understanding of impurity physics in the SOL one needs a rather complex combination of different aspects. The impurity production process has to be understood, then the effects of impurities in terms of radiation losses have to be included and finally impurity transport is necessary. This will be introduced with rising complexity starting with simple estimates, analysing then the detailed parallel force balance and the flow pattern of impurities. Using this, impurity compression and radiation instabilities will be studied. This part ends, combining all the elements introduced before, with specific, detailed results from different machines. Then, the effect of drifts and currents is introduced and their consequences presented. Finally, some work on deriving scaling laws for the anomalous turbulent transport based on automatic edge transport code fitting procedures will be described. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions. The additional conditions (called T1 and T2 here) are implicit in the work of Erdahl [Int. J. Quantum Chem. 13, 697 (1978)] and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Formulating the reduced density matrix computation using the standard dual formulation of semidefinite programming, as opposed to the primal one, results in substantial computational savings and makes it possible to study larger systems than was done previously. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, singly and doubly substituted configuration interaction, Brueckner doubles (with triples), coupled cluster singles and doubles with perturbational treatment of triples, and full configuration interaction calculations. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q, and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations.

We report full-dimensional, ab initio potential energy and dipole moment surfaces, denoted PES and DMS, respectively, for arbitrary numbers of water monomers. The PES is a sum of 1-, 2-, and 3-body potentials which can also be augmented by semiempirical long-range higher-body interactions. The 1-body potential is a spectroscopically accurate monomer potential, and the 2- and 3-body potentials are permutationally invariant fits to tens of thousands of CCSD(T)/aug-cc-pVTZ and MP2/aug-cc-pVTZ electronic energies, respectively. The DMS is a sum of 1- and 2-body DMS, which are covariant fits to tens of thousands MP2/aug-cc-pVTZ dipole moment data. We present the details of these new 2- and 3-body potentials and then extensive applications and tests of this PES are made to the structures, classical binding energies, and harmonic frequencies of water clusters up to the 22-mer. In addition, we report the dipole moment for these clusters at various minima and compare the results against available and new ab initio calculations.

Reaction pathways that bypass the conventional saddle-point transition state (TS) are of considerable interest and importance. An example of such a pathway, termed ''roaming,'' has been described in the photodissociation of H 2CO. In a combined experimental and theoretical study, we show that roaming pathways are important in the 308-nm photodissociation of CH 3CHO to CH4 ؉ CO. The CH 4 product is found to have extreme vibrational excitation, with the vibrational distribution peaked at Ϸ95% of the total available energy. Quasiclassical trajectory calculations on fulldimensional potential energy surfaces reproduce these results and are used to infer that the major route to CH 4 ؉ CO products is via a roaming pathway where a CH 3 fragment abstracts an H from HCO. The conventional saddle-point TS pathway to CH 4 ؉ CO formation plays only a minor role. H-atom roaming is also observed, but this is also a minor pathway. The dominance of the CH 3 roaming mechanism is attributed to the fact that the CH3 ؉ HCO radical asymptote and the TS saddle-point barrier to CH 4 ؉ CO are nearly isoenergetic. Roaming dynamics are therefore not restricted to small molecules such as H 2CO, nor are they limited to H atoms being the roaming fragment. The observed dominance of the roaming mechanism over the conventional TS mechanism presents a significant challenge to current reaction rate theory.reaction dynamics ͉ roaming mechanisms ͉ photochemistry ͉ quasiclassical trajectories ͉ transition state S ince its introduction by Eyring in 1935 (1), the concept of the ''transition state'' (TS) has been central to chemistry because the products, rates, and dynamics of a reaction are often determined by this special molecular configuration (2). For reactions with potential barriers, the TS is a transient molecular structure at the highest point along the minimum energy path connecting reactants to products and thus is a central construct in reaction rate theory and the classification of reaction types. In transition state theory (TST), the reaction rate coefficient is obtained from the ''one-way'' flux through a dividing surface containing the TS. In the more general variational version of TST, denoted VTST, the TS dividing surface is chosen to minimize the reactive flux. This theory is widely used in mathematical modeling of reaction rates in combustion, atmospheric, and biological chemistry, impacting fields as diverse as energy production (3), climate change (4), and enzyme function (5).Although the conventional transition state paradigm will remain essential to chemists, several reaction pathways have been reported in the last 8 years (6-13) in which it is not obvious how to use present implementations of TST or VTST. If such mechanisms are common, they may represent a significant challenge for reaction rate theories. In this report, we show that the ''roaming atom mechanism'' in formaldehyde (H 2 CO) dissociation (9) is not unique to H 2 CO but also occurs in acetaldehyde (CH 3 CHO) dissociation. Moreover, in CH 3 CHO, we find that the roa...

