Analytic nuclear forces and molecular properties from full configuration interaction quantum Monte Carlo

Unbiased stochastic sampling of the one- and two-body reduced density matrices is achieved in full configuration interaction quantum Monte Carlo with the introduction of a second, "replica" ensemble of walkers, whose population evolves in imaginary time independently from the first, and which entails only modest additional computational overheads. The matrices obtained from this approach are shown to be representative of full configuration-interaction quality, and hence provide a realistic opportunity to achieve high-quality results for a range of properties whose operators do not necessarily commute with the hamiltonian. A density-matrix formulated quasi-variational energy estimator having been already proposed and investigated, the present work extends the scope of the theory to take in studies of analytic nuclear forces, molecular dipole moments and polarisabilities, with extensive comparison to exact results where possible. These new results confirm the suitability of the sampling technique and, where sufficiently large basis sets are available, achieve close agreement with experimental values, expanding the scope of the method to new areas of investigation.Comment: 11 page

Lower Bounds for Ground States of Condensed Matter Systems

Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems. Here we study a complementary method that determines lower bounds on the ground state energy in a systematic fashion, scales polynomially in the system size and gives direct access to correlation functions. This is achieved by relaxing the positivity constraint on the density matrix and replacing it by positivity constraints on moment matrices, thus yielding a semi-definite programme. Further, the number of free parameters in the optimization problem can be reduced dramatically under the assumption of translational invariance. A novel numerical approach, principally a combination of a projected gradient algorithm with Dykstra's algorithm, for solving the optimization problem in a memory-efficient manner is presented and a proof of convergence for this iterative method is given. Numerical experiments that determine lower bounds on the ground state energies for the Ising and Heisenberg Hamiltonians confirm that the approach can be applied to large systems, especially under the assumption of translational invariance.Comment: 16 pages, 4 figures, replaced with published versio

Correct quantum chemistry in a minimal basis from effective Hamiltonians

We describe how to create ab-initio effective Hamiltonians that qualitatively describe correct chemistry even when used with a minimal basis. The Hamiltonians are obtained by folding correlation down from a large parent basis into a small, or minimal, target basis, using the machinery of canonical transformations. We demonstrate the quality of these effective Hamiltonians to correctly capture a wide range of excited states in water, nitrogen, and ethylene, and to describe ground and excited state bond-breaking in nitrogen and the chromium dimer, all in small or minimal basis sets

Variational two-particle density matrix calculation for the Hubbard model below half filling using spin-adapted lifting conditions

The variational determination of the two-particle density matrix is an interesting, but not yet fully explored technique that allows to obtain ground-state properties of a quantum many-body system without reference to an $N$-particle wave function. The one-dimensional fermionic Hubbard model has been studied before with this method, using standard two- and three-index conditions on the density matrix [J. R. Hammond {\it et al.}, Phys. Rev. A 73, 062505 (2006)], while a more recent study explored so-called subsystem constraints [N. Shenvi {\it et al.}, Phys. Rev. Lett. 105, 213003 (2010)]. These studies reported good results even with only standard two-index conditions, but have always been limited to the half-filled lattice. In this Letter we establish the fact that the two-index approach fails for other fillings. In this case, a subset of three-index conditions is absolutely needed to describe the correct physics in the strong-repulsion limit. We show that applying lifting conditions [J.R. Hammond {\it et al.}, Phys. Rev. A 71, 062503 (2005)] is the most economical way to achieve this, while still avoiding the computationally much heavier three-index conditions. A further extension to spin-adapted lifting conditions leads to increased accuracy in the intermediate repulsion regime. At the same time we establish the feasibility of such studies to the more complicated phase diagram in two-dimensional Hubbard models.Comment: 10 pages, 2 figure

Increase of CSF inflammatory profile in a case of highly active multiple sclerosis

BACKGROUND: Clinical and imaging follow-up coupled with cerebrospinal fluid (CSF) and possibly serum profiling could provide information on disease activity and disability evolution in multiple sclerosis patients. CASE PRESENTATION: We describe the case of a relapsing-remitting MS patient whose history was characterized by failure of several therapeutic approaches and sustained disease activity. By using a highly sensitive immunoassay methodology, we examined protein expression of 70 inflammatory/cytotoxic molecules in two consecutive paired CSF and serum samples, obtained respectively in 2006 and 2013. At disease diagnosis, elevated CSF protein levels of an inflammatory pattern, including CXCL13, CXCL12, IFNγ, TNF, sTNFR1, IL8, sCD163, APRIL, BAFF, pentraxin III and MMP2 were found compared with a group of controls. At the second lumbar puncture, sustained disease activity was accompanied by considerable (more than 2 fold changes) increase expression of most of these inflammatory molecules while no significant changes in serum inflammatory markers were detected in the two consecutive serum samples. CONCLUSIONS: Elevated CSF protein expression of pro-inflammatory mediators, possibly specifically associated to GM demyelination, could remain stable or increase over time in patients with active multiple sclerosis. We underline the role of fluid analysis in understanding the pathophysiology of the disease and providing information on possible markers of disease activity and evolution

