Molecular integrals over generalized gaussian basis sets

A method is given for obtaining the common molecular integrals over generalized gaussian functions: The present algorithms are expected to be more efficient than those given in earlier work by the same author.     

Uniform convergence and computation of the generalized exponential integrals

In this paper, uniform convergence of the generalized exponential (GE) integrals is investigated. We also study the continuity, differentiability, summability and asymptotic behaviour of GE integrals. Then we give an accurate and efficient computation algorithm for these integrals.     

Molecular integrals in the generalized hylleraas–CI method

In the generalized Hylleraas–CI method, the original correlation factor r^v_ij is multiplied by a Gaussian geminal. Using the approach of generating functions, the general formulas of molecular integrals in this method are derived over Cartesian Gaussian orbitals. From differentiations of the generating functions, the expanding length in the incomplete Gamma functions is reduced, and some cancellations presented in other approaches are avoided. Preliminary calculations for H₂ and H₂—H₂ systems are carried out over STO -3G basis. The results are encouraging.     

A generalized method to calculate diffusion rates in polydisperse systems. Further results on Rouse dynamics in the concentrated regime

Experiments designed to thoroughly test a recently proposedgeneralized method to calculate diffusion rates in polydisperse systems have been carried out. Polydisperse polystyrene (PS) samples were allowed to diffuse in a poly(phenylene oxide) (PPO) matrix. Designed blends were made from anionically polymerized PS with molecular weights which cover most of the ranges where Rouse dynamics control the diffusion processes. The diffusion temperatures range from (T_g – 1 K) to (T_g + 105 K), causing the monomeric friction factor values for PS to change by up to seven orders of magnitude along the diffusion coordinate. Calculations performed with the above mentioned method agree with Raman and DMA experimental data.     

Further results on systematic regularities of molecular SCF energies

Two new approximate formulas to compute molecular electronic energy are tested with regard to a set of 55 molecules of nearly double-zeta quality in order to complement previous work. Although qualitative results are in line with recent findings, the numerical data shows a potentially significant disagreement.     

Some properties of generalized secant integrals: extended definition and recurrence relations

Line sources with slab shields represent typical source–shield configurations in gamma-ray attenuation problems. Such shielding problems often lead to the generalized secant integrals of the form

Recently, the author has developed rapidly convergent infinite-series representation of generalized secant integrals involving incomplete gamma functions. The validity of this representation was established for zero and positive values of the integral parameter a (a0). In this paper the definition is extended to include negative real a values. It is demonstrated that the introduced series representation is still valid. In addition, general recurrence relations are established that allow precise calculation of the integral for negative a values.     

Efficient electronic integrals and their generalized derivatives for object oriented implementations of electronic structure calculations

For the new parallel implementation of electronic structure methods in ACES III (Lotrich et al., in preparation) the present state-of-the-art algorithms for the evaluation of electronic integrals and their generalized derivatives were implemented in new object oriented codes with attention paid to efficient execution on modern processors with a deep hierarchy of data storage including multiple caches and memory banks. Particular attention has been paid to define proper integral blocks as basic building objects. These objects are stand-alone units and are no longer tied to any specific software. They can hence be used by any quantum chemistry code without modification. The integral blocks can be called at any time and in any sequence during the execution of an electronic structure program. Evaluation efficiency of these integral objects has been carefully tested and it compares well with other fast integral programs in the community. Correctness of the objects has been demonstrated by several application runs on real systems using the ACES III program.     

