Double factorial function

The double action pistol enables the firer firstly to cock the hammer and rotate the cylinder and then to release the hammer - all as a result of one long trigger pull. In most designs the weapon can also be thumb-cocked like a single action revolver. The first double action revolver of significance was produced by Beaumont in London in 1855. This could function as either a double action or single action revolver, and the idea was used in the Adams revolver which became the official Brit service revolver. Colt then gave up his Brit factory in 1857 and returned to the USA. His six-chambered percussion 1860 model in. 44 cal was extensively used in the American Civil War and more than 200,000 were made... 

Full configuration interaction (FCI) by definition gives the exact n-particle energy within the given basis set. (Since it is the exact solution, this happens irrespective of the quality of the zero-order wave function.) Because its computational requirements ascend factorially with the size of the system, application to practical systems using one-particle basis sets of useful size will be essentially impossible for the foreseeable future. Even using the fastest available computational hardware and parallelized codes, an FCI calculation on H2O in a double-zeta plus polarization basis set is about the state of the art at present. ... 

Of particular interest with respect to applications in nanotechnology is the rotary supramolecular motor, FoFi-ATP synthase (Figure 1) (S). This enzyme is actually a double rotary motor. Proton flux across the membrane drives rotation of the Fo unit and the y spindle of the Fi unit. Rotation of the y spindle within the stationary Fi unit, in turn, drives the synthesis of ATP from ADP and inorganic phosphate. While the rotary motion of this device qualifies it as a motor, this motion is merely a mechanism, enabling its biological function as a factory for a ubiquitous fuel needed by cells. 

How might we approximate the variational CCD approach discussed above, without incurring its factorial computational cost Let us briefly re-examine the conventional CCD energy ansatz as a prelude to discussing how we have chosen to go beyond it. In conventional CC theory the equations that determine the doubles amplitudes can be obtained by minimizing the following functional ... 

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