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Francesco FAGLIONI

Professore Associato
Dipartimento di Scienze Chimiche e Geologiche - Sede Dipartimento di Scienze Chimiche e Geologiche


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Pubblicazioni

2023 - A novel iterative algorithm to improve segmentations with deep convolutional neural networks trained with synthetic X-ray computed tomography data (i.S.Sy.Da.T.A) [Articolo su rivista]
Tsamos, A; Evsevleev, S; Fioresi, R; Faglioni, F; Bruno, G
abstract

We propose a novel iterative segmentation algorithm (i.S.Sy.Da.T.A: Iterative Segmentation Synthetic Data Training Algorithm) employing Deep Convolutional Neural Networks and synthetic training data for X-ray tomographic reconstructions of complex microstructures. In our method, we reinforce the synthetic training data with experimental XCT datasets that were automatically segmented in the previous iteration. This strategy produces better segmentations in successive iterations. We test our algorithm with experimental XCT re-constructions of a 6-phase Al-Si Matrix Composite reinforced with ceramic fibers and particles. We perform the analysis in 3D with a special network architecture that demonstrates good generalization with synthetic training data. We show that our iterative algorithm returns better segmentations compared to the standard single training approach. More specifically, phases possessing similar attenuation coefficients can be better segmented: for Al2O3 fibers, SiC particles, and Intermetallics, we see an increase of the Dice score with respect to the classic approach: from 0.49 to 0.54, from 0.66 to 0.72, and from 0.55 to 0.66 respectively. Furthermore, the overall Dice score increases from 0.77 to 0.79. The methods presented in this work are also applicable to other materials and imaging techniques.


2023 - Synthetic Data Generation for Automatic Segmentation of X-ray Computed Tomography Reconstructions of Complex Microstructures [Articolo su rivista]
Tsamos, Athanasios; Evsevleev, Sergei; Fioresi, Rita; Faglioni, Francesco; Bruno, Giovanni
abstract

The greatest challenge when using deep convolutional neural networks (DCNNs) for automatic segmentation of microstructural X-ray computed tomography (XCT) data is the acquisition of sufficient and relevant data to train the working network. Traditionally, these have been attained by manually annotating a few slices for 2D DCNNs. However, complex multiphase microstructures would presumably be better segmented with 3D networks. However, manual segmentation labeling for 3D problems is prohibitive. In this work, we introduce a method for generating synthetic XCT data for a challenging six-phase Al-Si alloy composite reinforced with ceramic fibers and particles. Moreover, we propose certain data augmentations (brightness, contrast, noise, and blur), a special in-house designed deep convolutional neural network (Triple UNet), and a multi-view forwarding strategy to promote generalized learning from synthetic data and therefore achieve successful segmentations. We obtain an overall Dice score of 0.77. Lastly, we prove the detrimental effects of artifacts in the XCT data on achieving accurate segmentations when synthetic data are employed for training the DCNNs. The methods presented in this work are applicable to other materials and imaging techniques as well. Successful segmentation coupled with neural networks trained with synthetic data will accelerate scientific output.


2023 - Thermodynamics modeling of deep learning systems for a temperature based filter pruning technique [Articolo su rivista]
Lapenna, M; Faglioni, F; Fioresi, R
abstract

We analyse the dynamics of convolutional filters' parameters of a convolutional neural networks during and after training, via a thermodynamic analogy which allows for a sound definition of temperature. We show that removing high temperature filters has a minor effect on the performance of the model, while removing low temperature filters influences majorly both accuracy and loss decay. This result could be exploited to implement a temperature-based pruning technique for the filters and to determine efficiently the crucial filters for an effective learning.


2021 - On the Thermodynamic Interpretation of Deep Learning Systems [Relazione in Atti di Convegno]
Fioresi, R.; Faglioni, F.; Morri, F.; Squadrani, L.
abstract

In the study of time evolution of the parameters in Deep Learning systems, subject to optimization via SGD (stochastic gradient descent), temperature, entropy and other thermodynamic notions are commonly employed to exploit the Boltzmann formalism. We show that, in simulations on popular databases (CIFAR10, MNIST), such simplified models appear inadequate: different regions in the parameter space exhibit significantly different temperatures and no elementary function expresses the temperature in terms of learning rate and batch size, as commonly assumed. This suggests a more conceptual approach involving contact dynamics and Lie Group Thermodynamics.


