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

Second-order Møller-Plesset perturbation theory without basis set superposition error : II : open-shell systems

The basis set superposition error-free second-order MØller-Plesset perturbation theory of intermolecular interactions was studied. The difficulties of the counterpoise (CP) correction in open-shell systems were also discussed. The calculations were performed by a program which was used for testing the new variants of the theory. It was shown that the CP correction for the diabatic surfaces should be preferred to the adiabatic ones

C-H···O H-bonded complexes: how does basis set superposition error change their potential-energy surfaces?

Geometries, vibrational frequencies, and interaction energies of the CNH⋯O3 and HCCH⋯O3 complexes are calculated in a counterpoise-corrected (CP-corrected) potential-energy surface (PES) that corrects for the basis set superposition error (BSSE). Ab initio calculations are performed at the Hartree-Fock (HF) and second-order Møller-Plesset (MP2) levels, using the 6-31G(d,p) and D95++(d,p) basis sets. Interaction energies are presented including corrections for zero-point vibrational energy (ZPVE) and thermal correction to enthalpy at 298 K. The CP-corrected and conventional PES are compared; the unconnected PES obtained using the larger basis set including diffuse functions exhibits a double well shape, whereas use of the 6-31G(d,p) basis set leads to a flat single-well profile. The CP-corrected PES has always a multiple-well shape. In particular, it is shown that the CP-corrected PES using the smaller basis set is qualitatively analogous to that obtained with the larger basis sets, so the CP method becomes useful to correctly describe large systems, where the use of small basis sets may be necessary

How does basis set superposition error change the potential surfaces for hydrogen-bonded dimers?

We describe a simple method to automate the geometric optimization of molecular orbital calculations of supermolecules on potential surfaces that are corrected for basis set superposition error using the counterpoise (CP) method. This method is applied to the H-bonding complexes HF/HCN, HF/H2O, and HCCH/H2O using the 6-31G(d,p) and D95 + + (d,p) basis sets at both the Hartree-Fock and second-order Møller-Plesset levels. We report the interaction energies, geometries, and vibrational frequencies of these complexes on the CP-optimized surfaces; and compare them with similar values calculated using traditional methods, including the (more traditional) single point CP correction. Upon optimization on the CP-corrected surface, the interaction energies become more negative (before vibrational corrections) and the H-bonding stretching vibrations decrease in all cases. The extent of the effects vary from extremely small to quite large depending on the complex and the calculational method. The relative magnitudes of the vibrational corrections cannot be predicted from the H-bond stretching frequencies alone

Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization

To obtain a state-of-the-art benchmark potential energy surface (PES) for the archetypal oxidative addition of the methane C-H bond to the palladium atom, we have explored this PES using a hierarchical series of ab initio methods (Hartree-Fock, second-order Møller-Plesset perturbation theory, fourth-order Møller-Plesset perturbation theory with single, double and quadruple excitations, coupled cluster theory with single and double excitations (CCSD), and with triple excitations treated perturbatively [CCSD(T)]) and hybrid density functional theory using the B3LYP functional, in combination with a hierarchical series of ten Gaussian-type basis sets, up to g polarization. Relativistic effects are taken into account either through a relativistic effective core potential for palladium or through a full four-component all-electron approach. Counterpoise corrected relative energies of stationary points are converged to within 0.1-0.2 kcal/mol as a function of the basis-set size. Our best estimate of kinetic and thermodynamic parameters is -8.1 (-8.3) kcal/mol for the formation of the reactant complex, 5.8 (3.1) kcal/mol for the activation energy relative to the separate reactants, and 0.8 (-1.2) kcal/mol for the reaction energy (zero-point vibrational energy-corrected values in parentheses). This agrees well with available experimental data. Our work highlights the importance of sufficient higher angular momentum polarization functions, f and g, for correctly describing metal-d-electron correlation and, thus, for obtaining reliable relative energies. We show that standard basis sets, such as LANL2DZ+ 1f for palladium, are not sufficiently polarized for this purpose and lead to erroneous CCSD(T) results. B3LYP is associated with smaller basis set superposition errors and shows faster convergence with basis-set size but yields relative energies (in particular, a reaction barrier) that are ca. 3.5 kcal/mol higher than the corresponding CCSD(T) values

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Intramolecular basis set superposition error effects on the planarity of benzene and other aromatic molecules: A solution to the problem

Recently, the surprising result that ab initio calculations on benzene and other planar arenes at correlated MP2, MP3, configuration interaction with singles and doubles (CISD), and coupled cluster with singles and doubles levels of theory using standard Pople’s basis sets yield nonplanar minima has been reported. The planar optimized structures turn out to be transition states presenting one or more large imaginary frequencies, whereas single-determinant-based methods lead to the expected planar minima and no imaginary frequencies. It has been suggested that such anomalous behavior can be originated by two-electron basis set incompleteness error. In this work, we show that the reported pitfalls can be interpreted in terms of intramolecular basis set superposition error (BSSE) effects, mostly between the C–H moieties constituting the arenes. We have carried out counterpoise-corrected optimizations and frequency calculations at the Hartree–Fock, B3LYP, MP2, and CISD levels of theory with several basis sets for a number of arenes. In all cases, correcting for intramolecular BSSE fixes the anomalous behavior of the correlated methods, whereas no significant differences are observed in the single-determinant case. Consequently, all systems studied are planar at all levels of theory. The effect of different intramolecular fragment definitions and the particular case of charged species, namely, cyclopentadienyl and indenyl anions, respectively, are also discussed

Prognostic value of serial blood S100B determinations in stage IIB-III melanoma patients: a corollary study to EORTC trial 18952.

