On the performance of natural orbital functional approximations in the Hubbard model

Strongly correlated materials are now under intense development, and natural orbital functional (NOF) methods seem to be able to capture the physics of these systems. We present a benchmark based on the Hubbard model for a class of commonly used NOF approximations (also known as reduced density matrix functional approximations). Our findings highlight the importance of imposing ensemble N-representability conditions in order to obtain consistent results in systems with either weak or strong electronic correlation, such as the Hubbard system with a varying two-particle interaction parameter. Based on the accuracy of the results obtained using PNOF7, which retrieves a large amount of the total strong nondynamic correlation, the Hubbard model points out that N-representability gives solid foundations for NOF development.

Dispersion interactions within the Piris natural orbital functional theory: The helium dimer

The authors have investigated the description of the dispersion interaction within the Piris natural orbital functional (PNOF) theory. The PNOF arises from an explicit antisymmetric approach for the two-particle cumulant in terms of two symmetric matrices, Delta and Lambda. The functional forms of these matrices are obtained from the generalization of the two-particle system expressions, except for the off-diagonal elements of Delta. The mean value theorem and the partial sum rule obtained for the off-diagonal elements of Delta provide a prescription for deriving practical functionals. In particular, the previous employed approximation {Jpp/2} for the mean values {Jp*} affords several molecular properties but it is incapable to account for dispersion effects. In this work, the authors analyze a new approach for Jp* obtained by factorization of the matrix Delta within the bounds on its off-diagonal elements imposed by the positivity conditions of the two-particle reduced density matrix. Additional terms for the matrix elements of Lambda proportional to the square root of the holes are again introduced to describe properly the occupation numbers of the lowest occupied levels. The authors have found that the cross products between weakly occupied orbitals must be removed from the functional form of Lambda to obtain a correct long-range asymptotic behavior. The PNOF is used to predict the binding energy as well as the equilibrium distance of the helium dimer. The results are compared with the full configuration-interaction calculations and the corresponding experimental data.

Assessment of a new approach for the two-electron cumulant in natural-orbital-functional theory

The Piris natural orbital functional (PNOF) based on a new approach for the two-electron cumulant has been used to predict adiabatic ionization potentials, equilibrium bond distances, and harmonic vibrational frequencies of 18 diatomic molecules. Vertical ionization potentials have been calculated for the same set of diatomic molecules and another set of 20 polyatomic molecules using energy-difference methods as well as the extended Koopman theorem. The PNOF properties compare favorably with the coupled-cluster-doubles results. The calculated PNOF values are in good agreement with the corresponding experimental data, considering the basis sets used (6-31G**).

CD30 expression in follicular lymphoma

The CD30 antigen is a characteristic phenotypic feature of Sternberg-Reed and Hodgkin cells and is also found in a subset of large cell non-Hodgkin's lymphomas. The finding of CD30 positive cells in some centroblastic/centrocytic (cb/cc) follicular lymphomas prompted us to characterize the presence and distribution of CD30 positive cells in this type of lymphoma, using the monoclonal antibody BerH2. CD30 positive cells were present in 17/19 of the cases studied, located mainly at the edge of the neoplastic follicles, but also in some cases in perinodular or T-cell areas. This distribution resembles that found in reactive tonsils and lymph nodes. The majority of these CD30 positive cells in cb/cc lymphoma seem to be B-cells, as suggested by their reactivity with B-cell markers demonstrated by double immunostaining. The nature of these CD30 positive cells is unclear, but they should be taken into consideration in the differential diagnosis of cb/cc lymphoma with lymphocyte predominance Hodgkin's disease.

CD30 expression in non-Hodgkin's lymphoma

The CD30 antigen has been reported as the immunophenotypic hallmark of a recently described category of non-Hodgkin's lymphoma, termed anaplastic large cell lymphoma. From a series of approximately 500 lymphomas, 17 cases showing typical anaplastic features have been identified. They were strongly labelled by monoclonal antibodies recognizing CD30 (Ki-1 or BerH2). However, 36 other lymphomas, mainly high-grade, of non-anaplastic cytology also expressed CD30, either diffusely or focally, with a staining pattern identical to that seen in anaplastic large cell lymphomas. This clearly suggests that such lymphomas cannot be identified solely on the basis of being high-grade non-Hodgkin's lymphomas showing CD30 positivity. From the present results, the distinction between the anaplastic and non-anaplastic types would be better made with antibodies to epithelial membrane antigen than to CD30. Clinical data, available for 48 of the patients (16 with anaplastic large cell lymphomas and 32 with non-anaplastic) revealed no significant differences with regard to age at presentation, sex or clinical signs. A short-term follow-up study of 25 patients revealed that for the first 2 years after diagnosis there were no significant differences in patient survival between anaplastic large cell lymphoma, other CD30+ high-grade lymphomas and all high-grade non-Hodgkin's lymphomas considered together. These findings, which must be confirmed by larger studies, suggest that in a general lymphoma clinic there is probably little justification for differentiating anaplastic large cell lymphomas or CD30+ lymphomas from other high-grade non-Hodgkin's lymphomas.

[Ki-1 non-Hodgkin's lymphoma. A multihospital study of 21 cases]

The Ki-1 monoclonal antibody recognizes a specific membrane antigen of activated lymphoid cells and stains large-cell non Hodgkin's lymphomas and Hodgkin's disease. Thus, it is widely used in the diagnosis of anaplastic lymphomas. Morphologically, the Ki-1 monoclonal non Hodgkin's lymphoma are diffuse of multifocal either classical or cell anaplastic type. The clinical behaviour is similar to the rest of the high grade lymphomas, disseminated at diagnosis but may reach remission after aggressive chemotherapy. The immunophenotype showed T, B or null nature of the latter. The clinical and pathological results of our study carried out in a group of 21 cases ki-1 positive lymphomas is herewith reported.