Basis set superposition error-counterpoise corrected potential energy surfaces : application to hydrogen peroxide ... X (X=F-, Cl-, Br-, Li+, Na+) complexes

Møller-Plesset (MP2) and Becke-3-Lee-Yang-Parr (B3LYP) calculations have been used to compare the geometrical parameters, hydrogen-bonding properties, vibrational frequencies and relative energies for several X- and X+ hydrogen peroxide complexes. The geometries and interaction energies were corrected for the basis set superposition error (BSSE) in all the complexes (1-5), using the full counterpoise method, yielding small BSSE values for the 6-311 + G(3df,2p) basis set used. The interaction energies calculated ranged from medium to strong hydrogen-bonding systems (1-3) and strong electrostatic interactions (4 and 5). The molecular interactions have been characterized using the atoms in molecules theory (AIM), and by the analysis of the vibrational frequencies. The minima on the BSSE-counterpoise corrected potential-energy surface (PES) have been determined as described by S. Simón, M. Duran, and J. J. Dannenberg, and the results were compared with the uncorrected PES

Effect of basis set superposition error on the electron density of molecular complexes

The effect of basis set superposition error (BSSE) on molecular complexes is analyzed. The BSSE causes artificial delocalizations which modify the first order electron density. The mechanism of this effect is assessed for the hydrogen fluoride dimer with several basis sets. The BSSE-corrected first-order electron density is obtained using the chemical Hamiltonian approach versions of the Roothaan and Kohn-Sham equations. The corrected densities are compared to uncorrected densities based on the charge density critical points. Contour difference maps between BSSE-corrected and uncorrected densities on the molecular plane are also plotted to gain insight into the effects of BSSE correction on the electron density

Implementation and application of basis set superposition error-correction schemes to the theoretical modeling of weak intermolecular interactions

This thesis deals with the so-called Basis Set Superposition Error (BSSE) from both a methodological and a practical point of view. The purpose of the present thesis is twofold: (a) to contribute step ahead in the correct characterization of weakly bound complexes and, (b) to shed light the understanding of the actual implications of the basis set extension effects in the ab intio calculations and contribute to the BSSE debate. The existing BSSE-correction procedures are deeply analyzed, compared, validated and, if necessary, improved. A new interpretation of the counterpoise (CP) method is used in order to define counterpoise-corrected descriptions of the molecular complexes. This novel point of view allows for a study of the BSSE-effects not only in the interaction energy but also on the potential energy surface and, in general, in any property derived from the molecular energy and its derivatives A program has been developed for the calculation of CP-corrected geometry optimizations and vibrational frequencies, also using several counterpoise schemes for the case of molecular clusters. The method has also been implemented in Gaussian98 revA10 package. The Chemical Hamiltonian Approach (CHA) methodology has been also implemented at the RHF and UHF levels of theory for an arbitrary number interacting systems using an algorithm based on block-diagonal matrices. Along with the methodological development, the effects of the BSSE on the properties of molecular complexes have been discussed in detail. The CP and CHA methodologies are used for the determination of BSSE-corrected molecular complexes properties related to the Potential Energy Surfaces and molecular wavefunction, respectively. First, the behaviour of both BSSE-correction schemes are systematically compared at different levels of theory and basis sets for a number of hydrogen-bonded complexes. The Complete Basis Set (CBS) limit of both uncorrected and CP-corrected molecular properties like stabilization energies and intermolecular distances has also been determined, showing the capital importance of the BSSE correction. Several controversial topics of the BSSE correction are addressed as well. The application of the counterpoise method is applied to internal rotational barriers. The importance of the nuclear relaxation term is also pointed out. The viability of the CP method for dealing with charged complexes and the BSSE effects on the double-well PES blue-shifted hydrogen bonds is also studied in detail. In the case of the molecular clusters the effect of high-order BSSE effects introduced with the hierarchical counterpoise scheme is also determined. The effect of the BSSE on the electron density-related properties is also addressed. The first-order electron density obtained with the CHA/F and CHA/DFT methodologies was used to assess, both graphically and numerically, the redistribution of the charge density upon BSSE-correction. Several tools like the Atoms in Molecules topologycal analysis, density difference maps, Quantum Molecular Similarity, and Chemical Energy Component Analysis were used to deeply analyze, for the first time, the BSSE effects on the electron density of several hydrogen bonded complexes of increasing size. The indirect effect of the BSSE on intermolecular perturbation theory results is also pointed out It is shown that for a BSSE-free SAPT study of hydrogen fluoride clusters, the use of a counterpoise-corrected PES is essential in order to determine the proper molecular geometry to perform the SAPT analysis.

