Variation method spirit

Variational electrostatic projection method. In some instances, the calculation of PMF profiles in multiple dimensions for complex chemical reactions might not be feasible using full periodic simulation with explicit waters and ions even with the linear-scaling QM/MM-Ewald method [67], To remedy this, we have developed a variational electrostatic projection (VEP) method [75] to use as a generalized solvent boundary potential in QM/MM simulations with stochastic boundaries. The method is similar in spirit to that of Roux and co-workers [76-78], which has been recently... 

Within each type of distilled spirits, wide variations of flavor can be achieved by the type and amount of starting grains or other fermentable materials, methods of preparation, types of yeasts, fermentation conditions, distillation process, maturation time and temperature, blending, and use of new technologies such as membrane separation. 

Distillation.—At this stage of the process there are several interesting variations from Scotch and Irish methods of distillation. Note, on the diagrams, that by means of a bypass system the beer well may be connected to either the whiskey or spirit stills these are both termed beer columns, although they are really distinct kinds of stills. 

Presently, the widely used post-Hartree-Fock approaches to the correlation problem in molecular electronic structure calculations are basically of two kinds, namely, those of variational and those of perturbative nature. The former are typified by various configuration interaction (Cl) or shell-model methods, and employ the linear Ansatz for the wave function in the spirit of Ritz variation principle (c/, e.g. Ref. [21]). However, since the dimension of the Cl problem rapidly increases with increasing size of the system and size of the atomic orbital (AO) basis set employed (see, e.g. the so-called Paldus-Weyl dimension formula [22,23]), one has to rely in actual applications on truncated Cl expansions (referred to as a limited Cl), despite the fact that these expansions are slowly convergent, even when based on the optimal natural orbitals (NOs). Unfortunately, such limited Cl expansions (usually truncated at the doubly excited level relative to the IPM reference, resulting in the CISD method) are unable to properly describe the so-called dynamic correlation, which requires that higher than doubly excited configurations be taken into account. Moreover, the energies obtained with the limited Cl method are not size-extensive. 

The difficulty with VMC is exactly identical in spirit to all the problems of traditional methods the basis-set problem. Although the wavefunction is vastly improved in VMC, it is difficult to know when the wavefunction form is sufficiently flexible, and therefore it is always necessary to show that the basis-set limit of a given class of trial function has been reached. Moreover, the accuracy of energy in no way implies accuracy of other properties. One can assume that many of the variational errors cancel out in going from one system to another, but it is not very hard to find counterexamples. With the current class of wavefunctions it seems that we are far from getting chemical accuracies from VMC when applied to systems more complex than the electron gas or a single atom. In addition, in VMC one can waste a lot of time trying new forms rather than have the computer do the work. This problem is solved in a different way in the next two methods we discuss. 

These experimental modifications represent various applications of the Fourier method and all can be accommodated within the design spirit of Figure 1. Furthermore, the optical features of the Michel son interferometer shown in Figure 1 are only schematic. In the actual design and construction of interferometers which operate in the visible/UV region, several variations from this schematic representation have been implemented. 

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