Conditions for describing triplet states in reduced density matrix functional theory

We consider necessary conditions for the one-body-reduced density matrix (1RDM) to correspond to a triplet wave-function of a two electron system. The conditions concern the occupation numbers and are different for the high spin projections, $S_z=\pm 1$, and the $S_z=0$ projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in reduced density matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied

How accurate is the strongly orthogonal geminal theory in predicting excitation energies? Comparison of the extended random phase approximation and the linear response theory approaches

Performance of the antisymmetrized product of strongly orthogonal geminal (APSG) ansatz in describing ground states of molecules has been extensively explored in the recent years. Not much is known, however, about possibilities of obtaining excitation energies from methods that would rely on the APSG ansatz. In the paper we investigate the recently proposed extended random phase approximations, ERPA and ERPA2, that employ APSG reduced density matrices. We also propose a time-dependent linear response APSG method (TD-APSG). Its relation to the recently proposed phase including natural orbital theory is elucidated. The methods are applied to Li2, BH, H2O, and CH2O molecules at equilibrium geometries and in the dissociating limits. It is shown that ERPA2 and TD-APSG perform better in describing double excitations than ERPA due to inclusion of the so-called diagonal double elements. Analysis of the potential energy curves of Li2, BH, and H2O reveals that ERPA2 and TD-APSG describe correctly excitation energies of dissociating molecules if orbitals involved in breaking bonds are involved. For single excitations of molecules at equilibrium geometries the accuracy of the APSG-based methods approaches that of the time-dependent Hartree-Fock method with the increase of the system size. A possibility of improving the accuracy of the TD-APSG method for single excitations by splitting the electron-electron interaction operator into the long- and short-range terms and employing density functionals to treat the latter is presented

Structure of Fermionic Density Matrices: Complete N-representability Conditions

We present a constructive solution to the N-representability problem---a full characterization of the conditions for constraining the two-electron reduced density matrix (2-RDM) to represent an N-electron density matrix. Previously known conditions, while rigorous, were incomplete. Here we derive a hierarchy of constraints built upon (i) the bipolar theorem and (ii) tensor decompositions of model Hamiltonians. Existing conditions D, Q, G, T1, and T2, known classical conditions, and new conditions appear naturally. Subsets of the conditions are amenable to polynomial-time computations of strongly correlated systems

The \gamma function in quantum theory II. Mathematical challenges and paradoxa

While the square root of Dirac’s [Formula: see text] is not defined in any standard mathematical formalism, postulating its existence with some further assumptions defines a generalized function called [Formula: see text] which permits a quasi-classical treatment of simple systems like the H atom or the 1D harmonic oscillator for which accurate quantum mechanical energies were previously reported. The so-defined [Formula: see text] is neither a traditional function nor a distribution, and it remains to be seen that any consistent mathematical approaches can be set up to deal with it rigorously. A straightforward use of [Formula: see text] generates several paradoxical situations which are collected here. The help of the scientific community is sought to resolve these paradoxa

The polymer phase of the TDAE-C60_{60} organic ferromagnet

The high-pressure Electron Spin Resonance (ESR) measurements were preformed on TDAE-C$_{60}$ single crystals and stability of the polymeric phase was established in the $P - T$ parameter space. At 7 kbar the system undergoes a ferromagnetic to paramagnetic phase transition due to the pressure-induced polymerization. The polymeric phase remains stable after the pressure release. The depolymerization of the pressure-induced phase was observed at the temperature of 520 K. Below room temperature, the polymeric phase behaves as a simple Curie-type insulator with one unpaired electron spin per chemical formula. The TDAE$^+$ donor-related unpaired electron spins, formerly ESR-silent, become active above the temperature of 320 K and the Curie-Weiss behavior is re-established.Comment: Submitted to Phys. Rev.

Effect of partitioning on the convergence properties of the Rayleigh-Schrödinger perturbation series

Convergence features of the Rayleigh-Schrödinger perturbation theory (PT) strongly depend on the partitioning applied. We investigate the large order behavior of the Møller-Plesset and Epstein Nesbet partitionings in comparison with a less known partitioning obtained by level shift parameters minimizing the norm of operator QW, with W being the perturbation operator while Q standing for the reduced resolvent of the zero order Hamiltonian H^0. Numerical results, presented for molecular systems for the first time, indicate that it is possible to find level shift parameters in this way which convert divergent perturbation expansions to convergent ones in some cases. Besides numerical calculations of high-order PT terms, convergence radii of the corresponding perturbation expansions are also estimated using quadratic Padé approximants