S100B is a prognostic factor for melanoma as elevated levels correlate with disease progression and poor outcome. We determined its prognostic value based on updated information using serial determinations in stage IIb/III melanoma patients. 211 Patients who participated in the EORTC 18952 trial, evaluating efficacy of adjuvant intermediate doses of interferon α2b (IFN) versus observation, entered a corollary study. Over a period of 36 months, 918 serum samples were collected. The Cox time-dependent model was used to assess prognostic value of the latest (most recent) S100B determination. At first measurement, 178 patients had S100B values <0.2 μg/l and 33 ≥ 0.2 μg/l. Within the first group, 61 patients had, later on, an increased value of S100B (≥ 0.2 μg/l). An initial increased value of S100B, or during follow-up, was associated with worse distant metastasis-free survival (DMFS); hazard ratio (HR) of S100B ≥ 0.2 versus S100B < 0.2 was 5.57 (95% confidence interval (CI) 3.81-8.16), P < 0.0001, after adjustment for stage, number of lymph nodes and sex. In stage IIb patients, the HR adjusted for sex was 2.14 (95% CI 0.71, 6.42), whereas in stage III, the HR adjusted for stage, number of lymph nodes and sex was 6.76 (95% CI 4.50-10.16). Similar results were observed regarding overall survival (OS). Serial determination of S100B in stage IIb-III melanoma is a strong independent prognostic marker, even stronger compared to stage and number of positive lymph nodes. The prognostic impact of S100B ≥ 0.2 μg/l is more pronounced in stage III disease compared with stage IIb.

Multisensor change detection with nonlinear canonical correlation

The analysis of multi-modal and multi-sensor images is nowadays of paramount importance for Earth Observation (EO) applications. There exist a variety of methods that aim at fusing the different sources of information to obtain a compact representation of such datasets. However, for change detection existing methods are often unable to deal with heterogeneous image sources and very few consider possible nonlinearities in the data. Additionally, the availability of labeled information is very limited in change detection applications. For these reasons, we present the use of a semi-supervised kernel-based feature extraction technique. It incorporates a manifold regularization accounting for the geometric distribution and jointly addressing the small sample problem. An exhaustive example using Landsat 5 data illustrates the potential of the method for multi-sensor change detection.

Non-invasive and non-occlusive blood pressure estimation via a chest sensor.

The clinical demand for a device to monitor Blood Pressure (BP) in ambulatory scenarios with minimal use of inflation cuffs is increasing. Based on the so-called Pulse Wave Velocity (PWV) principle, this paper introduces and evaluates a novel concept of BP monitor that can be fully integrated within a chest sensor. After a preliminary calibration, the sensor provides non-occlusive beat-by-beat estimations of Mean Arterial Pressure (MAP) by measuring the Pulse Transit Time (PTT) of arterial pressure pulses travelling from the ascending aorta towards the subcutaneous vasculature of the chest. In a cohort of 15 healthy male subjects, a total of 462 simultaneous readings consisting of reference MAP and chest PTT were acquired. Each subject was recorded at three different days: D, D+3 and D+14. Overall, the implemented protocol induced MAP values to range from 80 ± 6 mmHg in baseline, to 107 ± 9 mmHg during isometric handgrip maneuvers. Agreement between reference and chest-sensor MAP values was tested by using intraclass correlation coefficient (ICC = 0.78) and Bland-Altman analysis (mean error = 0.7 mmHg, standard deviation = 5.1 mmHg). The cumulative percentage of MAP values provided by the chest sensor falling within a range of ±5 mmHg compared to reference MAP readings was of 70%, within ±10 mmHg was of 91%, and within ±15mmHg was of 98%. These results point at the fact that the chest sensor complies with the British Hypertension Society (BHS) requirements of Grade A BP monitors, when applied to MAP readings. Grade A performance was maintained even two weeks after having performed the initial subject-dependent calibration. In conclusion, this paper introduces a sensor and a calibration strategy to perform MAP measurements at the chest. The encouraging performance of the presented technique paves the way towards an ambulatory-compliant, continuous and non-occlusive BP monitoring system.

Monitoring multiple angiogenesis-related molecules in the blood of cancer patients shows a correlation between VEGF-A and MMP-9 levels before treatment and divergent changes after surgical vs. conservative therapy.