Clinical validation of an algorithm to correct the error in the keratometric estimation of corneal power for normal eyes

To validate clinically an algorithm for correcting the error in the keratometric estimation of corneal power by using a variable keratometric index of refraction (nk) in a normal healthy population.

Minimizing the IOL Power Error Induced by Keratometric Power

Purpose. To evaluate theoretically in normal eyes the influence on IOL power (PIOL) calculation of the use of a keratometric index (nk) and to analyze and validate preliminarily the use of an adjusted keratometric index (nkadj) in the IOL power calculation (PIOLadj). Methods. A model of variable keratometric index (nkadj) for corneal power calculation (Pc) was used for IOL power calculation (named PIOLadj). Theoretical differences ($PIOL) between the new proposed formula (PIOLadj) and which is obtained through Gaussian optics (PIOL Gauss) were determined using Gullstrand and Le Grand eye models. The proposed new formula for IOL power calculation (PIOLadj) was prevalidated clinically in 81 eyes of 81 candidates for corneal refractive surgery and compared with Haigis, HofferQ, Holladay, and SRK/T formulas. Results. A theoretical PIOL underestimation greater than 0.5 diopters was present in most of the cases when nk = 1.3375 was used. If nkadj was used for Pc calculation, a maximal calculated error in $PIOL of T0.5 diopters at corneal vertex in most cases was observed independently from the eye model, r1c, and the desired postoperative refraction. The use of nkadj in IOL power calculation (PIOLadj) could be valid with effective lens position optimization nondependent of the corneal power. Conclusions. The use of a single value of nk for Pc calculation can lead to significant errors in PIOL calculation that may explain some IOL power overestimations with conventional formulas. These inaccuracies can be minimized by using the new PIOLadj based on the algorithm of nkadj.

Influence of the Difference Between Corneal and Refractive Astigmatism on LASIK Outcomes Using Solid-State Technology

Purpose: To evaluate the influence of the difference between preoperative corneal and refractive astigmatism [ocular residual astigmatism (ORA)] on outcomes obtained after laser in situ keratomileusis (LASIK) surgery for correction of myopic astigmatism using the solid-state laser technology. Methods: One hundred one consecutive eyes with myopia or myopic astigmatism of 55 patients undergoing LASIK surgery using the Pulzar Z1 solid-state laser (CustomVis Laser Pty Ltd, currently CV Laser) were included. Visual and refractive changes at 6 months postoperatively and changes in ORA and anterior corneal astigmatism and posterior corneal astigmatism (PCA) were analyzed. Results: Postoperatively, uncorrected distance visual acuity improved significantly (P < 0.01). Likewise, refractive cylinder magnitude and spherical equivalent were reduced significantly (P < 0.01). In contrast, no significant changes were observed in ORA magnitude (P = 0.81) and anterior corneal astigmatism (P = 0.12). The mean overall efficacy and safety indices were 0.96 and 1.01, respectively. These indices were not correlated with preoperative ORA (r = −0.15, P = 0.15). Furthermore, a significant correlation was found between ORA (r = 0.81, P < 0.01) and PCA postoperatively, but not preoperatively (r = 0.12, P = 0.25). Likewise, a significant correlation of ORA with manifest refraction was only found postoperatively (r = −0.38, P < 0.01). Conclusions: The magnitude of ORA does not seem to be a predictive factor of efficacy and safety of myopic LASIK using a solid-state laser platform. The higher relevance of PCA after surgery in some cases may explain the presence of unexpected astigmatic residual refractive errors.

