Free Complement Research Articles

Relativistic free complement method for correctly solving the Dirac equation with the applications to hydrogen isoelectronic atoms

The accuracy of the relativistic free complement (FC) method, which was previously reported for solving the Dirac–Coulomb equations of atoms and molecules, has been strictly examined with the applications to hydrogen isoelectronic atoms. The FC wave function grown up by the Hamiltonian automatically takes care of the correct relationship between large and small components, i.e., FC or ICI balance. Combining the FC method with the inverse Hamiltonian method can help to obtain correct solutions safely against to several obstacles characteristic to the Dirac–Coulomb equation. To ensure the exactness of the obtained wave function, we examined the total square deviation from the exact wave function, local energy constancy, H-square error, and energy upper and lower bounds for hydrogen-like atoms.

SOLVING THE SCHRÖDINGER AND DIRAC EQUATIONS FOR A HYDROGEN ATOM IN THE UNIVERSE'S STRONGEST MAGNETIC FIELDS WITH THE FREE COMPLEMENT METHOD

The free complement method for solving the Schr¨ odinger and Dirac equations has been applied to the hydrogen atom in extremely strong magnetic fields. For very strong fields such as those observed on the surfaces of white dwarf and neutron stars, we calculate the highly accurate non-relativistic and relativistic energies of the hydrogen atom. We extended the calculations up to field strengths that exceed the strongest magnetic field (∼10 15 G) ever observed in the universe on a magnetar surface. These are the first reported accurate quantum mechanical calculations ever to include such strong fields. Certain excited state bands in extremely strong fields showed perfect diamagnetism with an infinite number of degenerate states with the same energies as for a hydrogen atom in the absence of a field. Our method of solving the Schr¨ odinger and Dirac equations provides an accurate theoretical

LiH potential energy curves for ground and excited states with the free complement local Schrödinger equation method

The two lowest singlet and triplet Σ + potential energy curves of LiH were calculated using the free complement (FC) local Schrödinger equation (LSE) method. The overall potential curves and the properties calculated therefrom, like equilibrium bond length, dissociation energy, adiabatic and vertical excitation energies, zero point energy, vibrational spacings, etc., demonstrated the high accuracy of the FC LSE method for both the ground and excited states in comparison to the reference calculations and experiments.

Mannose binding lectin deficiency and triglyceride-rich lipoprotein metabolism in normolipidemic subjects

Mannose binding lectin (MBL) is one of the three initiators of complement activation and is therefore closely linked to inflammation. MBL deficiency has been associated with the generation of atherosclerosis. Since atherosclerosis, the complement system and postprandial lipemia are linked to inflammation, we studied postprandial lipoprotein metabolism in MBL deficiency. An observational study was carried out in 107 volunteers (21% MBL deficient). Classical cardiovascular risk factors were not different between subjects with and without MBL deficiency. Oral fat loading tests in 8 MBL deficient and 14 MBL sufficient subjects showed similar postprandial triglyceride, free fatty acid, hydroxybutyric acid and complement component 3 concentrations. MBL deficient subjects had 2.4 times lower postprandial Sf > 400 (chylomicron)–apoB48 concentrations, but in contrast a 2–3.5 times increased Sf 60–400 (VLDL1–TG) and Sf 60–400–apoB100 response. MBL activity was inversely related to the postprandial Sf 60–400–TG increase. Despite lower postprandial Sf > 400–apoB48 concentrations, MBL deficient subjects show an accumulation of Sf 60–400 lipoproteins.

Solving non-Born–Oppenheimer Schrödinger equation for hydrogen molecular ion and its isotopomers using the free complement method

The Schrödinger equations for the hydrogen molecular ion (H(2)(+)) and its isotopomers (D(2)(+), T(2)(+), HD(+), HT(+), and DT(+)) were solved very accurately using the free iterative complement interaction method, which is referred to in short as the free complement (FC) method, in the non-Born-Oppenheimer (non-BO) level, i.e., in the nonrelativistic limit. Appropriate complement functions for both electron and nuclei were generated automatically by the FC procedure with the use of the non-BO Hamiltonian, which contains both electron and nuclear operators on an equal footing. Quite accurate results were obtained not only for the ground state but also for the vibronic excited states. For example, we obtained the ground-state energy of H(2)(+) as -0.597 139 063 123 405 074 834 134 096 025 974 142 a.u., which is variationally the best in literature. The difference in the nuclear spin states of (1)S (para) and (3)P (ortho) of H(2)(+) and some physical expectation values for several of the isotopomers shown above were also examined. The present study is the first application of the FC method to molecular systems with the non-BO Hamiltonian.

