IRPF90: a programming environment for high performance computing

IRPF90 is a Fortran programming environment which helps the development of large Fortran codes. In Fortran programs, the programmer has to focus on the order of the instructions: before using a variable, the programmer has to be sure that it has already been computed in all possible situations. For large codes, it is common source of error. In IRPF90 most of the order of instructions is handled by the pre-processor, and an automatic mechanism guarantees that every entity is built before being used. This mechanism relies on the {needs/needed by} relations between the entities, which are built automatically. Codes written with IRPF90 execute often faster than Fortran programs, are faster to write and easier to maintain.Comment: 18 pages, 14 figure

An efficient implementation of Slater-Condon rules

Slater-Condon rules are at the heart of any quantum chemistry method as they allow to simplify $3N$-dimensional integrals as sums of 3- or 6-dimensional integrals. In this paper, we propose an efficient implementation of those rules in order to identify very rapidly which integrals are involved in a matrix element expressed in the determinant basis set. This implementation takes advantage of the bit manipulation instructions on x86 architectures that were introduced in 2008 with the SSE4.2 instruction set. Finding which spin-orbitals are involved in the calculation of a matrix element doesn't depend on the number of electrons of the system.Comment: 8 pages, 5 figure

Fixed-Node Diffusion Monte Carlo potential energy curve of the fluorine molecule F2 using selected configuration interaction trial wavefunctions

The potential energy curve of the F$_2$ molecule is calculated with Fixed-Node Diffusion Monte Carlo (FN-DMC) using Configuration Interaction (CI)-type trial wavefunctions. To keep the number of determinants reasonable (the first and second derivatives of the trial wavefunction need to be calculated at each step of FN-DMC), the CI expansion is restricted to those determinants that contribute the most to the total energy. The selection of the determinants is made using the so-called CIPSI approach (Configuration Interaction using a Perturbative Selection made Iteratively). Quite remarkably, the nodes of CIPSI wavefunctions are found to be systematically improved when increasing the number of selected determinants. To reduce the non-parallelism error of the potential energy curve a scheme based on the use of a $R$-dependent number of determinants is introduced. Numerical results show that improved FN-DMC energy curves for the F$_2$ molecule are obtained when employing CIPSI trial wavefunctions. Using the Dunning's cc-pVDZ basis set the FN-DMC energy curve is of a quality similar to that obtained with FCI/cc-pVQZ. A key advantage of using selected CI in FN-DMC is the possibility of improving nodes in a systematic and automatic way without resorting to a preliminary multi-parameter stochastic optimization of the trial wavefunction performed at the Variational Monte Carlo level as usually done in FN-DMC.Comment: 16 pages, 15 figure

A Sparse SCF algorithm and its parallel implementation: Application to DFTB

We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density functional based tight binding method, for which most of the computational time is spent in the linear algebra routines (diagonalization of the Fock/Kohn-Sham matrix). We show that with this algorithm (i) single point calculations on very large systems (millions of atoms) can be performed on large SMP machines (ii) calculations involving intermediate size systems (1~000--100~000 atoms) are also strongly accelerated and can run efficiently on standard servers (iii) the error on the total energy due to the use of a cut-off in the molecular orbital coefficients can be controlled such that it remains smaller than the SCF convergence criterion.Comment: 13 pages, 11 figure

Efficient Monte Carlo Calculations of the One-Body Density

An alternative Monte Carlo estimator for the one-body density rho(r) is presented. This estimator has a simple form and can be readily used in any type of Monte Carlo simulation. Comparisons with the usual regularization of the delta-function on a grid show that the statistical errors are greatly reduced. Furthermore, our expression allows accurate calculations of the density at any point in space, even in the regions never visited during the Monte Carlo simulation. The method is illustrated with the computation of accurate Variational Monte Carlo electronic densities for the Helium atom (1D curve) and for the water dimer (3D grid containing up to 51x51x51=132651 points).Comment: 12 pages with 3 postscript figure