New-Generation Hybrid Contact Lens for the Management of Extreme Irregularity in a Thin Cornea After Unsuccessful Excimer Laser Refractive Surgery

Purpose: To report a very successful outcome obtained with the fitting of a new-generation hybrid contact lens of reverse geometry in a thin cornea with extreme irregularity due to the presence of a central island after unsuccessful myopic excimer laser refractive surgery. Methods: A 32-year-old man attended to our clinic complaining of very poor vision in his right eye after bilateral laser in situ keratomileusis (treatment or surgery) for myopia correction and some additional retreatments afterward. After a comprehensive ocular evaluation, contact lens fitting with a reverse geometry hybrid contact lens (SynergEyes PS, SynergEyes, Carlsbad, CA) was proposed as a solution for this case. Visual, refractive, and ocular aberrometric outcomes with the contact lens were evaluated. Results: Distance visual acuity improved from a prefitting uncorrected value of 20/200 to a postfitting corrected value of 20/16. Prefitting manifest refraction was +6.00 sphere and −3.00 cylinder at 70°, with a corrected distance visual acuity of 20/40. Higher order root mean square for a 5-mm pupil changed from a prefitting value of 1.45 to 0.34 µm with the contact lens. The contact lens wearing was reported as comfortable, and the patient was very satisfied with this solution. Conclusions: The SynergEyes PS contact lens seems to be an excellent option for the visual rehabilitation of corneas with extreme irregularity after myopic excimer laser surgery, minimizing the level of higher order aberrations and providing an excellent visual outcome.

Effect of uncorrected astigmatism on vision

PURPOSE: To examine the effect of uncorrected astigmatism in older adults. SETTING: University Vision Clinic METHOD: Twenty-one healthy presbyopes, aged 58.9±2.8 years, had astigmatism of 0.0 to -4.0 x 90?DC and -3.0DC of cylinder at 90?, 180? and 45? induced with spectacle lenses, with the mean spherical equivalent compensated to plano, in random order. Visual acuity was assessed binocularly using a computerised test chart at 95%, 50% and 10% contrast. Near acuity and reading speed were measured using standardised reading texts. Light scatter was quantified with the cQuant and driving reaction times with a computer simulator. Finally visual clarity of a mobile phone and computer screen was subjectively rated. RESULTS: Distance visual acuity decreased with increasing uncorrected astigmatic power (F=174.50, p<0.001) and was reduced at lower contrasts (F=170.77, p<0.001). Near visual acuity and reading speed also decreased with increasing uncorrected astigmatism power (p<0.001). Light scatter was not significantly affected by uncorrected astigmatism (p>0.05), but the reliability and variability of measurements decreased with increasing uncorrected astigmatic power (p<0.05). Driving simulator performance was also unaffected by uncorrected astigmatism (p>0.05), but subjective rating of clarity decreased with increasing uncorrected astigmatic power (p<0.001). Uncorrected astigmatism at 45? or 180? orientation resulted in a worse distance and near visual acuity, and subjective rated clarity than 90? orientation (p<0.05). CONCLUSION: Uncorrected astigmatism, even as low as 1.0DC, causes a significant burden on a patient’s vision. If left uncorrected, this could impact significantly on their independence, quality of life and wellbeing.

Higher-order aberrations in amblyopia:an analysis of pre- and post-wavefront-guided laser refractive correction