How does the free complement wave function become accurate and exact finally for the hydrogen atom starting from the Slater and Gaussian initial functions and for the helium atom on the cusp conditions?

AbstractThe free complement (FC) method, or the free iterative‐complement‐interaction (ICI) method, for generating the exact wave function from an approximate initial wave function has been applied to the hydrogen atom starting from the Slater and Gaussian functions for comparison. The process of improvement was followed by checking the wave function itself and other quantities that have definite exact values. Because the exact wave function is simple in this case, we could make clear analyses for many aspects of the wave function. We examined the energy, the wave function itself, the wave function error, the H‐square error, the local energy near the nucleus, and the cusp. Both the Slater and Gaussian functions gave similar convergence rates to the exact function with respect to the order of the FC method, but the number of complement functions at a particular order is three times larger for the Gaussian case than for the Slater case. Although the cusp value of the Gaussian initial function is zero, it grows as the FC calculation proceeds and finally becomes essentially exact at convergence. The same was true for all the quantities studied here, irrespective of the type of the initial wave function. For the helium atom, the cusp conditions including the electron–electron cusp were also examined with the FC wave function calculated before and shown to converge to the exact values. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

How Accurately Does the Free Complement Wave Function of a Helium Atom Satisfy the Schrödinger Equation?

The local energy defined by Hpsi/psi must be equal to the exact energy E at any coordinate of an atom or molecule, as long as the psi under consideration is exact. The discrepancy from E of this quantity is a stringent test of the accuracy of the calculated wave function. The H-square error for a normalized psi, defined by sigma2 identical with psi|(H-E)2|psi, is also a severe test of the accuracy. Using these quantities, we have examined the accuracy of our wave function of a helium atom calculated using the free complement method that was developed to solve the Schrödinger equation. Together with the variational upper bound, the lower bound of the exact energy calculated using a modified Temple's formula ensured the definitely correct value of the helium fixed-nucleus ground state energy to be -2.903,724,377,034,119,598,311,159,245, 194,4 a.u., which is correct to 32 digits.

Comparative hepatic gene expression profiling of rats treated with 1H,1H,2H,2H-heptadecafluorodecan-1-ol or with pentadecafluorooctanoic acid

Pentadecafluorooctanoic acid is an established peroxisome proliferator. Little is known about effects of treatment with 1H,1H,2H,2H-heptadecafluorodecan-1-ol, which is metabolized to pentadecafluorooctanoic acid. We compared effects of various dosages (3, 10, or 25 mg/kg body wt) of each of these compounds on hepatic gene expression in rats with microarrays. Microarray data were validated by real-time RT-PCR. Expression data were also correlated with hepatic activities of selected enzymes and with hepatic levels of pentadecafluorooctanoic acid and 1H,1H,2H,2H-heptadecafluorodecan-1-ol. Pentadecafluorooctanoic acid caused the more powerful change in gene expression, in terms of both number of genes affected and extent of change in expression. Across the dosages used pentadecafluorooctanoic acid and 1H,1H,2H,2H-heptadecafluorodecan-1-ol caused significant (P < or = 0.05) changes in expression for 441 and 105 genes, respectively. With 1H,1H,2H,2H-heptadecafluorodecan-1-ol approximately 38% of the 105 genes exhibited decreased expression with a dose of 25 mg/kg body wt, these genes also appearing less responsive to treatment at the lower dosages. Bioinformatic analysis suggested that these genes are associated with regulatory functions. With pentadecafluorooctanoic acid, increasing dosage up to 10 mg/kg body wt brought about progressive increase in expression of affected genes. Pathways analysis suggested similar effects of the two compounds on lipid and amino acid metabolism. Marked differences were also found, particularly with respect to effects on genes related to oxidative phosphorylation, oxidative metabolism, free radical scavenging, xenobiotic metabolism, and complement and coagulation cascades.

