We have used an exact stochastic simulation of the Scbroedinger equation for charged Bosons and Fermions to calculate the correlation energies, to locate the transitions to their respective crystal phases at zero temperature within 10%, and to establish the stability at intermediate densities of a ferro magnetic fluid of electrons.-DBClAmil-Irat book war prappyd »*i icnum ot aork ronraora) by at ajney ot tm UniM SUM GMmnM. Naithar Urn Undid Sut«t GoMnmant mr my urncy tfarool. nc viy of (Mr fanloyaa. iraka any warranty, ctprtr* or Itnpliad. or moras any tagai Udtaitv or naxrndbiUiy tor Tht auonjcy, ton«i«unan. or irartutnoi ol any htfUfiiraiiuo. raarattM. product, or pracM dhdoMl, or nprotoon tfut Hi ma would not Intrinpt pntataly onnod rfcd3& rWwnEi naiaki to any ajatJtlc ra-nmarcirj product, proom. or artica by traao nana, tiaoaraark. rratkitacnira-, or tfntrani, ekaa not iwuswiay ecratllutl Or brdy In ndgnaon, njoomnanDBtion. or tOronra oy tta) (Jornal Scans CoMjmaiii or my aarcy Thmat.Thi alara md oplntonj at authori yatpntad ranrin do not i'OLiaoinvint»oirofladityM»olTniUyta3 5lawGorai»iaiiiort«fy«^r^

~ metho~ is outli~ed by which it is possible to calculate exactly the behavior of several hundred inter-act~ng claSSical par~lcles. The ~tudy of this many-body problem is carried out by an electronic computer which solves numencally the simultaneous equations of motion. The limitations of this numerical scheme are enum.erat:? and t~e important steps in ~aking the program efficient on the computers are indicated. The. al?phcablhty ?f t~s ~ethod to the solutIOn of many problems in both equilibrium and nonequilibrium statistical mechamcs IS discussed.

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The ground-state energies of H2, LiH, Li2, and H2O are calculated by a fixed-node quantum Monte Carlo method, which is presented in detail. For each molecule, relatively simple trial wave functions ΨT are chosen. Each ΨT consists of a single Slater determinant of molecular orbitals multiplied by a product of pair-correlation (Jastrow) functions. These wave functions are used as importance functions in a stochastic approach that solves the Schrödinger equation by treating it as a diffusion equation. In this approach, ΨT serves as a ‘‘guiding function’’ for a random walk of the electrons through configuration space. In the fixed-node approximation used here, the diffusion process is confined to connected regions of space, bounded by the nodes (zeros) of ΨT. This approximation simplifies the treatment of Fermi statistics, since within each region an electronic probability amplitude is obtained which does not change sign. Within these approximate boundaries, however, the Fermi problem is solved exactly. The energy obtained by this procedure is shown to be an upper bound to the true energy. For the molecular systems treated, at least as much of the correlation energy is accounted for with the relatively simple ΨT’s used here as by the best configuration interaction calculations presently available.

No abstract