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Difference sets and their generalisations to difference families arise from the study of designs and many other applications. Here we give a brief survey of some of these applications, noting in particular the diverse definitions of difference families and the variations in priorities in constructions. We propose a definition of disjoint difference families that encompasses these variations and allows a comparison of the similarities and disparities. We then focus on two constructions of disjoint difference families arising from frequency hopping sequences and showed that they are in fact the same. We conclude with a discussion of the notion of equivalence for frequency hopping sequences and for disjoint difference families.

We adapt the method of Monte Carlo configuration interaction to calculate core-hole states and use this for the computation of X-ray emission and absorption values. We consider CO, CH$_{4}$, NH$_{3}$, H$_{2}$O, HF, HCN, CH$_{3}$OH, CH$_{3}$F, HCl and NO using a 6-311G** basis. We also look at carbon monoxide with a stretched geometry and discuss the dependence of its results on the cutoff used. The Monte Carlo configuration interaction results are compared with EOM-CCSD values for X-ray emission and with experiment for X-ray absorption. Oscillator strengths are also computed and we quantify the multireference nature of the wavefunctions to suggest when approaches based on a single reference would be expected to be successful., Comment: 13 pages, 2 figures

We propose using sum-over-states calculations with the compact wavefunctions of Monte Carlo configuration interaction to approach accurate values for higher-order dipole properties up to second hyperpolarizabilities in a controlled way. We apply the approach to small systems that can generally be compared with full configuration interaction (FCI) results. We consider hydrogen fluoride with a 6-31g basis and then look at results, including frequency dependent properties, in an aug-cc-pVDZ basis. We extend one calculation beyond FCI by using an aug-cc-pVTZ basis. The properties of an H$_{4}$ molecule with multireference character are calculated in an aug-cc-pVDZ basis. We then investigate this method on a strongly multireference system with a larger FCI space by modelling the properties of carbon monoxide with a stretched geometry. The behavior of the approach with increasing basis size is considered by calculating results for the neon atom using aug-cc-pVDZ to aug-cc-pVQZ. We finally test if the unusual change in polarizability between the first two states of molecular oxygen can be reproduced by this method in a 6-31g basis., Comment: 11 pages, 14 figures

We calculate potential curves for transition metal dimers using Monte Carlo configuration interaction (MCCI). These results, and their associated spectroscopic values, are compared with experimental and computational studies. The multireference nature of the MCCI wavefunction is quantified and we estimate the important orbitals. We initially consider the ground state of the chromium dimer. Next we calculate potential curves for Sc$_{2}$ where we contrast the lowest triplet and quintet states. We look at the molybdenum dimer where we compare non-relativistic results with the partial inclusion of relativistic effects via effective core potentials, and report results for scandium nickel., Comment: 9 pages and 8 figures

We introduce state-averaging into the method of Monte Carlo configuration interaction (SA-MCCI) to allow the stable and efficient calculation of excited states. We show that excited potential curves for H$_{3}$, including a crossing with the ground state, can be accurately reproduced using a small fraction of the FCI space. A recently introduced error measure for potential curves [J. P. Coe and M. J. Paterson, J. Chem. Phys., 137, 204108 (2012)] is shown to also be a fair approach when considering potential curves for multiple states. We demonstrate that potential curves for LiF using SA-MCCI agree well with the FCI results and the avoided crossing occurs correctly. The seam of conical intersections for CH$_{2}$ found by Yarkony [J. Chem. Phys., 104, 2932 (1996)] is used as a test for SA-MCCI and we compare potential curves from SA-MCCI with FCI results for this system for the first three triplet states. We then demonstrate the improvement from using SA-MCCI on the dipole of the $2$ $^{1}A_{1}$ state of carbon monoxide. We then look at vertical excitations for small organic molecules up to the size of butadiene where the SA-MCCI energies and oscillator strengths are compared with CASPT2 values [M. Schreiber, M. R. Silva-Junior, S. P. A. Sauer, and W. Thiel, J. Chem. Phys., 128, 134110 (2008)]. We finally see if the SA-MCCI results for these excitation energies can be improved by using MCCIPT2 with approximate natural orbitals when the PT2 space is not onerously large., Comment: 12 pages, 9 figures

We introduce natural transition geminals as a means to qualitatively understand a transition where double excitations are important. The first two $A_{1}$ singlet states of the CH cation are used as an initial example. We calculate these states with configuration interaction singles (CIS) and state-averaged Monte Carlo configuration interaction (SA-MCCI). For each method we compare the important natural transition geminals with the dominant natural transition orbitals. We then compare SA-MCCI and full configuration interaction (FCI) with regards to the natural transition geminals using the beryllium atom. We compare using the natural transition geminals with analyzing the important configurations in the CI expansion to give the dominant transition for the beryllium atom and the carbon dimer. Finally we calculate the natural transition geminals for two electronic excitations of formamide., Comment: 15 pages, 2 figures. Mol. Phys. (2013)