For more than a century it has been known that the eye is not a perfect optical system, but rather a system that suffers from aberrations beyond conventional prescriptive descriptions of defocus and astigmatism. Whereas traditional refraction attempts to describe the error of the eye with only two parameters, namely sphere and cylinder, measurements of wavefront aberrations depict the optical error with many more parameters. What remains questionable is the impact these additional parameters have on visual function. Some authors have argued that higher-order aberrations have a considerable effect on visual function and in certain cases this effect is significant enough to induce amblyopia. This has been referred to as ‘higher-order aberration-associated amblyopia’. In such cases, correction of higher-order aberrations would not restore visual function. Others have reported that patients with binocular asymmetric aberrations display an associated unilateral decrease in visual acuity and, if the decline in acuity results from the aberrations alone, such subjects may have been erroneously diagnosed as amblyopes. In these cases, correction of higher-order aberrations would restore visual function. This refractive entity has been termed ‘aberropia’. In order to investigate these hypotheses, the distribution of higher-order aberrations in strabismic, anisometropic and idiopathic amblyopes, and in a group of visual normals, was analysed both before and after wavefront-guided laser refractive correction. The results show: (i) there is no significant asymmetry in higher-order aberrations between amblyopic and fixing eyes prior to laser refractive treatment; (ii) the mean magnitude of higher-order aberrations is similar within the amblyopic and visually normal populations; (iii) a significant improvement in visual acuity can be realised for adult amblyopic patients utilising wavefront-guided laser refractive surgery and a modest increase in contrast sensitivity was observed for the amblyopic eye of anisometropes following treatment (iv) an overall trend towards increased higher-order aberrations following wavefront-guided laser refractive treatment was observed for both visually normal and amblyopic eyes. In conclusion, while the data do not provide any direct evidence for the concepts of either ‘aberropia’ or ‘higher-order aberration-associated amblyopia’, it is clear that gains in visual acuity and contrast sensitivity may be realised following laser refractive treatment of the amblyopic adult eye. Possible mechanisms by which these gains are realised are discussed.

Outcome analysis of intracorneal ring segments for the treatment of keratoconus based on visual, refractive, and aberrometric impairment

PURPOSE: To analyze the outcomes of intracorneal ring segment (ICRS) implantation for the treatment of keratoconus based on preoperative visual impairment. DESIGN: Multicenter, retrospective, nonrandomized study. METHODS: A total of 611 eyes of 361 keratoconic patients were evaluated. Subjects were classified according to their preoperative corrected distance visual acuity (CDVA) into 5 different groups: grade I, CDVA of 0.90 or better; grade II, CDVA equal to or better than 0.60 and worse than 0.90; grade III, CDVA equal to or better than 0.40 and worse than 0.60; grade IV, CDVA equal to or better than 0.20 and worse than 0.40; and grade plus, CDVA worse than 0.20. Success and failure indices were defined based on visual, refractive, corneal topographic, and aberrometric data and evaluated in each group 6 months after ICRS implantation. RESULTS: Significant improvement after the procedure was observed regarding uncorrected distance visual acuity in all grades (P < .05). CDVA significantly decreased in grade I (P < .01) but significantly increased in all other grades (P < .05). A total of 37.9% of patients with preoperative CDVA 0.6 or better gained 1 or more lines of CDVA, whereas 82.8% of patients with preoperative CDVA 0.4 or worse gained 1 or more lines of CDVA (P < .01). Spherical equivalent and keratometry readings showed a significant reduction in all grades (P ≤ .02). Corneal higher-order aberrations did not change after the procedure (P ≥ .05). CONCLUSIONS: Based on preoperative visual impairment, ICRS implantation provides significantly better results in patients with a severe form of the disease. A notable loss of CDVA lines can be expected in patients with a milder form of keratoconus.

Development of error correction techniques for nitrate-N load estimation models

Excess nutrient loads carried by streams and rivers are a great concern for environmental resource managers. In agricultural regions, excess loads are transported downstream to receiving water bodies, potentially causing algal blooms, which could lead to numerous ecological problems. To better understand nutrient load transport, and to develop appropriate water management plans, it is important to have accurate estimates of annual nutrient loads. This study used a Monte Carlo sub-sampling method and error-corrected statistical models to estimate annual nitrate-N loads from two watersheds in central Illinois. The performance of three load estimation methods (the seven-parameter log-linear model, the ratio estimator, and the flow-weighted averaging estimator) applied at one-, two-, four-, six-, and eight-week sampling frequencies were compared. Five error correction techniques; the existing composite method, and four new error correction techniques developed in this study; were applied to each combination of sampling frequency and load estimation method. On average, the most accurate error reduction technique, (proportional rectangular) resulted in 15% and 30% more accurate load estimates when compared to the most accurate uncorrected load estimation method (ratio estimator) for the two watersheds. Using error correction methods, it is possible to design more cost-effective monitoring plans by achieving the same load estimation accuracy with fewer observations. Finally, the optimum combinations of monitoring threshold and sampling frequency that minimizes the number of samples required to achieve specified levels of accuracy in load estimation were determined. For one- to three-weeks sampling frequencies, combined threshold/fixed-interval monitoring approaches produced the best outcomes, while fixed-interval-only approaches produced the most accurate results for four- to eight-weeks sampling frequencies.

