|Posted on June 18, 2014 at 6:45 PM|
In the last years we have worked in the design of a new approximation to the third-order density that just got accepted for publication in J. Chem. Theory Comput. The nth order density is a well-known quantity in quantum mechanics that gives the probability of finding n particles (usually electrons) simultaneously in different location of the molecular space. The first and second-order densities are actually needed for the calculation of the electronic energy of a given molecular system. In principle, higher-order densities do not enter the energy expression, however, the calculations performed with the contracted Schrödinger Equation and its antiHermitian version do use three and four-order density. In addition, the probability of finding three and four electrons depends on these densities. The latter is main focus of our development, since we want to use these quantities to calculate three and four-center indices. In particular, in this paper we study systems with three-center bonds, such as diborane, which contains a three-center two-electron bond.
The approximations we suggest for the third-order densities can be casted in the following expression:
where gamma is the pure three-body part and depends on a parameter a:
This expression can be used with a=1 (HF-like approach) and a=1/2 and a=1/3, which are the approximations suggested in this work. The calculation on a series of molecules proves that a=1/3 works significantly better than other approximations to the third-order density such as Valdemoro's, Mazziotti's or Nakatsuji's. We are currently trying to understand why our approximations works so well and see if its applicability can be extended to other properties.