Solving the Schrödinger and Dirac equations of hydrogen molecular ion accurately by the free iterative complement interaction method

The nonrelativistic Schrödinger equation and the relativistic four-component Dirac equation of H(2) (+) were solved accurately in an analytical expansion form by the free iterative complement interaction (ICI) method combined with the variational principle. In the nonrelativistic case, we compared the free ICI wave function with the so-called "exact" wave function as two different expansions converging to the unique exact wave function and found that the free ICI method is much more efficient than the exact method. In the relativistic case, we first used the inverse Hamiltonian to guarantee Ritz-type variational principle and obtained accurate result. We also showed that the ordinary variational calculation also gives a nice convergence when the g function is appropriately chosen, since then the free ICI calculation guarantees a correct relationship between the large and small components of each adjacent order, which we call ICI balance. This is the first application of the relativistic free ICI method to molecule. We calculated both ground and excited states in good convergence, and not only the upper bound but also the lower bound of the ground-state energy. The error bound analysis has assured that the present result is highly accurate.

Solving the Schrödinger equation of helium and its isoelectronic ions with the exponential integral (Ei) function in the free iterative complement interaction method

We introduce here the exponential integral (Ei) function for variationally solving the Schrödinger equation of helium and its isoelectronic ions with the free iterative complement interaction (ICI) method. In our previous study [J. Chem. Phys., 2007, 127, 224104], we could calculate very accurate energies of these atoms by using the logarithmic function as the starting function of the free ICI calculation. The Ei function has a weak singularity at the origin, similarly to the logarithmic function, which is important for accurately describing the three-particle coalescence region. The logarithmic function, however, has a node and a maximum along the radial coordinate which may be physically meaningless. In contrast, the Ei function does not have such unphysical behaviors and so would provide an improvement over the logarithmic function. Actually, using the Ei function, instead of the logarithmic function, we obtained the energy, E= -2.903 724 377 034 119 598 311 159 245 194 404 446 696 924 865 a.u. for the helium ground state with 21 035 functions, which is a slight improvement over our previous result (the bold face shows the digits that are believed to have converged). This result supports the suggestion that the Ei function is better than the logarithmic function for describing the three-particle coalescence region.

Solving the Schrödinger Equation of Atoms and Molecules without Analytical Integration Based on the Free Iterative-Complement-Interaction Wave Function

A local Schrödinger equation (LSE) method is proposed for solving the Schrödinger equation (SE) of general atoms and molecules without doing analytic integrations over the complement functions of the free ICI (iterative-complement-interaction) wave functions. Since the free ICI wave function is potentially exact, we can assume a flatness of its local energy. The variational principle is not applicable because the analytic integrations over the free ICI complement functions are very difficult for general atoms and molecules. The LSE method is applied to several 2 to 5 electron atoms and molecules, giving an accuracy of 10(-5) Hartree in total energy. The potential energy curves of H2 and LiH molecules are calculated precisely with the free ICI LSE method. The results show the high potentiality of the free ICI LSE method for developing accurate predictive quantum chemistry with the solutions of the SE.

Solving the Schrödinger equation for helium atom and its isoelectronic ions with the free iterative complement interaction (ICI) method

The Schrodinger equation was solved very accurately for helium atom and its isoelectronic ions (Z=1-10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions. For helium, the calculated energy was -2.903,724,377,034,119,598,311,159,245,194,404,446,696,905,37 a.u., correct over 40 digit accuracy, and for H(-), it was -0.527,751,016,544,377,196,590,814,566,747,511,383,045,02 a.u. These results prove numerically that with the free ICI method, we can calculate the solutions of the Schrodinger equation as accurately as one desires. We examined several types of scaling function g and initial function psi(0) of the free ICI method. The performance was good when logarithm functions were used in the initial function because the logarithm function is physically essential for three-particle collision area. The best performance was obtained when we introduce a new logarithm function containing not only r(1) and r(2) but also r(12) in the same logarithm function.