Anti-angiogenic therapies are currently in cancer clinical trials, but to date there are no established tests for evaluating the angiogenic status of a patient. We measured 11 circulating angiogenesis-associated molecules in cancer patients before and after local treatment. The purpose of our study was to screen for possible relationships among the different molecules and between individual molecules and tumor burden. We measured VEGF-A, PlGF, SCF, MMP-9, EDB+ -fibronectin, sVEGFR-2, sVEGFR-1, salphaVbeta3, sTie-2, IL-8 and CRP in the blood of 22 healthy volunteers, 17 early breast, 17 early colorectal, and 8 advanced sarcoma/melanoma cancer patients. Breast cancer patients had elevated levels of VEGF-A and sTie-2, colorectal cancer patients of VEGF-A, MMP-9, sTie-2, IL-8 and CRP, and melanoma/sarcoma patients of sVEGFR-1. salphaVbeta3 was decreased in colorectal cancer patients. A correlation between VEGF-A and MMP-9 was found. After tumor removal, MMP-9 and salphaVbeta3 significantly decreased in breast and CRP in colorectal cancer, whereas sVEGFR-1 increased in colorectal cancer patients. In sarcoma/melanoma patients treated regionally with TNF and chemotherapy we observed a rise in VEGF-A, SCF, VEGFR-2, MMP-9, Tie-2 and CRP, a correlation between CRP and IL-8, and a decreased in sVEGFR-1 levels. In conclusion, among all factors measured, only VEGF-A and MMP-9 consistently correlated to each other, elevated CRP levels were associated with tumor burden, whereas sVEGF-R1 increased after tumor removal in colorectal cancer. Treatment with chemotherapy and TNF induced changes consistent with an angiogenic switch. These results warrant a prospective study to compare the effect of surgical tumor removal vs. chemotherapy on some of these markers and to evaluate their prognostic/predictive value.

Right coronary artery flow velocity and volume assessment with spiral K-space sampled breathhold velocity-encoded MRI at 3 tesla: accuracy and reproducibility.

PURPOSE: To evaluate accuracy and reproducibility of flow velocity and volume measurements in a phantom and in human coronary arteries using breathhold velocity-encoded (VE) MRI with spiral k-space sampling at 3 Tesla. MATERIALS AND METHODS: Flow velocity assessment was performed using VE MRI with spiral k-space sampling. Accuracy of VE MRI was tested in vitro at five constant flow rates. Reproducibility was investigated in 19 healthy subjects (mean age 25.4 +/- 1.2 years, 11 men) by repeated acquisition in the right coronary artery (RCA). RESULTS: MRI-measured flow rates correlated strongly with volumetric collection (Pearson correlation r = 0.99; P < 0.01). Due to limited sample resolution, VE MRI overestimated the flow rate by 47% on average when nonconstricted region-of-interest segmentation was used. Using constricted region-of-interest segmentation with lumen size equal to ground-truth luminal size, less than 13% error in flow rate was found. In vivo RCA flow velocity assessment was successful in 82% of the applied studies. High interscan, intra- and inter-observer agreement was found for almost all indices describing coronary flow velocity. Reproducibility for repeated acquisitions varied by less than 16% for peak velocity values and by less than 24% for flow volumes. CONCLUSION: 3T breathhold VE MRI with spiral k-space sampling enables accurate and reproducible assessment of RCA flow velocity.

Impact of antenna correlation on the capacity of multiantenna channels

This paper applies random matrix theory to obtain analytical characterizations of the capacity of correlated multiantenna channels. The analysis is not restricted to the popular separable correlation model, but rather it embraces a more general representation that subsumesmost of the channel models that have been treated in the literature. For arbitrary signal-to-noise ratios (SNR), the characterization is conducted in the regime of large numbers of antennas. For the low- and high-SNR regions, in turn, we uncover compact capacity expansions that are valid for arbitrary numbers of antennas and that shed insight on how antenna correlation impacts the tradeoffs between power, bandwidth and rate.

Correlation of diffusion tensor tractography and intraoperative macrostimulation during deep brain stimulation for Parkinson disease.

Object The purpose of this study was to investigate whether diffusion tensor imaging (DTI) of the corticospinal tract (CST) is a reliable surrogate for intraoperative macrostimulation through the deep brain stimulation (DBS) leads. The authors hypothesized that the distance on MRI from the DBS lead to the CST as determined by DTI would correlate with intraoperative motor thresholds from macrostimulations through the same DBS lead. Methods The authors retrospectively reviewed pre- and postoperative MRI studies and intraoperative macrostimulation recordings in 17 patients with Parkinson disease (PD) treated by DBS stimulation. Preoperative DTI tractography of the CST was coregistered with postoperative MRI studies showing the position of the DBS leads. The shortest distance and the angle from each contact of each DBS lead to the CST was automatically calculated using software-based analysis. The distance measurements calculated for each contact were evaluated with respect to the intraoperative voltage thresholds that elicited a motor response at each contact. Results There was a nonsignificant trend for voltage thresholds to increase when the distances between the DBS leads and the CST increased. There was a significant correlation between the angle and the voltage, but the correlation was weak (coefficient of correlation [R] = 0.36). Conclusions Caution needs to be exercised when using DTI tractography information to guide DBS lead placement in patients with PD. Further studies are needed to compare DTI tractography measurements with other approaches such as microelectrode recordings and conventional intraoperative MRI-guided placement of DBS leads.