Further results on the triple point temperature of pure Ne and Ne

The paper reports further results following the 2010 determinations at INRIM of the triple point temperature of the neon isotopes ²⁰Ne and ²²Ne, obtained on nearly-pure samples sealed in cryogenic cells, carrying an uncertainty much lower than the previous determinations. The further results, performed in the same experimental apparatus with an expanded uncertainty (k ≈ 2) of ≈30 μK for a single cell and ≈50 μK for the comparison of sample pairs, were obtained using the same model of cryogenic metal sealed cell for each sample, and by measuring different samples from the same gas batch of each isotope and from different gas batches showing a different content of isotopic and chemical impurities. The new determinations were intended to check the effect of measuring different samples and the gas batches, and of performing corrections based on different analytical assays for the isotopic and chemical impurities. The new results are in agreement with the previous determinations, confirming, with greater confidence, the value of the temperature difference for the two pure isotopes, 0.14658 K with an expanded uncertainty of 0.00007 K, and the temperature values on ITS-90 24.5422 K for ²⁰Ne and 24.6888 K for ²²Ne, within the larger expanded uncertainty, 0.00032 K, due to the present ambiguity of the ITS-90 definition. These values are also consistent with new determinations published by other laboratories. In addition, the ITS-90 values of INRIM 2010 determinations of T_tp of samples of neon (INRIM Ec2Ne, INRIM E4Ne, PTB Ne12, NPL Ne2) of natural isotopic composition with different ²²Ne amount concentrations are reported, consistent with the values obtained for pure isotopes.     

Predictive aging results in radiation environments

We have previously derived a time-temperature-dose rate superposition methodology, which, when applicable, can be used to predict polymer degradation versus dose rate, temperature and exposure time. This methodology results in predictive capabilities at the low dose rates and long time periods appropriate, for instance, to ambient nuclear power plant environments. The methodology was successfully applied to several polymeric cable materials and then verified for two of the materials by comparisons of the model predictions with 12 year, low-dose-rate aging data on these materials from a nuclear environment. In this paper, we provide a more detailed discussion of the methodology and apply it to data obtained on a number of additional nuclear power plant cable insulation (a hypalon, a silicone rubber and two ethylene-tetrafluoroethylenes) and jacket (a hypalon) materials. We then show that the predicted, low-dose-rate results for our materials are in excellent agreement with long-term (7–9 year) low-dose-rate results recently obtained for the same material types actually aged under bnuclear power plant conditions. Based on a combination of the modelling and long-term results, we find indications of reasonably similar degradation responses among several different commercial formulations for each of the following “generic” materials: hypalon, ethylene-tetrafluoroethylene, silicone rubber and PVC. If such “generic” behavior can be further substantiated through modelling and long-term results on additional formulations, predictions of cable life for other commercial materials of the same generic types would be greatly facilitated.     

High-precision quantum thermochemistry on nonquasiharmonic potentials: converged path-integral free energies and a systematically convergent family of generalized Pitzer-Gwinn approximations

Accurate quantum mechanical (QM) vibrational-rotational partition functions for HOOD, D(2)O(2), H(18)OOH, H(2)(18)O(2), D(18)OOH, and H(18)OOD are determined using a realistic potential energy surface for temperatures ranging from 300 to 2400 K by using the TT-FPI-ESPE path-integral Monte Carlo method. These data, together with our prior results for H(2)O(2), provide benchmarks for testing approximate methods of estimating isotope effects for systems with torsional motions. Harmonic approximations yield poor accuracy for these systems, and although the well-known Pitzer-Gwinn (PG) approximation provides better results for absolute partition functions, it yields the same results as the harmonic approximation for isotope effects because these are intrinsically quantal phenomena. We present QM generalizations of the PG approximation that can provide high accuracy for both isotope effects and absolute partition functions. These approximations can be systematically improved until they approach the accurate result and converge rapidly. These methods can also be used to obtain affordable estimates of zero-point energies from accurate partition functions-even those at relatively high temperatures.     

Restriction on approximations of molecular integrals

The results of LCAO-MO-SCF calculations applied to molecules have to be invariant with respect to orthogonal transformations of the basis set of atomic orbitals. However, if the multicenter repulsion integrals needed for such a calculation are approximated, invariancy will in general not be retained. For two methods of approximation the behaviour of the multicenter integrals under such transformations has been investigated, along with the conditions which have to be fulfilled to ensure this invariancy.

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Zusammenfassung Ergebnisse von LCAO-MO-SCF-Rechungen an Molekülen werden nichtinvariant gegen orthogonale Basistransformationen, wenn für die Mehrzentrenintegrale Näherungsausdrücke verwendet werden. Für zwei Näherungsmethoden wird der Einfluß der Transformationen auf die Mehrzentrenintegrale untersucht; Bedingungen für bestimmte Invarianzeigenschaften werden angegeben.

