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.

Time-reversible Born-Oppenheimer molecular dynamics

We present a time-reversible Born-Oppenheimer molecular dynamics scheme, based on self-consistent Hartree-Fock or density functional theory, where both the nuclear and the electronic degrees of freedom are propagated in time. We show how a time-reversible adiabatic propagation of the electronic degrees of freedom is possible despite the non-linearity and incompleteness of the self-consistent field procedure. Time-reversal symmetry excludes a systematic long-term energy drift for a microcanonical ensemble and the number of self-consistency cycles can be kept low (often only 2-4 cycles per nuclear time step) thanks to a good initial guess given by the adiabatic propagation of the electronic degrees of freedom. The time-reversible Born-Oppenheimer molecular dynamics scheme therefore combines a low computational cost with a physically correct time-reversible representation of the dynamics, which preserves a detailed balance between propagation forwards and backwards in time.Comment: 4 pages, 4 figure

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

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

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

O(N) methods in electronic structure calculations

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high performance computers. The linear scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas is then discussed. The applications of linear scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear scaling methods are discussed.Comment: 85 pages, 15 figures, 488 references. Resubmitted to Rep. Prog. Phys (small changes

Carer's perception of and reaction to reassurance seeking in obsessive compulsive disorder

The purpose of the present study is to explore the experience of being asked for reassurance from the perspective of carers of OCD sufferers, and to examine its relationship to sufferers’ reassurance seeking by a direct comparison with data obtained from the person they normally offer reassurance to. Forty-two individuals with OCD and their carers completed alternate versions of the Reassurance Seeking Questionnaire. Result suggest that carers report most commonly providing reassurance when asked to do so, and the frequency of their reassurance provision is associated with how carefully sufferers seek reassurance, rather than their OCD symptom severity. The carer's perspectives on the impact of reassurance provision was accurate; both sufferers and carers perceive that reassurance works only temporarily, but even if the anxiety-relieving effect of reassurance decreases in the medium term, it is likely to be perceived as beneficial because carers accurately perceived that sufferers would feel much worse if they refuse to provide reassurance. The present study is the first to quantitatively investigate carer’s experiences of reassurance provision, and elucidate why carers feel the need to provide it

CXCL13, CCL21, and CXCL12 expression in salivary glands of patients with Sjogren's syndrome and MALT lymphoma: Association with reactive and malignant areas of lymphoid organization

The chemokines (CKs) CXCL13, CCL21, and CXCL12 are known to play differential roles in the organization of the lymphoid tissues and the development of lymphoid malignancies. We investigated the expression of these CKs and their receptors in the salivary glands of Sjogren's syndrome patients with lymphoepithelial lesions (lymphoepithelial sialadenitis or LESA) and in MALT lymphoma to understand their involvement in salivary gland lymphomagenesis. We demonstrate that within salivary glands with LESA and MALT lymphoma the lymphoid CKs CXCL13 and CCL21 are selectively associated with areas of reactive lymphoid proliferation, whereas no significant expression of these molecules was detected in the malignant lymphoid aggregate. Conversely, CXCL12 was observed predominantly in infiltrated ducts and malignant B cells. Accordingly, CXCL13 and CCL21 transcript levels were significantly increased in LESA samples while CXCL12 levels were increased in MALT lymphoma and isolated tumor cells. Low levels of CK receptors were detected on lymphoma-extracted lymphocytes, suggesting down-regulation in the abundance of ligands. Our findings suggest that in salivary gland MALT lymphoma the lymphoid CKs CXCL13 and CCL21 are directly implicated in the organization of ectopic reactive lymphoid tissue, whereas CXCL12 is associated with the infiltrated epithelium and malignant B cell component and is possibly involved in the regulation of malignant B cell survival