2020 - Parity Violation Energy of Biomolecules - V: Protein Metal Centers [Articolo su rivista]
Faglioni, F.; Fracassini, B.; Perrone, L.
abstract

The parity-violation difference between mirror images of chiral metal centers found in naturally occurring proteins and enzymes is computed at the Dirac-Hartree-Fock level, for both equilibrium and transition state configurations. The systems, selected on the likelihood of yielding high parity violation energies based on atomic mass and coordination geometry, are extracted from: type I Blue Copper Protein active site, Zn and Cd Carbon Anhydrase, Ni Acetyl-Coenzyme-A Synthase, and Mo based CO-Dehydrogenase. Our values provide an approximate upper limit to possible parity-violation effects in biological systems based on static effects.


2019 - Deep learning techniques for detecting preneoplastic and neoplastic lesions in human colorectal histological images [Articolo su rivista]
Sena, P.; Fioresi, R.; Faglioni, F.; Losi, L.; Faglioni, G.; Roncucci, L.
abstract

Trained pathologists base colorectal cancer identification on the visual interpretation of microscope images. However, image labeling is not always straightforward and this repetitive task is prone to mistakes due to human distraction. Significant efforts are underway to develop informative tools to assist pathologists and decrease the burden and frequency of errors. The present study proposes a deep learning approach to recognize four different stages of cancerous tissue development, including normal mucosa, early preneoplastic lesion, adenoma and cancer. A dataset of human colon tissue images collected and labeled over a 10-year period by a team of pathologists was partitioned into three sets. These were used to train, validate and test the neural network, comprising several convolutional and a few linear layers. The approach used in the present study is ‘direct’; it labels raw images and bypasses the segmentation step. An overall accuracy of >95% was achieved, with the majority of mislabeling referring to a near category. Tests on an external dataset with a different resolution yielded accuracies >80%. The present study demonstrated that the neural network, when properly trained, can provide fast, accurate and reproducible labeling for colon cancer images, with the potential to significantly improve the quality and speed of medical diagnoses.


2019 - On the simulation of vibrationally resolved electronic spectra of medium-size molecules: the case of styryl substituted BODIPYs [Articolo su rivista]
Fortino, Mariagrazia; Bloino, Julien; Collini, Elisabetta; Bolzonello, Luca; Trapani, Mariachiara; Faglioni, Francesco; Pedone, Alfonso
abstract

BODIPY dyes are used in a variety of applications because of their peculiar spectroscopic and photo-physical properties that vary depending on the stereochemistry of the functional groups attached to the boron-dipyrromethene core structure. In this work, we have applied several computational methods, adapted for semi-rigid molecules based on the Franck-Condon principle, for the study of the optical properties of BODIPY systems and for the understanding of the influence of functional groups on their spectroscopic features. We have analyzed the electronic spectra of two styryl substituted BODIPY molecules of technological interest, properly taking into account the vibronic contribution. For comparison with recently recorded experimental data in methanol, the vibrationally resolved electronic spectra of these systems were computed using both Time-Independent (TI) and Time-Dependent (TD) formalisms. The first step toward the analysis of optical properties of the styryl modified BODIPYs was a benchmark of several density functionals, to select the most appropriate one. We have found that all benchmarked functionals provide good results in terms of band shape but some of them show strong discrepancies in terms of band position. Beyond the issue of the electronic structure calculation method, different levels of sophistication can be adopted for the calculation of vibronic transitions. In this study, the effect of mode couplings and the influence of the Herzberg-Teller terms on the theoretical spectra has been investigated. It has been found that all levels of theory considered give reproducible results for the investigated systems: band positions and shapes are similar at all levels and little improvements have been found in terms of band shape with the inclusion of Herzberg-Teller effect. Inclusion of temperature effects proved to be challenging due to the important impact of large amplitude motions. Better agreement can be achieved by adopting a suitable set of coordinates coupled with a reduced-dimensionality scheme.