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Résumé Les résultats d'un calcul LCAO-MO-SCF doivent être invariants par rapport aux transformations orthogonales de la base des orbitales atomiques. Cette invariance n'est en général pas respectée si les intégrales de répulsion multicentriques nécessaires pour un tel calcul sont évaluées d'une manière approchée. Le comportement des intégrales multicentriques lors de telles transformations a été étudié par deux méthodes d'approximation; on a envisagé les conditions à remplir pour satisfaire à l'invariance.

     

Further examination of the BEBO model with the results of ab initio calculations of a reaction series

The BEBO (bond energy-bond order) model is further examined with results of ab initio calculations on a series of metathetic reactions involving hydrogen transfer. Energies are calculated at the 6–31G^**/PMP2=full/6–31G^** level while the bond-orders are estimated using the 6–31G^** basis set with the geometry optimisation at the single configuration unrestricted Hartree-Fock frame. Our analysis reveals that for all thermoneutral reactions where the making and breaking bonds are collinear in the transition state, the reduced distensions in the transition state structures are same and independent of the bond-order exponent in the BEBO model. For others such displacements increase with the square of the energy changes during reactions. The Bronsted coefficient is examined and is found to be neither strictly parallel to the position of the barrier in the reaction path nor a measure of the ‘transition state’ structure of the system.     

Proof of a conjecture by Dacre on the symmetry of two-electron integrals

A format proof is given of a statement by Dacre concerning the effect of symmetry operators on two-electron integrals.     

Influence of solar ultraviolet-B radiation on Antarctic terrestrial plants: results from a 4-year field study.

We examined the influence of solar ultraviolet-B radiation (UV-B; 280-315 nm) on the performance of Antarctic vascular plants (Colobanthus quitensis and Deschampsia antarctica) by placing filters that either absorbed or transmitted most solar UV-B over tundra along the Antarctic Peninsula for four consecutive growing seasons. The difference in biologically effective UV-B levels between our treatments was 65%, which was similar to the enhancement in ambient UV-B levels that appeared attributable to ozone depletion during the first 2 months of the growing season (November and December) at our site (62%). In both species, exposure to UV-B reduced vegetative growth, primarily through slower leaf elongation rates that led to shorter fully expanded leaves. In C. quitensis, exposure to UV-B also led to reductions in leaf longevity, branch production, cushion diameter growth, aboveground biomass, and thickness of the non-green cushion base and litter layer. Exposure to UV-B accelerated the development of reproductive structures and increased the number of panicles (D. antarctica) and capsules (C. quitensis) that reached maturity per unit of ground surface area covered by mother plants. However, this effect was offset by a tendency for these panicles and capsules to produce fewer spikelets and seeds. Ultimately, UV-B exposure did not effect the numbers of spikelets or seeds produced per unit of ground surface area. While seeds from plants exposed to UV-B tended to be lighter, germination rates were similar between UV-B treatments. The relative reductions in leaf elongation rates in D. antarctica attributable to UV-B exposure increased from the first (23%) through the fourth (43%) growing season, and relative reductions in leaf longevity in C. quitensis tended to increase from the first (9%) through the fourth (19%) growing season, suggesting that UV-B growth responses tended to be cumulative over successive years.     

Evaluation of two-center,two- and three-electron integrals involving correlation factors over Slater-type orbitals. II. Kinetic and potential energy integrals and examples of numerical results

This article is concerned with the construction of the general algorithm for evaluating two-center, two- and three-electron integrals occurring in matrix elements of one-electron operators in the basis of variational correlated functions. This problem has been solved here in prolate spherical coordinates, using the modified and extended form of the Neumann expansion of the interelectronic distance function r^k_ij derived in Part I of this series for k = ?1, 0, 1, 2. This work expands the method proposed by one of us in the preceding paper for integrals of the types mentioned above. The results of numerical calculations for different types of the two- and three-electron integrals are presented. The problem of convergence of the proposed procedures used is also discussed.