Eagle Ford shale

A much-quoted fact is that ab initio calculations scale as the fourth power of the number of basis functions for ground-state, closed-shell systems. This scaling factor arises because each two-electron integral (pr Arr) involves four basis functions, so the number of two-electron integrals would be expected to increase in proportion to the fourth power of the number of basis functions. In fact, the number of such integrals is not exactly equal to the fourth power of the number of basis functions because many of the integrals are related by symmetry. We can calculate exactly the number of two-electron integrals that are required in a Hartree-Fock ab initio calculation as follows. There are seven different types of two-electron integral  [c.139]

We shall now comment in some detail on the approach developed by Banow, Dixon, and Duxbury (BDD) [74], bistorically the first one of those we classify in the category of pragmatic ones. BDD extracted from the complete vibration-rotation Hamiltonian the terms describing the bending vibrations and the z-axis rotations. They employed the operator derived by Freed and Lombaidi (FL) [75], differing from Eqs. (35)-(37) in the choice of the molecule-bound coordinate system. In the FL s Hamiltonian, the axes of the moving system are attached to the instantaneous principal moments of inertia of the molecule, being the optimal choice for handling the molecular rotations. In the case of symmetric triatomics (ABA) undergoing infinitesimal stretching vibrations, the axes of the HC s molecule-bound frame [48,50] coincide with those prefened by FL (note that the last term in the FL s operator should be multiplied by 2 to become equal to the correspond term in the HC Hamiltonian).  [c.510]

The force of propulsion must be exerted by some object other than the one being propelled. Forces always appear as pairs. As expressed by Newton s third law, the object being propelled and the propelling agent interact by equal, opposite and simultaneous forces. For instance a runner pushes against the starting blocks and the starting blocks push against the runner, impelling him forward. A ship s screw pushes against the water propelling it backward, and the water pushes against the ship s screw, propelling the ship foiward. The rocket exhaust thrusts against the rocket, propelling it forward as the rocket thrusts the exhaust hackw ard. And the wind pushes against the sail, propelling the boat forward as the sail pushes against the wind, slowing it down or deflecting its motion.  [c.966]

See pages that mention the term Eagle Ford shale : [c.242]   
Sourse beds of petroleum (1942) -- [ c.4 , c.292 , c.293 , c.294 , c.295 , c.296 , c.297 , c.298 , c.299 , c.300 , c.301 , c.302 , c.303 , c.304 , c.305 , c.306 , c.307 , c.308 , c.309 , c.310 , c.311 , c.312 , c.313 , c.314 , c.315 , c.316 , c.317 , c.318 , c.319 , c.320 , c.321 , c.322 , c.323 , c.324 , c.325 , c.326 , c.327 , c.328 , c.329 , c.330 , c.331 , c.332 , c.333 , c.334 ]