Density matrix functional theory

A. Nagy, Density-matrix functional theory. Phys. Rev. A 66, 022505 (2002). 

A. Nagy and C. Amovilli, Effective potential in density matrix functional theory. J. Chem. Phys. 121, 6640-6648 (2004). 

Zumbach G, Maschke K (1985) Density-matrix functional theory for the A -particle ground state, J Chem Phys, 82 5604-5607... 

Yasuda K (2002) Local approximation of the correlation energy functional in the density matrix functional theory, Phys Rev Lett, 88 053001... 

Lathiotakis NN, Helbig N, Gross EKU (2005) Open shells in reduced-density-matrix-functional theory, Phys Rev A, 72 030501... 

Pernal K, Cioslowski J (2002) Density matrix functional theory of weak intermolecular interactions, J Chem Phys, 116 4802-4807... 

Regions (i), (ii) and (iii) correspond to the TF semiclassical form already discussed above. Region (iv), as Lieb et al. [36] point out, can be treated by a simple density matrix functional theory. It is, however, region (v) which can be discussed very naturally in terms of the Pauli potential introduced above. 

If one compares the attempts reviewed in sec. 3.2 to base majiy-electron quantum mechanics on the two-particle density matrix, i.e. a 2-particle density matrix functional theory with the current density functional theory one realizes that for the former the functional is exactly known, while the full n-representability condition is unknown. For DFT on the other hand, the functional is unknown, but the n representability does not cause problems. Why should one take incomplete information on n-representability as more serious as lack of information on the exact functional Possibly there was just more reluctance in the two-particle-density matrix functional community to be satisfied with approximate n-representability conditions than in the density functional community to accept approximate density functionals, and that this different attitude was decisive for the historical development. 

The DFT will of course be further elaborated. There are already investigations under way, which will allow us to calculate the dispersion energy. The impetus will probably be directed towards such methods as the Density Matrix Functional Theory (DMFT) proposed by Levy, and currently being developed by Jerzy Cioslowski. The idea is to abandon p(r) as the central quantity, and instead use the one-particle density matrix F(r, r )... 

Shells in Reduced-Density-Matrix-Functional Theory. 

The feasibility of time-dependent density matrix functional theory (TDDMFT) for calculating response properties has been demonstrated by proposing an improvement over the static approximation of the coupling matrix K(co) and by applying it to the HeH prototype system. 

Yang WT, Zhang YK, Ayers PW (2000) Degenerate ground states and fractional number of electrons in density and reduced density matrix functional theory. Phys Rev Lett 84 5172-5175... 

Equation (95) reveals an interesting link between g-density functional theory and g-matrix functional theory. Consider rewriting Eq. (95) in a form analogous to Eq. (83),... 

We have recently suggested yet another approach [48] based upon the conclusions of the density matrix functional analysis of Donnelly and Parr [61]. It follows from their analysis that in the absence of the fixed occupation constraints of the HF theory, i.e., in the Natural Orbital (NO) representation,... 

The influence functional theory, as it was formulated by Feyman and Vernon, relies on the additional assumption concerning factorization of the total (system and bath) density matrix in the past. Without this assumption the theory requires a triple path integral, with one thermal integration over the imaginary time axis [Grabert et al. 1988]. 

It is clear that the density matrix formalism renders a considerable simplification of the basis for the quantum theory of many-particle systems. It emphasizes points of essential physical and chemical interests, and it avoids more artificial or conventional ideas, as for instance different types of basic orbitals. The question is, however, whether this formalism can be separated from the wave function idea itself as a fundament. Research on this point is in progress, and one can expect some interesting results within the next few years. 

It is also of interest to study the "inverse" problem. If something is known about the symmetry properties of the density or the (first order) density matrix, what can be said about the symmetry properties of the corresponding wave functions In a one electron problem the effective Hamiltonian is constructed either from the density [in density functional theories] or from the full first order density matrix [in Hartree-Fock type theories]. If the density or density matrix is invariant under all the operations of a space CToup, the effective one electron Hamiltonian commutes with all those elements. Consequently the eigenfunctions of the Hamiltonian transform under these operations according to the irreducible representations of the space group. We have a scheme which is selfconsistent with respect to symmetty. 

Forda, M.J., Hoft, R.C. and Gale, J.D. (2006) Adsorption and dimerisation of thiol molecules on Au(lll) using a Z-matrix approach in density functional theory. Molecular Simulation, 32, 1219-1225. 

White, C. A., Head-Gordon, M., 1996, A 7-Matrix Engine for Density Functional Theory Calculations , J. Chem. 

Nowak, M. J., L. Lapinski, J. S. Kwiatkowski, and J. Leszczynski. 1996. Molecular Structure and Infrared Spectra of Adenine—Experimental Matrix Isolation and Density Functional Theory Study of Adenine N-15 Isotopomers. J. Phys. Chem. 100, 3527. 

---