Approximate natural orbitals are investigated as a way to improve a Monte Carlo configuration interaction (MCCI) calculation. We introduce a way to approximate the natural orbitals in MCCI and test these and approximate natural orbitals from MP2 and QCISD in MCCI calculations of single-point energies. The efficiency and accuracy of approximate natural orbitals in MCCI potential curve calculations for the double hydrogen dissociation of water, the dissociation of carbon monoxide and the dissociation of the nitrogen molecule are then considered in comparison with standard MCCI when using full configuration interaction as a benchmark. We also use the method to produce a potential curve for water in an aug-cc-pVTZ basis. A new way to quantify the accuracy of a potential curve is put forward that takes into account all of the points and that the curve can be shifted by a constant. We adapt a second-order perturbation scheme to work with MCCI (MCCIPT2) and improve the efficiency of the removal of duplicate states in the method. MCCIPT2 is tested in the calculation of a potential curve for the dissociation of nitrogen using both Slater determinants and configuration state functions., Comment: 11 pages, 11 figures

This paper describes the use of a distributed cloud computing system for high-throughput computing (HTC) scientific applications. The distributed cloud computing system is composed of a number of separate Infrastructure-as-a-Service (IaaS) clouds that are utilized in a unified infrastructure. The distributed cloud has been in production-quality operation for two years with approximately 500,000 completed jobs where a typical workload has 500 simultaneous embarrassingly-parallel jobs that run for approximately 12 hours. We review the design and implementation of the system which is based on pre-existing components and a number of custom components. We discuss the operation of the system, and describe our plans for the expansion to more sites and increased computing capacity.

The method of Monte Carlo configuration interaction (MCCI) [1,2] is applied to the calculation of multipole moments. We look at the ground and excited state dipole moments in carbon monoxide. We then consider the dipole of NO, the quadrupole of the nitrogen molecule and of BH. An octupole of methane is also calculated. We consider experimental geometries and also stretched bonds. We show that these non-variational quantities may be found to relatively good accuracy when compared with FCI results, yet using only a small fraction of the full configuration interaction space. MCCI results in the aug-cc-pVDZ basis are seen to generally have reasonably good agreement with experiment. We also investigate the performance of MCCI when applied to ionisation energies and electron affinities of atoms in an aug-cc-pVQZ basis. We compare the MCCI results with full configuration-interaction quantum Monte Carlo [3,4] and `exact' non-relativistic results [3,4]. We show that MCCI could be a useful alternative for the calculation of atomic ionisation energies however electron affinities appear much more challenging for MCCI. Due to the small magnitude of the electron affinities their percentage errors can be high, but with regards to absolute errors MCCI performs similarly for ionisation energies and electron affinities., Comment: 12 pages, 20 figures

We apply the method of Monte Carlo configuration interaction (MCCI) to calculate ground-state potential energy curves for a range of small molecules and compare the results with full configuration interaction. We show that the MCCI potential energy curve can be calculated to relatively good accuracy, as quantified using the non-parallelity error, using only a very small fraction of the FCI space. In most cases the potential curve is of better accuracy than its constituent single-point energies. We finally test the MCCI program on systems with basis sets beyond full configuration interaction: a lattice of fifty hydrogen atoms and ethylene. The results for ethylene agree fairly well with other computational work while for the lattice of fifty hydrogens we find that the fraction of the full configuration interaction space we were able to consider appears to be too small as, although some qualitative features are reproduced, the potential curve is less accurate., Comment: 14 pages, 22 figures

We show that distributed Infrastructure-as-a-Service (IaaS) compute clouds can be effectively used for the analysis of high energy physics data. We have designed a distributed cloud system that works with any application using large input data sets requiring a high throughput computing environment. The system uses IaaS-enabled science and commercial clusters in Canada and the United States. We describe the process in which a user prepares an analysis virtual machine (VM) and submits batch jobs to a central scheduler. The system boots the user-specific VM on one of the IaaS clouds, runs the jobs and returns the output to the user. The user application accesses a central database for calibration data during the execution of the application. Similarly, the data is located in a central location and streamed by the running application. The system can easily run one hundred simultaneous jobs in an efficient manner and should scale to many hundreds and possibly thousands of user jobs., Comment: 6 pages, 4 figures, conference paper

The availability of Infrastructure-as-a-Service (IaaS) computing clouds gives researchers access to a large set of new resources for running complex scientific applications. However, exploiting cloud resources for large numbers of jobs requires significant effort and expertise. In order to make it simple and transparent for researchers to deploy their applications, we have developed a virtual machine resource manager (Cloud Scheduler) for distributed compute clouds. Cloud Scheduler boots and manages the user-customized virtual machines in response to a user's job submission. We describe the motivation and design of the Cloud Scheduler and present results on its use on both science and commercial clouds., Comment: 10 pages, 1 figure