2019 - Role of solvent-anion charge transfer in oxidative degradation of battery electrolytes [Articolo su rivista]
Fadel, E. R.; Faglioni, F.; Samsonidze, G.; Molinari, N.; Merinov, B. V.; Goddard III, W. A.; Grossman, J. C.; Mailoa, J. P.; Kozinsky, B.
abstract

Electrochemical stability windows of electrolytes largely determine the limitations of operating regimes of lithium-ion batteries, but the degradation mechanisms are difficult to characterize and poorly understood. Using computational quantum chemistry to investigate the oxidative decomposition that govern voltage stability of multi-component organic electrolytes, we find that electrolyte decomposition is a process involving the solvent and the salt anion and requires explicit treatment of their coupling. We find that the ionization potential of the solvent-anion system is often lower than that of the isolated solvent or the anion. This mutual weakening effect is explained by the formation of the anion-solvent charge-transfer complex, which we study for 16 anion-solvent combinations. This understanding of the oxidation mechanism allows the formulation of a simple predictive model that explains experimentally observed trends in the onset voltages of degradation of electrolytes near the cathode. This model opens opportunities for rapid rational design of stable electrolytes for high-energy batteries.


2018 - Factors affecting cyclic durability of all-solid-state lithium batteries using poly(ethylene oxide)-based polymer electrolytes and recommendations to achieve improved performance [Articolo su rivista]
Faglioni, Francesco; Merinov, Boris V; Goddard, William A; Kozinsky, Boris
abstract

A detailed experimental analysis of the factors affecting cyclic durability of all-solid-state lithium batteries using poly(ethylene oxide)-based polymer electrolytes was published in EES by Nakayama et al. We use quantum mechanics to interpret these results, identifying processes involved in the degradation of rechargeable lithium batteries based on polyethylene oxide (PEO) polymer electrolyte with LiTFSI. We consider that ionization of the electrolyte near the cathode at the end of the recharge step is probably responsible for this degradation. We find that an electron is likely removed from PEO next to a TFSI anion, triggering a sequence of steps leading to neutralization of a TFSI anion and anchoring of another TFSI to the PEO. This decreases the polymer conductivity near the cathode, making it easier to ionize additional PEO and leading to complete degradation of the battery. We refer to this as the Cathode Overpotential Driven Ionization of the Solvent (CODIS) model. We suggest possible ways to confirm experimentally our interpretation and propose modifications to suppress or reduce electrolyte degradation.


2018 - Medical Database for Detecting Neoplastic Lesions in Human Colorectal Cancer with Deep Learning [Articolo su rivista]
Fioresi, Rita; Faglioni, Francesco; Sena, Paola
abstract

Medical databases are fundamental for developing new techniques for early detection of neoplastic cells. They are however difficult to obtain, since the labelling of the images is often operator dependent, requires specialized skills and the written informed consent of the patient. The variability of structures in biological tissue poses a challenge to both manual and automated analysis of histopathology slides. Although some authors showed moderate to good agreement among expert pathologists, and satisfactory results on their intra-observer reliability, other studies found that even experienced pathologists frequently disagree on tissue classification, which may lead to the conclusion that solely using expert scoring as gold standard for histopathological assessment could be insufficient. Hence, there is a growing demand for robust computational methods in order to increase reproducibility of diagnoses. In this note we present a database containing images of preneoplastic and neoplastic colorectal tissues and in a forthcoming paper we will describe our proposed DL algorithm to classify them into the following categories: normal mucosa, early preneoplastic lesions, adenomas, cancer.


2016 - Computational Study of the Stability of Nanotube Fragments [Articolo su rivista]
Fantini, Beatrice; Faglioni, Francesco
abstract

Extremely short (<1 nm) fragments of zig-zag carbon nanotubes are studied with ab-initio techniques to determine their geometric and electronic structure as well as their magnetic susceptibility. It is found that for lengths of a few carbon–carbon bonds, each fragment can be viewed as composed of crowns, that is, zig-zag rings of carbon atoms along the circumference of the tube. In this case, two kinds of electronic structures are found, depending on whether the number of carbon atoms in each crown is even or odd. Systems comprising three or more crowns either have a high spin ground state or involve a charge transfer across the length of the fragment. Conjugation changes qualitatively when the length of the fragment approaches and surpasses its girth. Indications regarding the predicted chemical stability and electronic response are provided and interpreted in terms of current densities induced within each crown by a magnetic field along the tube axis.