In vitro blood reactivity to hydroxylated and non-hydroxylated polymer surfaces

Complement activation on hydroxyl-group-bearing surfaces is regarded as the main reason for granulocyte activation in applications of blood-contacting medical devices such as extracorporeal blood purification. However, the factors inducing the cell adhesion so far remained ambiguous. For a dedicated research, whole blood was incubated with a set of structurally similar polymer coatings on glass with either hydroxy or ether functionalities. By co-incubation of an activating with a non-activating surface, the reaction of granulocytes activated by complement fragments on non-activating surfaces could be evaluated. As expected, hydroxyl-terminated polymer layers induced much higher levels of complement activation than those with ether functionalities. Leukocyte activation, as measured by the expression of CD11b, correlated closely with the presence of free complement fragment C5a. However, adhesion of leukocytes was rather associated with the adsorption of activated fragments of C3 than with the activation level of the cells. Moreover, it was found that adsorbed quantities of fibrin and fibrinogen had little influence on leukocyte adhesion. It is concluded that the activation of leukocytes is triggered by soluble complement factors such as C5a while their adhesion on hydroxy-bearing surfaces is mainly triggered by the presence of surface-bound complement fragment C3b.

Measurement of HO2NO2 in the free troposphere during the Intercontinental Chemical Transport Experiment–North America 2004

The first direct in situ measurements of HO2NO2 in the upper troposphere were performed from the NASA DC‐8 during the Intercontinental Chemical Transport Experiment–North America 2004 with a chemical ionization mass spectrometer (CIMS). These measurements provide an independent diagnostic of HOx chemistry in the free troposphere and complement direct observations of HOx, because of the dual dependency of HO2NO2 on HOx and NOx. On average, the highest HO2NO2 mixing ratio of 76 pptv (median = 77 pptv, σ = 39 pptv) was observed at altitudes of 8–9 km. Simple steady state calculations of HO2NO2, constrained by measurements of HOx, NOx, and J values, are in good agreement (slope = 0.90, R2 = 0.60, and z = 5.5–7.5 km) with measurements in the midtroposphere where thermal decomposition is the major loss process. Above 8 km the calculated steady state HO2NO2 is in poor agreement with observed values (R2 = 0.20) and is typically larger by a factor of 2.4. Conversely, steady state calculations using model‐derived HOx show reasonable agreement with the observed HO2NO2 in both the midtroposphere (slope = 0.96, intercept = 7.0, and R2 = 0.63) and upper troposphere (slope = 0.80, intercept = 32.2, and R2 = 0.58). These results indicate that observed HO2 and HO2NO2 are in poor agreement in the upper troposphere but that HO2NO2 levels are consistent with current photochemical theory.

Preconditioners for the discretized time‐harmonic Maxwell equations in mixed form

AbstractWe introduce a new preconditioning technique for iteratively solving linear systems arising from finite element discretization of the mixed formulation of the time‐harmonic Maxwell equations. The preconditioners are motivated by spectral equivalence properties of the discrete operators, but are augmentation free and Schur complement free. We provide a complete spectral analysis, and show that the eigenvalues of the preconditioned saddle point matrix are strongly clustered. The analytical observations are accompanied by numerical results that demonstrate the scalability of the proposed approach. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Antioxidant and complement modulating activities of five essential oils

(LE) (Citrus limon (L.) Burman fil.), rosemary (RO) (Rosmarinus officinalis L.), Spanish oregano (SO) (Thymbra capitata Griseb.) and thyme (TH) (Thymus zygis L.), were investigated for their activity on the complement system and their antioxidant properties by in vitro assays. Oils were obtained from commercial sources. Their main components (identified by GC-MS and quantified by GC-FID) were as follow: eugenol (86.2%) for CL; limonene (71.6%), s-pinene (12.2%) and γ-terpinene (6.9%) for LE; 1,8 cineole (49.7%), α-pinene (9,9%) and camphor (9,6%) for RO; carvacrol (73,5%) for SO, and thymol (56,6%) and p-cymene (28,4%) for TH. Free radical scavenging activity was evaluated using 1,1-diphenyl2-picrylhydrazyl (DPPH) [1]. The activity on classical complement pathway was determined in human serum by hemolytic assay [2]. Positive control was quercetin for both assays, showing an IC =10.5±4.6µg/mL for the DPPH test and an IC =33.7±4.3µg/mL for the assay on the complement system. Only CL showed antioxidant activity in the DPPH (IC =13.2±2.9µg/mL), indicating that this oil has free radical scavenging activity. Results on inhibition of the classical pathway of the complement system, showed that TH and CL have similar weak activity, with IC =61.4±10,6µg/mL and 72.7±4.1µg/mL, respectively. SO, RO and LE showed no inhibitory effect on the complement system activated by the classical pathway. In conclusion, from the five oils tested, the clove essential showed the best combination of free radical scavenging and complement inhibitory activities.

