Expansion algorithm for the density matrix

A purification algorithm for expanding the single-particle density matrix in terms of the Hamiltonian operator is proposed. The scheme works with a predefined occupation and requires less than half the number of matrix-matrix multiplications compared to existing methods at low (90%) occupancy. The expansion can be used with a fixed chemical potential in which case it is an asymmetric generalization of and a substantial improvement over grand canonical McWeeny purification. It is shown that the computational complexity, measured as number of matrix multiplications, essentially is independent of system size even for metallic materials with a vanishing band gap.Comment: 5 pages, 4 figures, to appear in Phys. Rev.

Density Matrix Perturbation Theory

An expansion method for perturbation of the zero temperature grand canonical density matrix is introduced. The method achieves quadratically convergent recursions that yield the response of the zero temperature density matrix upon variation of the Hamiltonian. The technique allows treatment of embedded quantum subsystems with a computational cost scaling linearly with the size of the perturbed region, O(N_pert.), and as O(1) with the total system size. It also allows direct computation of the density matrix response functions to any order with linear scaling effort. Energy expressions to 4th order based on only first and second order density matrix response are given.Comment: 4 pages, 2 figure

Fear of childbirth during pregnancy: associations with observed mother-infant interactions and perceived bonding.

Fear of childbirth (FOC) is a common phenomenon that can impair functioning in pregnancy but potential longer term implications for the mother-infant relationship are little understood. This study was aimed at investigating postpartum implications of FOC on the mother-infant relationship. A UK sample of 341 women in a community setting provided data on anxiety, mood and FOC in mid-pregnancy and subsequently completed self-report measures of postnatal bonding in a longitudinal cohort study. Postnatal observations of mother-infant interactions were collected and rated for a subset of 141 women. FOC was associated with maternal perception of impaired bonding, even after controlling for sociodemographic factors, concurrent depression and the presence of anxiety disorders (Coef = 0.10, 95% CI 0.07-0.14, p < 0.001). Observed mother-infant interactions were not associated with FOC (Coef = -0.01-0.03 CI - 0.02 to 0.02, p = 0.46), weakly with concurrent depression (Coef = - 0.10, CI - 0.19 to 0.00, p = 0.06) and not associated with anxiety disorders. The self-efficacy component of FOC was most strongly associated with lower reported bonding (Coef 0.37, 95% CI 0.25-0.49, p < 0.001) FOC makes a distinct contribution to perceived postpartum bonding difficulties but observed mother-infant interaction quality was not affected. This may be due to low self-efficacy impacting psychological adjustment during pregnancy. Targeted interventions during pregnancy focusing both on treatment of key childbirth fears and bonding could help women adjust earlier

Linear Scaling Solution of the Coulomb problem using wavelets

The Coulomb problem for continuous charge distributions is a central problem in physics. Powerful methods, that scale linearly with system size and that allow us to use different resolutions in different regions of space are therefore highly desirable. Using wavelet based Multi Resolution Analysis we derive for the first time a method which has these properties. The power and accuracy of the method is illustrated by applying it to the calculation of of the electrostatic potential of a full three-dimensional all-electron Uranium dimer

Design and Evaluation of Image Guidance Systems for RARP

INTRODUCTION: There is a strong appetite amongst laparoscopic surgeons for image guidance during the procedure. It seems intuitively obvious that providing the surgeon with additional information on the location of unseen anatomy can only improve patient outcomes. This is not necessarily the case however. If the system gives information that is not relevant to the procedure it becomes a distraction. Similarly, if the system has large alignment errors the information may be dangerously wrong. One danger is that image guidance systems can be developed on an ad-hoc basis based not on targeted clinical goals but on the technical expertise and research goals of the scientists and engineers involved. Such a system may or may not benefit the patient. However, there is a real danger, as discussed by [1], that such systems will be introduced into surgical practice without proper assessment. We present our minimalist image guidance system for robot assisted radical prostatectomy together with a design and evaluation framework built upwards from the desired clinical outcomes

Linear scaling computation of the Fock matrix VII. Periodic Density Functional Theory at the Γ\Gamma-point

Linear scaling quantum chemical methods for Density Functional Theory are extended to the condensed phase at the $\Gamma$-point. For the two-electron Coulomb matrix, this is achieved with a tree-code algorithm for fast Coulomb summation [J. Chem. Phys. {\bf 106}, 5526 (1997)], together with multipole representation of the crystal field [J. Chem. Phys. {\bf 107}, 10131 (1997)]. A periodic version of the hierarchical cubature algorithm [J. Chem. Phys. {\bf 113}, 10037 (2000)], which builds a telescoping adaptive grid for numerical integration of the exchange-correlation matrix, is shown to be efficient when the problem is posed as integration over the unit cell. Commonalities between the Coulomb and exchange-correlation algorithms are discussed, with an emphasis on achieving linear scaling through the use of modern data structures. With these developments, convergence of the $\Gamma$-point supercell approximation to the ${\bf k}$-space integration limit is demonstrated for MgO and NaCl. Linear scaling construction of the Fockian and control of error is demonstrated for RBLYP/6-21G* diamond up to 512 atoms

Ab initio linear scaling response theory: Electric polarizability by perturbed projection

A linear scaling method for calculation of the static {\em ab inito} response within self-consistent field theory is developed and applied to calculation of the static electric polarizability. The method is based on density matrix perturbation theory [Niklasson and Challacombe, cond-mat/0311591], obtaining response functions directly via a perturbative approach to spectral projection. The accuracy and efficiency of the linear scaling method is demonstrated for a series of three-dimensional water clusters at the RHF/6-31G** level of theory. Locality of the response under a global electric field perturbation is numerically demonstrated by approximate exponential decay of derivative density matrix elements.Comment: 4.25 pages in PRL format, 2 figure