2016 - Room-Temperature Lithium Phases from Density Functional Theory [Articolo su rivista]
Faglioni, Francesco; Merinov, Boris V.; Goddard, William A.
abstract

Metallic lithium is a promising electrode material for developing next generation rechargeable batteries, but it suffers from dendrite formation upon recharging. This compromises both efficiency and safety of these systems. The surface phenomena responsible for dendrite formation are difficult to characterize experimentally, making it important to use Quantum Mechanics (QM) to provide the understanding needed to design improved systems. The most accurate practical level of QM for such studies is the PBE form of density functional theory (DFT.) We report here an assessment of the accuracy for PBE to predict the most stable four phases of bulk lithium. PBE predicts three phases, bcc, fcc, and hcp, to be nearly equal in stability (within 5 meV). Including the zero-point energy and enthalpy corrections at standard conditions (298 K and 1 atm), we predict bcc most stable, fcc at 0.0029 eV, hcp at 0.0036 eV, and cI16 at 0.0277 eV. Indeed their experimental free energies under ambient conditions differ only by a few meV, with bcc considered most stable. Experimentally, the fourth phase becomes stable at high pressure (>30-40 GPa) and low temperature (<200 K). To use QM calculations to predict growth mechanisms, it is essential to bias the calculations by imposing the desired crystal structure in the underlying layers. We consider that this will allow QM studies of dendritic growth far from the crystalline phase due to the lower surface energy of bcc. (Figure Presented).


2013 - Chiral discrimination via nuclear magnetic resonance spectroscopy [Articolo su rivista]
Stefano, Pelloni; Faglioni, Francesco; Lazzeretti, Paolo
abstract

Calculations of nuclear magnetic shielding polarisabilities of cyclic C4H2X2 molecules, for X = O, S, Se and Te, have been carried out. Pseudoscalars of the nuclear magnetic shielding polarisability computed for the heavier nuclei are at least two orders of magnitude larger than those reported so far. Calculations of the rf voltage produced by the rotating chiral electric polarisation, induced by the permanent magnetic dipole moment of 77Se nucleus in 1,2-diselenin and 125Te nucleus in 1,2-ditellurin, are predicted to be &40 nV and &80 nV, respectively, detectable in principle with a proper experimental set-up. Also the chiral chemical shifts are evaluated and they are found near the experimental detection limit.


2013 - Parity violation energies of C_4 H_4 X_2 molecules for X=O, S, Se, Te and Po [Articolo su rivista]
Stefano, Pelloni; Faglioni, Francesco; Lazzeretti, Paolo
abstract

Parity-violating contributions, with the same magnitude but opposite sign, to the energies of 1,2 enantiomers of dioxin, dithiin, diselenin, ditellurin, and dipolonin have been calculated. Theoretical predictions, which can be classified among the largest reported so far, indicate that the P enantiomer is energetically more stable than M. As expected, non-relativistic effects increase with the first power of the neutron number and the fourth power of the atomic number for X= O, S, Se, Te, Po. The trend predicted by Laerdahl and Schwerdtfeger [Phys. Rev. A {60}, 4439 (1999)] and by Berger [J. Chem. Phys. {129}, 154105 (2008)] for H_2X_2 molecules, characterized by free rotation about the X-X internuclear axis, is therefore confirmed for the series of more rigid C_4 H_4 X_2 compounds, in which limited deformations can take place.


2012 - Predicting autoxidation stability of ether- and amide-based electrolyte solvents for Li-air batteries [Articolo su rivista]
V. S., Bryantsev; Faglioni, Francesco
abstract

Finding suitable solvents remains one of the most elusive challenges in rechargeable, nonaqueous Li-air battery technology. Although ether and amides are identified as stable classes of aprotic solvents against nucleophilic attack by superoxide, many of them are prone to autoxidation under oxygen atmosphere. In this work, we use density functional theory calculations coupled with an implicit solvent model to investigate the autoxidative stability of ether- and N,N-dialkylamide-based solvents. The change in the activation free energy for the C-H bond cleavage by O 2 is consistent with the extent of peroxide production for each class of solvent. Conversely, the thermodynamic stability alone is not sufficient to account for the observed variation in solvent reactivity toward O 2. A detailed understanding of the factors influencing the autoxidative stability provides several strategies for designing molecules with enhanced air/O 2 stability, comparable or superior to that of structurally related hydrocarbons. The mechanism of superoxide-mediated oxidation of hydroperoxides derived from ethers and amides is presented. The degradation mechanism accounts for the primary decomposition products (esters and carboxylates) observed in the Li-air battery with ether-based electrolytes. The identification of solvents having resistance to autoxidation is critical for the development of rechargeable Li-air batteries with long cycle life.


