In what follows a two-particle interacting system having a hxed and weU-dehned number of particles N will be considered. It will also be considered that the one-electron space is spanned by a hnite basis set of 2K orthonormal spin orbitals. Under these conditions the 1-RDM and 2-RDM elements are dehned in second [Pg.207]

Three types of two-particle interactions can occur. Each is represented by a horizontal dashed interaction line. For the nucleus-nucleus interaction this line is terminated by open dots, o, at both end, that is [Pg.46]

Of particular interest is a system of two particles interacting by way of a time-independent potential V(r — r2 that only depends on the relative coordinate r= (ri - r2). The classical Hamiltonian of the system is given by [Pg.334]

The Umn s of Eq. (3) contain two-particle interactions, including Coulomb, exchange, and dipole-dipole contributions, which are parameterized according to semi-empirical functional forms [61]. The parameters are adapted to PPV and are then transposed by scaling to other polymer species. [Pg.192]

The second term in our new total energy expression is a short-range repulsive two-particle interaction and contains a correction for double counting the electrons in the band energy. It is equal to E = - E. Symbolically, the new total energy expression can, therefore, be written as [Pg.238]

Hamiltonian for this problem, in terms of one- and two-particle interactions is [Pg.339]

Andersen,E.,andUHLHORN,U., r n K>m 13,165/ Approach to the quantum mechanical many-body problem with strong two-particle interaction/ [Pg.357]

We can justify the above conclusion as follows. If H involves at most two-particle interactions, it is expressible as [Pg.7]

If 5(2) is restricted to be an anti-Hermitian operator with no more than two-particle interactions, the variational degrees of freedom of 5(2) can be [Pg.334]

Rosina s theorem states that for an unspecified Hamiltonian with no more than two-particle interactions the ground-state 2-RDM alone has sufficient information to build the higher ROMs and the exact wavefunction [20, 51]. Cumulants allow us to divide the reconstruction functional into two parts (i) an unconnected part that may be written as antisymmetrized products of the lower RDMs, and (ii) a connected part that cannot be expressed as products of the lower RDMs. As shown in the previous section, cumulant theory alone generates all of the unconnected terms in RDM reconstruction, but cumulants do not directly indicate how to compute the connected portions of the 3- and 4-RDMs from the 2-RDM. In this section we discuss a systematic approximation of the connected (or cumulant) 3-RDM [24, 26]. [Pg.179]

Theorem 1 The 2-RDM for the antisymmetric, nondegenerate ground state of an unspecified N-particle Hamiltonian H with two-particle interactions has a unique preimage in the set of N-ensemble representable density matrices D. [Pg.171]

In these relationships the summation is carried out using (6.25), (6.26) and (6.18). Let us now introduce averaged submatrix elements of two-particle interactions separately for singlet states [Pg.136]

As we show later, the energy of the state of any system of N indistinguishable fermions or bosons can be expressed in terms of the Hamiltonian and D (12,1 2 ) if its Hamiltonian involves at most two-particle interactions. Thus it should be possible to find the ground-state energy by variation of the 2-matrix, which depends on four particles. Contrast this with current methods involving direct use of the wavefunction that involves N particles. A principal obstruction for this procedure is the A-representability conditions, which ensure that the proposed RDM could be obtained from a system of N identical fermions or bosons. [Pg.4]

The form of the potential for the system under study was discussed in many publications [28,202,207,208]. Effective pair potentials are widely used in theoretical estimates and numerical calculations. When a many-particle interatomic potential is taken into account, the quantitative description of experimental data improves. For example, the consideration of three-body interactions along with two-particle interactions made it possible to quantitatively describe the stratification curve for interstitial hydrogen in palladium [209]. Let us describe the pair interaction of all the components (hydrogen and metal atoms in the a. and (j phases) by the Lennard Jones potential cpy(ry) = 4 zi [(ff )12- / )6], where Sy and ai are the parameters of the corresponding potentials. All the distances ry, are considered within c.s. of radius r (1 < r < R), where R is the largest radius of the radii of interaction Ry between atoms / and /). [Pg.422]

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