Density matrix calculations for molecules and clusters I. Theoretical foundations

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Abstract
Binding properties of multiatomic systems are studied on the basis of the McWeeny density matrix method. Exchange and correlation is described by using the local density approximation which causes a non-linear dependence of the total energy on the charge density ρ(r). However, on separating off a suitably chosen background charge density ρ0(r), the exchange-correlation energy can be expressed in terms of the first and second power of the density difference. Hence the total energy becomes a second-degree function in the density matrix elements Dsαβ, depending on the spin orientation s. The minimum of the total energy in the space of these elements can be found directly by the steepest descent method, where the condition of charge conservation and a generalised condition of idempotency for the Dsαβ have to be satisfied. It appears to be an important feature of this method that it avoids explicit calculation of one-particle states.