Site-specific abnormalities in the visual system of a mouse model of CDKL5 deficiency disorder

CDKL5 deficiency disorder (CDD) is a neurodevelopmental disorder characterized by a severe global developmental delay and early-onset seizures. Notably, patients show distinctive visual abnormalities often clinically diagnosed as cortical visual impairment. However, the involvement of cerebral cortical dysfunctions in the origin of the symptoms is poorly understood. CDD mouse models also display visual deficits, and cortical visual responses can be used as a robust biomarker in CDKL5 mutant mice. A deeper understanding of the circuits underlying the described visual deficits is essential for directing preclinical research and translational approaches. Here, we addressed this question in two ways: first, we performed an in-depth morphological analysis of the visual pathway, from the retina to the primary visual cortex (V1), of CDKL5 null mice. We found that the lack of CDKL5 produced no alteration in the organization of retinal circuits. Conversely, CDKL5 mutants showed reduced density and altered morphology of spines and decreased excitatory synapse marker PSD95 in the dorsal lateral geniculate nucleus and in V1. An increase in the inhibitory marker VGAT was selectively present in V1. Second, using a conditional CDKL5 knockout model, we showed that selective cortical deletion of CDKL5 from excitatory cells is sufficient to produce abnormalities of visual cortical responses, demonstrating that the normal function of cortical circuits is dependent on CDKL5. Intriguingly, these deficits were associated with morphological alterations of V1 excitatory and inhibitory synaptic contacts. In summary, this work proposes cortical circuit structure and function as a critically important target for studying CDD

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.Comment: 11 pages, considerably enlarged introduction and motivation, remainder of the paper unchange

Variational determination of the two-electron reduced density matrix within the doubly occupied configuration interaction scheme: An extension to the study of open-shell systems

This work proposes to describe open-shell molecules or radicals using the framework of the doubly occupied configuration interaction (DOCI) treatments, so far limited to closed-shell system studies. The proposal is based on considering molecular systems in singlet states generated by adding extra hydrogen atoms located at infinite distance from the target radical system. The energy of this radical is obtained by subtracting the energies of the dissociated hydrogen atoms from that provided by the two-electron reduced density matrix corresponding to the singlet state system in the DOCI space, which is variationally calculated by imposing a set of N-representability conditions. This method is numerically assessed by describing potential energy curves and reduced density matrices in selected ionic and neutral open-shell systems in the doublet spin symmetry ground state.Fil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Torre, Alicia. Universidad del País Vasco; EspañaFil: Lain, Luis. Universidad del País Vasco; EspañaFil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; ArgentinaFil: Ríos, Elías Daniel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas; ArgentinaFil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Assessment of DXA derived bone quality indexes and bone geometry parameters in early breast cancer patients: A single center cross-sectional study

Background: Bone mineral density (BMD) lacks sensitivity in individual fracture risk assessment in early breast cancer (EBC) patients treated with aromatase inhibitors (AIs). New dual-energy X-ray absorptiometry (DXA) based risk factors are needed. Methods: Trabecular bone score (TBS), bone strain index (BSI) and DXA parameters of bone geometry were evaluated in postmenopausal women diagnosed with EBC. The aim was to explore their association with morphometric vertebral fractures (VFs). Subjects were categorized in 3 groups in order to evaluate the impact of AIs and denosumab on bone geometry: AI-naive, AI-treated minus (AIDen-) or plus (AIDen+) denosumab. Results: A total of 610 EBC patients entered the study: 305 were AI-naive, 187 AIDen-, and 118 AIDen+. In the AI-naive group, the presence of VFs was associated with lower total hip BMD and T-score and higher femoral BSI. As regards as bone geometry parameters, AI-naive fractured patients reported a significant increase in femoral narrow neck (NN) endocortical width, femoral NN subperiosteal width, intertrochanteric buckling ratio (BR), intertrochanteric endocortical width, femoral shaft (FS) BR and endocortical width, as compared to non-fractured patients. Intertrochanteric BR and intertrochanteric cortical thickness significantly increased in the presence of VFs in AIDen- patients, not in AIDen+ ones. An increase in cross-sectional area and cross-sectional moment of inertia, both intertrochanteric and at FS, significantly correlated with VFs only in AIDen+. No association with VFs was found for either lumbar BSI or TBS in all groups. Conclusions: Bone geometry parameters are variably associated with VFs in EBC patients, either AI-naive or AI treated in combination with denosumab. These data suggest a tailored choice of fracture risk parameters in the 3 subgroups of EBC patients