A goal in chemistry has been to use a pair of electrons to represent any number of electrons accurately. A new method allows the use of pairs or trios of electrons to approximate any number of electrons. Since 1993, we have had approximations that were 71-96% accurate. A new method is 95-100% accurate. University of Chicago chemist David Mazziotti has created an improved solution for the contracted Schrodinger equation.
The behavior of electrons in atoms and molecules affects many significant chemical reactions that govern everyday phenomena, including the fuel efficiency of combustion engines, the depletion of ozone in the atmosphere, and the design of new medicines.
The contracted Schrödinger equation may soon become solvable with a package of computer software, according to Mazziotti.
Motivated by the contracted Schrödinger equation, we have also recently developed variational two-electron methods with systematic, nontrivial N-representability conditions. This second class of two-electron methods directly computes the effective two-electron probability distribution of a many-electron atom or molecule without any higher-electron probability distributions. Variational optimization of the ground-energy energy in terms of only two effective electrons is treatable by a class of optimization techniques known as semidefinite programming. The variational two-electron method has been accurately applied to generating potential energy surfaces of molecules including the difficult-to-predict dissociation curve for N2 where wavefunction methods fail to give physically meaningful results.
While two-electron approaches are still in their early stages, the direct determination of chemical properties by mapping any atom or molecule onto an effective twoelectron problem offers a new level of accuracy and efficiency for electronic structure calculations.