A simple and efficient approach to the optimization of correlated wave functions

We present a simple and efficient method to optimize within energy minimization the determinantal component of the many-body wave functions commonly used in quantum Monte Carlo calculations. The approach obtains the optimal wave function as an approximate perturbative solution of an effective Hamiltonian iteratively constructed via Monte Carlo sampling. The effectiveness of the method as well as its ability to substantially improve the accuracy of quantum Monte Carlo calculations is demonstrated by optimizing a large number of parameters for the ground state of acetone and the difficult case of the $1{}^1{B}_{1u}$ state of hexatriene.Comment: 5 pages, 1 figur

A refutation of the practice style hypothesis: the case of antibiotics prescription by French general practitioners for acute rhinopharyngitis

Many researches in France or abroad have highlighted the medical practice variation (MPV)phenomenon, or even the inappropriateness of certain medical decisions. There is no consensus on the origin of this MPV between preference-centred versus opportunities and constraints approaches. This study principal purpose is to refute hypothesis which assume that physicians adopt for their patient a uniform practice style for each similar clinical decision beyond the time. More specifically, multilevel models are estimated: First to measure variability of antibiotics prescription by French general practitioners for acute rhinopharyngitis, a clinical decision making context with weak uncertainty, and to tests its significance; Second to prioritize its determinants, especially those relating to GP or its practice setting environment, by controlling visit or patient confounders. The study was based on the 2001 activity data, added by an ad hoc questionnaire, of a sample of 778 GPs arising from a panel of 1006 computerized French GPs. We observe that a great part of the total variation was due to intra-physician variability (70%). Hence, in the French general practice context, we find empirical support for the rejection of the ‘practice style’, the ’enthusiasm’ or the ‘surgical signature’ hypothesis. Thus, it is patients' characteristics that largely explain the prescription, even if physicians' characteristics (area of practice, level of activity, network participation, participation in ongoing medical training) and environmental factors (recent visit from pharmaceutical sales representatives) also exert considerable influence. The latter suggest that MPV are partly caused by differences in the type of dissemination or diffusion of information. Such findings may help us to develop and identify facilitators for promoting a better use of antibiotics in France and, more generally, for influencing GPs practice when it is of interest.Medical practice variation, Multilevel analysis, Upper respiratory tract infections, Rhinopharyngitis, Antibiotics, General practitioners, Panel, France

Perturbatively selected configuration-interaction wave functions for efficient geometry optimization in quantum Monte Carlo

We investigate the performance of a class of compact and systematically improvable Jastrow-Slater wave functions for the efficient and accurate computation of structural properties, where the determinantal component is expanded with a perturbatively selected configuration interaction scheme (CIPSI). We concurrently optimize the molecular ground-state geometry and full wave function -- Jastrow factor, orbitals, and configuration interaction coefficients-- in variational Monte Carlo (VMC) for the prototypical case of 1,3-trans-butadiene, a small yet theoretically challenging $\pi$-conjugated system. We find that the CIPSI selection outperforms the conventional scheme of correlating orbitals within active spaces chosen by chemical intuition: it gives significantly better variational and diffusion Monte Carlo energies for all but the smallest expansions, and much smoother convergence of the geometry with the number of determinants. In particular, the optimal bond lengths and bond-length alternation of butadiene are converged to better than one m\AA\ with just a few thousand determinants, to values very close to the corresponding CCSD(T) results. The combination of CIPSI expansion and VMC optimization represents an affordable tool for the determination of accurate ground-state geometries in quantum Monte Carlo

Le polyéthylène hautement réticulé de deuxième génération dopé à la vitamine E versus conventionnel dans l’arthroplastie totale de hanche : étude prospective randomisée à 3 ans minimum de recul

