Application of the two‐body density matrix of the ground state for calculations of some excited states

Abstract

AbstractsIt is pointed out that the density matrices of the ground state contain valuable information concerning the calculation of particle-hole excited states. As an illustration, results on the nuclei I6O, Ne, and "Si are presented, using small model spaces. 0I1 est mis en tvidence que les matrices densitks de I'ttat fondamental contiennent des informations importantes pour le calcul des 6tats excites de type particule-trou. A titre d'illustration on pr6sente des r6sultats pour les noyaux l60, 20Ne, et 28Si, obtenus avec de petits espaces de modble.Es wird darauf hingewiesen, dass die Dichtematrizen des Grundzustands wertvolle Information fur die Berechnung von angeregten Teilchen-Loch-Zustanden enthalten. Als Illustration werden Ergebnisse fur die Kerne l 6 0 , "Ne, und 28Si vorgelegt, die mit kleinen Modellraumen erhalten worden sind.

Energy Density Functional Theory of Many-Electron Systems

“…Harriman (1977;1978a, b; proposed a geometric analysis of N -representability problem, and in particular, derived the necessary conditions for the spin components of 2-matrices [See also Why man et al (1976)]. In that context the number of papers on applications of the N -representability problem has remained restricted to Yery few manybody systems [Elson et al (1969a,b), Kijewski nd Percus (1970), Lowdin and Lim (1970); Garrod et al (1975); r.Iihailovic and Rosina (1975); Rosina and Garrod (1975), Garrod and Fusco (1976), Garrod (1978), Rosina (1978), Erdhal (1979), and Erdhal et al (1979]. (1963), Coleman (1963Coleman ( ,1969Coleman ( ,1978Coleman ( ,1981Coleman ( ,1987, , Erdhal (1969Erdhal ( ,1987, Harriman (1973), Peat (1914Peat ( ,1975, Kryachko and Kruglyak (1975), Davidson (1976), ?lIestechkin (1977.…”

“…Kijewski and Percus (1969) have demonstrated that the Bopp's 2-matrices does not satisfy the Pauli condition. Such approach leads to "almost" N-representable 2matrices (Simons and Harriman, 1970;Simons, 1971;Garrod et al, 1975;Mihailm"ic and Rosina, 1975;Rosina and Garrod, 1975;Garrod and Fusco, 1976;Garrod, 1978;Rosina, 1978;Erdhal, 1979;Erdhal et al,1979). There is another way of applying the N -representability conditions in quantum chemical calculations which also leads to lower bounds.…”

The Ubiquitous Extended Koopmans’ Theorem

“…The third possibility uses the reconstruction idea that p ‐RDMs can be approximately expressed in terms of the q ‐RDM (). For instance, in the case of single excitations m = 1, Equation can be re‐casted in the form involving only the 2‐RDM, by neglecting the 3‐cRDM or by using the Hermitian or anti‐Hermitian operator method in which the higher RDMs are eliminated by selecting the basis functions to be Hermitian or anti‐Hermitian …”

Excited-State Spectra of Strongly Correlated Molecules from a Reduced-Density-Matrix Approach

“…In this Letter, we improve a theory for the computation of excited-state spectra from any ground-state two-electron reduced density matrix (2-RDM). − In the excited-spectra RDM theory known as the Hermitian operator method, − ,, the excited-state energies are computed in the space of p-electron transitions from the correlated ground-state wave function from a knowledge of only the 2 p -RDM. Previous work developed and applied the theory for p = 1 to small molecular systems with accurate results, ,,, but applications to both larger and more correlated molecules were hindered by ill-conditioning of the effective eigenvalue problem.…”

“…In this Letter, we present a Hamiltonian-shifted regularization of a family of excited-spectra RDM-based methods for computing excited-state energies from knowledge of ground-state RDMs. In particular, we focus on a specific ES-2RDM-based method with Hermitian single-particle transition operators, also known as the Hermitian operator method. − , The Hamiltonian-shifted regularization removes the singularities of the generalized eigenvalue equation that are not well-treated by the traditional deflation method. The 2-RDM method is explored through its application to a set of strongly correlated molecules including hydrogen and n -acene chains, a nickel dithiolate dianion, and a conjugated dye.…”