2011 - Parity-Violation Energy of Biomolecules-IV: Protein Secondary Structure [Articolo su rivista]
Faglioni, Francesco; I., Garcia Cuesta
abstract

The parity-violation energy difference between enantiomeric forms of the same amino acid sequence, from the amyloid beta-peptide involved in Alzheimer's desease, in both alpha-helix and beta-sheet configurations, is investigated with ab-initio techniques. To this end, we develop an extension of the N2 computational scheme that selectively includes neighboring amino acids to preserve the relevant H-bonds. In agreement with previous speculations, it is found that the helical alpha structure is associated with larger parity-violation energy differences than the corresponding beta form. Implications for the evolution of biological homochirality are discussed as well as the relative importance of various effects in determining the parity-violation energy.


2010 - Aqueous-phase quantitative NMR determination of amino acid enantiomer ratio by (13)C-NMR using chiral neodymium shift reagent [Articolo su rivista]
FLORINI, Nicola; FAGLIONI, Francesco; ZUCCHI, Claudia; L., Caglioti; PALYI, Gyula
abstract

A neodymium-(S)-PDTA (PDTA = N,N,N',N'-tetrakis[(hydroxycarbonyl)methyl]-1,2-diaminopropane) complex was found exceptionally useful in the quantitative determination of enantiomer ratios of water-soluble natural amino acids by (13)C-NMR. The method is demonstrated on mixtures of l- and d-enantiomers of various amino acids. The interactions of the chiral shift reagent with the amino acid molecules were rationalized by molecular orbital calculations.


2010 - Stability of Lithium Superoxide LiO(2) in the Gas Phase: Computational Study of Dimerization and Disproportionation Reactions [Articolo su rivista]
V. S., Bryantsev; M., Blanco; Faglioni, Francesco
abstract

Knowledge of the precise molecular mechanisms during the discharge and recharge processes in the lithium-air battery is critical for achieving desired improvements in specific capacity, current density, and cyclability. The initial oxygen reduction product formed in the presence of Li(+) ions is lithium superoxide LiO(2). In this study, we report the computed structures and thermodynamic parameters of LiO(2) dimerization in the gas phase, which enables us to provide a baseline for the reaction free energy profile of the subsequent disproportionation of (LiO(2))(2) to lithium peroxide Li(2)O(2) and O(2). Our calculations identified several low-lying (LiO(2))(2) dimers, with the singlet bipyramidal structure giving IR bands that are consistent with the characteristic IR vibration frequencies of (LiO(2))(2) in the oxygen matrix at T = 15-40 K. The activation barrier for (LiO(2))(2) = Li(2)O(2)+O(2) is 10.9 kcal/mol at the UCCSD(T)/CBS level (T = 298 K), suggesting that in the gas phase LiO(2) and its aggregates could only be observed at low temperatures.


2008 - On the track of absolute enantioselective catalysis [Articolo su rivista]
L., Caglioti; B., Barabas; Faglioni, Francesco; Florini, Nicola; Lazzeretti, Paolo; Maioli, Marco; K., Micskei; K., Rabai; Taddei, Ferdinando; Zucchi, Claudia; Palyi, Gyula
abstract

The main goal of this communication is to show the utility of empirical approaches combined with mathematical methods in the research regarding the molecular basis of biological chirality. Preparative results (enantiomeric excesses, e.e.) obtained in asymmetric autocatalysis with (AAC) and without (AES) chiral additive were analyzed. Statistical calculations show, that AES (absolute enantioselective synthesis) experiments yield two independent groups of results with prevalence of the R- or S-enantiomer. These are distributed asymmetrically in a second-order beta distribution. Empirical calculations both on AAC and EAS enable to identify the very low (statistical) e. e.-s amplified by AES. These initial e. e.-s show normal distribution. Possible molecular-level reasons of these results were controlled by quantum chemical MO calculations and compatible mechanism(s) are discussed.