The purpose of this prospective randomized study was to compare the minimum 3-­year follow-­ up penetration of cementless polyethylene sockets of the same design in two configurations in a consecutive series of total hip arthroplasty.Between May 2010 and May 2011, 100 patients (100 hips) with a mean age of 70.8 ± 7.5 years were randomized (power of 80%, alpha of 5%) to receive either vitamin E doped highly cross-­ linked (group Vitamys, 0.1% vitamin E blended, 10 Mrads of gamma radiation, 50 hips) or moderately cross‐linked (group RM, 3 Mrads of gamma radiation in nitrogen, 50 hips) material. The cementless polyethylene cups were coated with pure titanium particles. All other parameters, including the 28 mm diameter metal femoral head, stem, surgical approach and postoperative course were identical in both groups. The primary criterion for evaluation was linear head penetration measurement, using the Martell system, performed by an investigator blinded to the polyethylene type. Both creep and steady state wear were measured.At the time of the minimum 3-­year follow-­up evaluation, 34 hips in the Vitamys group and 32 hips in the RM group have had complete data available for analysis (median follow‐up of 3.02 and 3.13 years, respectively). The median creep measured 0.02 mm versus 0.3 in the Vitamys and RM groups, respectively (Mann-­Whitney, p=0.04). The median steady state penetration rate from one year onwards was ‐0.097 mm/year in the Vitamys group versus 0.064 mm/year in the RM group (Mann and Whitney test, p=0.04). No complication specific to the material was recorded, and no patient was revised because of wear and/or osteolysis.This study provides the first randomized in vivo wear measurements of Vitamin E doped highly cross-­linked acetabular components. These early 3-­year follow-­up results demonstrated encouraging wear performance of vitamin E blended highly cross-­linked polyethylene. Longer term follow-­up is necessary to monitor the performance of these devices.Nous avons prospectivement randomisé 100 arthroplasties primaires totales de hanche (âge moyen 70,8 ans) afin d’analyser la résistance à l’usure in vivo d’un polyéthylène monobloc non cimenté en fonction de sa réticulation. La cupule était soit en polyéthylène hautement réticulé dopé à la vitamine E (Vitamys®, Mathys) soit en polyéthylène conventionnel (RM®, Mathys). Il n’existait aucune différence significative démographique ou opératoire entre les deux groupes.Au recul moyen de 3,08 ans, 66 hanches ont été revues, radiologiquement et cliniquement, et aucune différence fonctionnelle n’était notée. Le taux de pénétration moyen de la tête fémorale était de 0,02 mm dans le groupe Vitamys® et de 0,3 mm dans le groupe RM® (p=0,04).Le taux d’usure moyen à régime constant était de -0,097 mm/an dans le groupe Vitamys® et de 0,064 mm/an dans le groupe RM® (p=0,04). Aucune complication spécifique mécanique liée au matériau n’a été constatée.Ces résultats à 3 ans de recul ont montré d’encourageantes performances en termes d’usure du polyéthylène hautement réticulé dopé à la vitamine E. Des résultats à long terme sont nécessaires pour confirmer l’intérêt de ce polyéthylène hautement réticulé dopé à la vitamine E, notamment au niveau de l’ostéolyse et du taux de survie des implants

Quantum Monte Carlo with very large multideterminant wavefunctions

An algorithm to compute efficiently the first two derivatives of (very) large multideterminant wavefunctions for quantum Monte Carlo calculations is presented. The calculation of determinants and their derivatives is performed using the Sherman-Morrison formula for updating the inverse Slater matrix. An improved implementation based on the reduction of the number of column substitutions and on a very efficient implementation of the calculation of the scalar products involved is presented. It is emphasized that multideterminant expansions contain in general a large number of identical spin-specific determinants: for typical configuration interaction-type wavefunctions the number of unique spin-specific determinants $N_{\rm det}^\sigma$ ($\sigma=\uparrow,\downarrow$) with a non-negligible weight in the expansion is of order ${\cal O}(\sqrt{N_{\rm det}})$. We show that a careful implementation of the calculation of the $N_{\rm det}$-dependent contributions can make this step negligible enough so that in practice the algorithm scales as the total number of unique spin-specific determinants, $\; N_{\rm det}^\uparrow + N_{\rm det}^\downarrow$, over a wide range of total number of determinants (here, $N_{\rm det}$ up to about one million), thus greatly reducing the total computational cost. Finally, a new truncation scheme for the multideterminant expansion is proposed so that larger expansions can be considered without increasing the computational time. The algorithm is illustrated with all-electron Fixed-Node Diffusion Monte Carlo calculations of the total energy of the chlorine atom. Calculations using a trial wavefunction including about 750 000 determinants with a computational increase of $\sim$ 400 compared to a single-determinant calculation are shown to be feasible.Comment: 9 pages, 3 figure