William H. Green

Upper bound on the yield for oxidative coupling of methane

An approach is presented for determining an upper bound on the yield of a catalytic process, which allows for variations in the catalytic chemistry. Scaling and thermodynamic arguments are used to set parameters of an elementary step surface mechanism at values resulting in optimal yields, subject only to physical constraints. Remaining unknowns are treated as independent variables and varied over a broad range. The result is a set of thermodynamically consistent mechanisms with optimal kinetics that can be incorporated into reactor-transport models to generate yield trajectories. With this approach, an upper bound on the yield for oxidative coupling of methane (OCM) was computed. Results show that even with optimal surface chemistry, limits exist on the attainable yield. Surface energetics necessary for superior OCM performance were identified and the origins of these requirements elucidated. The resulting upper bound on OCM yield under conventional, packed-bed, continuous-feed operation was found to be 28%.

An adaptive chemistry approach to modeling complex kinetics in reacting flows

Abstract Existing algorithms use a single chemical kinetic model over the entire domain of a reacting flow simulation. However, it is well known that the chemistry varies significantly in different regions of a flame. For combustion and other reacting flows with very complex chemistry, computing all possible reactions and species everywhere in the computational domain (the full chemistry approach) is very computationally demanding. Here we propose an adaptive chemistry approach that avoids computing species and reactions in regions where they are negligible. In this approach, a set of reduced chemical kinetic models is used in a simulation, each reduced model being used only under reaction conditions where it is faithful to the full model. A procedure to implement adaptive chemistry is presented, and compared with the conventional full chemistry approach. Adaptive chemistry fairly accurately reproduces the full chemistry solutions, while reducing the cost of the computation both in terms of CPU time and in terms of memory requirements. This was demonstrated by simulating a turbulent planar hydrogen/air shear layer flame and two axisymmetric laminar co-flowing partially premixed methane-air flames. The challenges that need to be overcome to make this method more broadly useful are summarized.

Vibration-rotation coordinates and kinetic energy operators for polyatomic molecules

In molecular vibration-rotation calculations it is frequently desirable to work in a nuclear coordinate system tailored to the nuclear potential energy surface. It is now possible to derive the kinetic energy operator for virtually any coordinate system by using computer algebra programs. We discuss how to choose coordinates for use in practical calculations, in particular variational energy level calculations, with special consideration of the vibration-rotation separation. As an example we present a kinetic energy operator suitable for calculating the rovibrational spectrum of sequentially bonded four-atomic molecules, using valence coordinates. We carry out a rigorous symmetry classification using the MS group, and also consider how the problem of singularities affects the choice of basis set.

THEORETICAL ASSIGNMENT OF THE VISIBLE SPECTRUM OF SINGLET METHYLENE

The potential energy surfaces of the two lowest‐lying singlet electronic states of methylene (CH2) are determined by internally contracted multireference configuration interaction calculations, using a full‐valence reference space, with an extended Gaussian basis set. The rotation–vibration levels on these surfaces are calculated by diagonalizing the rovibrational Hamiltonian matrix in a contracted basis. The rovibronic mixing due to the strong Renner–Teller interaction in this system is treated through the Coriolis term in the kinetic energy operator, using geometry‐dependent electronic angular momentum matrix elements calculated from ab initio wave functions. The agreement between experiment and this high‐quality ab initio calculation is sufficiently good that the calculation can be used to assign the observed vibronic bands in this very complex spectrum, where 90% of the observed lines remain unassigned. Many of the previous vibronic band labels are found to be incorrect. Most of the K>0 bands previous...

Global solution of semi-infinite programs

Abstract.Optimization problems involving a finite number of decision variables and an infinite number of constraints are referred to as semi-infinite programs (SIPs). Existing numerical methods for solving nonlinear SIPs make strong assumptions on the properties of the feasible set, e.g., convexity and/or regularity, or solve a discretized approximation which only guarantees a lower bound to the true solution value of the SIP. Here, a general, deterministic algorithm for solving semi-infinite programs to guaranteed global optimality is presented. A branch-and-bound (B&B) framework is used to generate convergent sequences of upper and lower bounds on the SIP solution value. The upper-bounding problem is generated by replacing the infinite number of real-valued constraints with a finite number of constrained inclusion bounds; the lower-bounding problem is formulated as a convex relaxation of a discretized approximation to the SIP. The SIP B&B algorithm is shown to converge finitely to ɛ−optimality when the subdivision and discretization procedures used to formulate the node subproblems are known to retain certain convergence characteristics. Other than the properties assumed by globally-convergent B&B methods (for finitely-constrained NLPs), this SIP algorithm makes only one additional assumption: For every minimizer x* of the SIP there exists a sequence of Slater points xn for which (cf. Section 5.4). Numerical results for test problems in the SIP literature are presented. The exclusion test and a modified upper-bounding problem are also investigated as heuristic approaches for alleviating the computational cost of solving a nonlinear SIP to guaranteed global optimality.

Ab initio prediction of fundamental, overtone and combination band infrared intensities

Abstract Programs have been implemented for calculating ab initio anharmonic force fields which are quartic in displacement coordinates and, likewise, dipole-moment expansions which are cubic in displacement coordinates. Knowledge of these, and the use of second-order perturbation theory, leads to predictions for fundamental, overtone and combination band infrared intensities as well as the usual spectroscopic constants. Here we use the ab initio MP2 method, with large basis sets, applied to H 2 O and H 2 CO. The results, including those for the overtone and combination band intensities, are in good agreement with the available experimental data.

Learnings from exchange-correlation potentials

Abstract Exchange-correlation potentials V xc ( r ) can be obtained (within an additive constant) from high-quality ab initio electron densities of atoms and small molecules. These potentials show qualitative features not captured by popular density functionals, and highlight unappreciated aspects of electron densities and density functionals. While V xc s generally scale with ρ 1/3 except at very long or short range, the proportionality is more similar to that of hydrogenic systems than to that of the homogeneous electron gas. The Fermi–Amaldi long-range approximation works well into the valence region. The size and location of the large feature at the valence–core transition is system-dependent. This qualitative information can guide the search for improved density functionals.