Clinical Efficacy and Biocompatibility of Three Different Leukocyte and Fat Removal Filters During Cardiac Surgery

Activated leukocytes and fat particles are associated with organ injury after a cardiac surgery. Filters are currently used to remove either leukocytes or fat particles. A novel approach with a filter that combines leukocyte and fat removal might be clinically useful. As it is not known which type of filter has a good and safe performance in both leukocyte and fat removal, we measured in this study the leukocyte and fat removal properties and the biocompatibility of three different filters. We used six Pall RS1 (Pall, Portsmouth, England) leukocyte removal filters, six Pall LipiGuard fat removal filters, and six Fresenius Biofil 02 (Fresenius, Emmer-Compascuum, The Netherlands) leukocyte removal filters and measured the passage times of 500 and 1000 mL of residual heart-lung machine blood. We determined the circulating leukocyte and platelet counts, and total hemoglobin, triglyceride, and free fatty acid concentration after the filters. In addition, we measured free hemoglobin, plasma elastase (Merck, Darmstadt, Germany), and complement C5-9 (Quidel, San Diego, CA, U.S.A.) to assess the biocompatibility of the filters. The circulating fat particles were calculated with an automated hematology analyzer. The passage time for the blood was shortest for the Biofil filter (P = 0.02, analysis of variance). The total leukocyte counts (P = 0.04) and fat particles (P = 0.02) were higher after the LipiGuard filter. This filter also had a higher increase in free hemoglobin concentration (P = 0.03). We conclude that the leukocyte removal filters were superior to the fat removal filter both in leukocyte and fat removal.

Pathophysiology of mesenteric ischemia/reperfusion: a review

During ischemia, the cell structures are progressively damaged, but restoration of the blood flow, paradoxically, intensifies the lesions caused by the ischemia. The mechanisms of ischemia injury and reperfusion (I/R) have not been completely defined and many studies have been realized in an attempt to find an ideal therapy for mesenteric I/R. The occlusion and reperfusion of the splanchnic arteries provokes local and systemic alterations principally derived from the release of cytotoxic substances and the interaction between neutrophils and endothelial cells. Substances involved in the process are discussed in the present review, like oxygen-derived free radicals, nitric oxide, transcription factors, complement system, serotonin and pancreatic proteases. The mechanisms of apoptosis, alterations in other organs, therapeutic and evaluation methods are also discussed.

Google Scholar: The New Generation of Citation Indexes

Google Scholar (http://scholar.google.com) provides a new method of locating potentially relevant articles on a given subject identifying subsequent articles that cite a previously published article. An important feature of Google Scholar is that researchers can use it to trace interconnections among authors citing articles on the same topic and to determine the frequency with which others cite a specific article, as it has a cited by feature. This study begins with an overview of how to use Google Scholar for citation analysis and identifies advanced search techniques not well documented Google Scholar. This study also compares the citation counts provided Web of Science and Google Scholar for articles in the field of Webometrics. It makes several suggestions for improving Google Scholar. Finally, it concludes that Google Scholar provides a free alternative or complement to other citation indexes.

Free radicals upregulate complement expression in rabbit isolated heart

Both free radicals and complement activation can injure tissue. Our study determined whether free radicals alter complement production by the myocardium. Isolated hearts from New Zealand White rabbits were perfused on a Langendorff apparatus and exposed to xanthine (X; 100 microM) plus xanthine oxidase (XO; 8 mU/ml) (X/XO). The free radical-generating system significantly (P < 0.05) increased C1q and also increased C1r, C3, C8, and C9 transcription compared with controls. Immunohistological examination revealed augmented membrane attack complex deposition on X/XO-treated tissue. X/XO-treated hearts also exhibited significant (P < 0.05) increases in coronary perfusion pressure and left ventricular end-diastolic pressure and a decrease in left-ventricular developed pressure. N-(2-mercaptopropionyl)-glycine (3 mM), in conjunction with the superoxide dismutase mimetic SC-52608 (100 microM), significantly (P < 0.05) reduced the upregulation of C1q, C1r, C3, C8, and C9 mRNA expression elicited by X/XO. The antioxidants also ameliorated the deterioration in function caused by X/XO. Local complement activation may represent a mechanism by which free radicals mediate tissue injury.