2007 - On the traces of absolute enantioselective synthesis [Relazione in Atti di Convegno]
B., Barabas; L., Caglioti; Faglioni, Francesco; Florini, Nicola; Lazzeretti, Paolo; Maioli, Marco; K., Micskei; G., Rabai; Taddei, Ferdinando; Zucchi, Claudia; Palyi, Gyula
abstract

The main goal of this communication is to show the utility of empirical approaches combined with mathematical methods in the research regarding the molecular basis of biological chirality. Preparative results (enantiomeric excesses, e.e.) obtained in asymmetric autocatalysis with (AAC) and without (AES) chiral additive were analyzed. Statistical calculations show, that AES (absolute enantioselective synthesis) experiments yield two independent groups of results with prevalence of the R- or S-enantiomer. These are distributed asymmetrically in a second-order beta distribution. Empirical calculations both on AAC and EAS enable to identify the very low (statistical) e.e.-s amplified by AES. These initial e.e.-s show normal distribution. Possible molecular-level reasons of these results were controlled by quantum chemical MO calculations and compatible mechanism(s) are discussed.


2007 - Parity violation energy of 5-pyrimidyl alkanol, a chiral autocatalytic molecule [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo; Palyi, Gyula
abstract

The energy of parity-violation due to weak-nuclear interactions between molecular electrons and nucleons associated with three molecules that participate in highly enantioselective autocatalytic reactions is estimated with ab initio techniques. The molecules, derivatives of (S)-5-pyrimidyl alkanol, are found to have very small parity-violation energy. Although our results are not conclusive, the computed parity-violation energy is not expected to have any effect on the direction of spontaneous symmetry breaking reported in the literature and leading to a preferential formation of the (S) form.


2006 - Alkylation of Phenol: A Mechanistic View [Articolo su rivista]
Q., Ma; D., Chakraborty; Faglioni, Francesco; R. P., Muller; W. A., GODDARD III
abstract

The current work utilizes the ab initio density functional theory (DFT) to develop a molecular level of the mechanistic understanding on the phenol alkylation in the presence of a cation-exchange resin catalyst, Amberlyst-15. The catalyst is modeled with the benzene sulfonic acid, and the effect of this acid on olefins such as isopropene (i-Pr) and tributene (t-Bu) in a phenol solution mimics the experimental condition. A neutral-pathway mechanism is established to account for early-stage high concentration of the phenolic ether observed in experiments. The mechanism involves an exothermic reaction between olefin and the benzene sulfonic acid to form ester followed by three reaction pathways leading to direct O-alkylation, o-C-alkylation, and p-C-alkylation. Our calculations conclude that O-alkylation to form the phenolic ether is the most energetically favorable in the neutral condition. An ionic rearrangement mechanism describes intramolecular migrations of the alkyl group from the phenolic ether to form C-alkylphenols, while the positively charged protonation significantly lowers transition barriers for these migrations. The ionic rearrangement mechanism accounts for high yields of o-C-alkylphenol and p-C-alkylphenol. Competition between the H atom and the alkyl R group at the substitutive site of the protonated ortho configuration is found to be the determining factor to the ortho/para ratio of C-alkylation products.


2006 - Parity violation energy of biomolecules - III: RNA [Articolo su rivista]
Faglioni, Francesco; Ig, Cuesta; Lazzeretti, Paolo
abstract

The energy of parity-violation associated with a typical RNA double helix is estimated with ab initio techniques. It is shown that weak nuclear interactions do not favour the formation of the double helices found in nature. Possible implications regarding the potential effect on the evolution of biological homochirality are discussed.


2006 - Topology of magnetic-field induced current-density field in diatropic mono-cyclic molecules [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo; Pelloni, Stefano; Zanasi, Riccardo
abstract

Concise information on the general features of the quantum-mechanical current density induced in the electrons of a molecule by a spatially uniform, time-independent magnetic field is obtained via a stagnation graph that shows the isolated singularities and the lines at which the current-density vector field vanishes. Stagnation graphs provide compact description of current-density vector fields and help the interpretation of molecular magnetic response, e.g., magnetic susceptibility and nuclear magnetic shielding. The stagnation graph of six cyclic, planar aromatic molecules has been obtained at the Hartree-Fock level via a procedure based on continuous transformation of the origin of the current density formally annihilating the diamagnetic contribution. Some common distinctive elements observed for cyclic aromatic rings CnHn, with n=3,4, . . . ,8, in the presence of a magnetic field normal to the molecular plane, are discussed. The results can be used for a general discussion of diatropism in aromatic systems.