Quantum calculations of the ground vibrational state tunneling splitting of H-atom and D-atom transfer in malonaldehyde are performed on a full-dimensional ab initio potential energy surface (PES). The PES is a fit to 11 147 near basis-set-limit frozen-core CCSD(T) electronic energies. This surface properly describes the invariance of the potential with respect to all permutations of identical atoms. The saddle-point barrier for the H-atom transfer on the PES is 4.1 kcalmol, in excellent agreement with the reported ab initio value. Model one-dimensional and "exact" full-dimensional calculations of the splitting for H- and D-atom transfer are done using this PES. The tunneling splittings in full dimensionality are calculated using the unbiased "fixed-node" diffusion Monte Carlo (DMC) method in Cartesian and saddle-point normal coordinates. The ground-state tunneling splitting is found to be 21.6 cm(-1) in Cartesian coordinates and 22.6 cm(-1) in normal coordinates, with an uncertainty of 2-3 cm(-1). This splitting is also calculated based on a model which makes use of the exact single-well zero-point energy (ZPE) obtained with the MULTIMODE code and DMC ZPE and this calculation gives a tunneling splitting of 21-22 cm(-1). The corresponding computed splittings for the D-atom transfer are 3.0, 3.1, and 2-3 cm(-1). These calculated tunneling splittings agree with each other to within less than the standard uncertainties obtained with the DMC method used, which are between 2 and 3 cm(-1), and agree well with the experimental values of 21.6 and 2.9 cm(-1) for the H and D transfer, respectively.

An accurate global potential-energy surface (PES) is reported for H5+ based on more than 100 000 CCSD(T)/aug-cc-pVTZ ab initio energies. This PES has full permutational symmetry with respect to interchange of H atoms and dissociates to H3+ and H2. Ten known stationary points of H5+ are characterized and compared to previous ab initio calculations. Quantum diffusion Monte Carlo calculations are performed on the PES to obtain the zero-point energy of H5+ and the anharmonic dissociation energy (D0) of H5+→H3++H2. The rigorous zero-point state of H4D+ is also calculated and discussed within the context of a strictly classical approach to obtain the branching ratio of the reaction H4D+→H3++HD and H2D++H2. Such an approach is taken using the PES and critiqued based on the properties of the quantum zero-point state. Finally, a simple procedure for adding the long range-interaction energy is described.

We report full-dimensional, ab initio potential energy (PES) and dipole moment surfaces (DMS) for water. The PES is a sum of one-, two- and three-body terms. The three-body potential is a fit, reported here, to roughly 30,000 intrinsic three-body energies obtained with second-order Møller-Plesset perturbation theory (MP2) and using the aug-cc-pVTZ basis set (avtz). The one- and two-body potentials are from an ab initio water dimer potential [Shank et al., J. Chem. Phys. 130, 144314 (2009)]. The predictive accuracy of the PES is demonstrated for the water trimer, tetramer, and hexamer by comparing the energies and harmonic frequencies obtained from the PES and new high level ab initio calculations at the respective global minima. The DMS is constructed from one- and two-body dipole moments, based on fits to MP2/avtz dipole moments. It is shown to be very accurate for the hexamer by comparison with direct calculations of the hexamer dipole. To illustrate the anharmonic character of the PES one-mode calculations of the 18 monomer fundamentals of the hexamer are reported in normal coordinates.