Prevalence of refractive errors and ocular disorders in preschool and school children of Ibiporã - PR, Brazil (1989 to 1996)

Purpose: To establish the prevalence of refractive errors and ocular disorders in preschool and schoolchildren of Ibiporã, Brazil. Methods: A survey of 6 to 12-year-old children from public and private elementary schools was carried out in Ibiporã between 1989 and 1996. Visual acuity measurements were performed by trained teachers using Snellen's chart. Children with visual acuity <0.7 in at least one eye were referred to a complete ophthalmologic examination. Results: 35,936 visual acuity measurements were performed in 13,471 children. 1.966 children (14.59%) were referred to an ophthalmologic examination. Amblyopia was diagnosed in 237 children (1.76%), whereas strabismus was observed in 114 cases (0.84%). Cataract (n=17) (0.12%), chorioretinitis (n=38) (0.28%) and eyelid ptosis (n=6) (0.04%) were also diagnosed. Among the 614 (4.55%) children who were found to have refractive errors, 284 (46.25%) had hyperopia (hyperopia or hyperopic astigmatism), 206 (33.55%) had myopia (myopia or myopic astigmatism) and 124 (20.19%) showed mixed astigmatism. Conclusions: The study determined the local prevalence of amblyopia, refractive errors and eye disorders among preschool and schoolchildren.

An empirical evaluation of imputation accuracy for association statistics reveals increased type-I error rates in genome-wide associations

Background: Genome wide association studies (GWAS) are becoming the approach of choice to identify genetic determinants of complex phenotypes and common diseases. The astonishing amount of generated data and the use of distinct genotyping platforms with variable genomic coverage are still analytical challenges. Imputation algorithms combine directly genotyped markers information with haplotypic structure for the population of interest for the inference of a badly genotyped or missing marker and are considered a near zero cost approach to allow the comparison and combination of data generated in different studies. Several reports stated that imputed markers have an overall acceptable accuracy but no published report has performed a pair wise comparison of imputed and empiric association statistics of a complete set of GWAS markers. Results: In this report we identified a total of 73 imputed markers that yielded a nominally statistically significant association at P < 10(-5) for type 2 Diabetes Mellitus and compared them with results obtained based on empirical allelic frequencies. Interestingly, despite their overall high correlation, association statistics based on imputed frequencies were discordant in 35 of the 73 (47%) associated markers, considerably inflating the type I error rate of imputed markers. We comprehensively tested several quality thresholds, the haplotypic structure underlying imputed markers and the use of flanking markers as predictors of inaccurate association statistics derived from imputed markers. Conclusions: Our results suggest that association statistics from imputed markers showing specific MAF (Minor Allele Frequencies) range, located in weak linkage disequilibrium blocks or strongly deviating from local patterns of association are prone to have inflated false positive association signals. The present study highlights the potential of imputation procedures and proposes simple procedures for selecting the best imputed markers for follow-up genotyping studies.

Innovation concept for measurement gross error detection and identification in power system state estimation

In this study, the innovation approach is used to estimate the measurement total error associated with power system state estimation. This is required because the power system equations are very much correlated with each other and as a consequence part of the measurements errors is masked. For that purpose an index, innovation index (II), which provides the quantity of new information a measurement contains is proposed. A critical measurement is the limit case of a measurement with low II, it has a zero II index and its error is totally masked. In other words, that measurement does not bring any innovation for the gross error test. Using the II of a measurement, the masked gross error by the state estimation is recovered; then the total gross error of that measurement is composed. Instead of the classical normalised measurement residual amplitude, the corresponding normalised composed measurement residual amplitude is used in the gross error detection and identification test, but with m degrees of freedom. The gross error processing turns out to be very simple to implement, requiring only few adaptations to the existing state estimation software. The IEEE-14 bus system is used to validate the proposed gross error detection and identification test.