2005 - Energetics of hydrogen coverage on group VIII transition metal surfaces and a kinetic model for adsorption/desorption [Articolo su rivista]
FAGLIONI, Francesco; W. A., GODDARD III
abstract

We determined the binding energy of hydrogen to the closest packed surface for all nine group VIII transition metals as a function of surface coverage using quantum mechanics (density functional theory with the generalized gradient approximation) with periodic boundary conditions. The study provides a systematic comparison of the most stable surfaces of the nine group VIII transition metals, leading to results consistent with available surface science studies. We then use these to develop a simple thermodynamic model useful in estimating the surface coverage under typical heterogeneous catalysis conditions and compare these results to temperature programmed desorption experiments.


2005 - Parity Violation Energy Of Biomolecules – I: Polypeptides [Articolo su rivista]
Faglioni, Francesco; Alessio, Passalacqua; Lazzeretti, Paolo
abstract

A computational algorithm is developed to compute the energy of parity-violation (E-pv) due to weak-nuclear forces acting within chain polymers. The method is applied to estimate the magnitude of E-pv associated with the folding of alpha-helices in polypeptide chains and, in turn, of typical proteins. Implications to the development of biological homochirality in nature are discussed in terms of a simple evolutionary model to assess the likelihood for energies of the order of the computed E-pv to have determined the direction of natural homochirality.


2005 - Parity violation energy of biomolecules - II: DNA [Articolo su rivista]
Faglioni, Francesco; P. S., D'Agostino; B., Cadioli; Lazzeretti, Paolo
abstract

The energy of parity-violation associated with a typical DNA double helix is estimated with ab initio techniques. It is shown that weak-nuclear interactions do not favor the formation of the double helices found in nature. Possible implications regarding the potential effect of parity-violation interactions on the evolution of biological homochirality are discussed.


2005 - Ring current effects on nuclear magnetic shielding of carbon in the benzene molecule [Articolo su rivista]
Mb, Ferraro; Faglioni, Francesco; Ligabue, Andrea; S., Pelloni; Lazzeretti, Paolo
abstract

The differential Biot-Savart law of classical electrodynamics was applied to develop a ring current model for the magnetic shielding of the carbon nucleus in benzene. It is shown that the local effect of the pi currents, induced by a magnetic field normal to the molecular plane, on the sigma(C) out-of-plane shielding tensor component vanishes. However, approximately 10% of sigma(C) is due to the shielding contributions from pi current density in the region of the other carbon atoms. Magnetic shielding density maps obtained via quantum mechanical procedures confirm the predictions of the classical model.


2005 - Why downfield proton chemical shifts are not reliable aromaticity indicators [Articolo su rivista]
Faglioni, F.; Ligabue, A.; Pelloni, S.; Soncini, A.; Viglione, R. G.; Ferraro, M. B.; Zanasi, R.; Lazzeretti, P.
abstract

(Chemical Equation Presented) Traces of magnetizability, traces of magnetic shielding at the hydrogen nuclei, and nucleus-independent chemical shift are not reliable aromaticity quantifiers for planar conjugated hydrocarbons. A measure of aromaticity is provided by the out-of-plane tensor components, whose magnitude is influenced by the π-ring currents. The failure of nucleus-independent chemical shift in this regard was proved for the molecule shown in the abstract graphic, sustaining a diatropic π-current. The validity of the ring-current model is reaffirmed. © 2005 American Chemical Society.


2004 - Molecular response to a time-independent non-uniform magnetic-field [Articolo su rivista]
Faglioni, Francesco; Ligabue, Andrea; S., Pelloni; A., Soncini; Lazzeretti, Paolo
abstract

The response of a molecule to a static inhomogeneous magnetic-field is rationalized via multipole magnetic susceptibilities and induced magnetic multipole and anapole moments. The energy of the molecule interacting with the external field is expressed as a Taylor series in the powers of the field and its gradient at the origin of the coordinate system. It involves magnetic multipole tensors of increasing rank, which can be evaluated via quantum mechanical approaches. An electronic energy shift is caused by the feedback interaction between the induced magnetic dipole moment and the external magnetic field, and between the induced magnetic quadrupole moment and the gradient of the magnetic field. It is shown that, for a static magnetic field with uniform gradient, the magnetic quadrupole moment is origin-dependent, but the total interaction energy and the induced magnetic dipole are invariant to a translation of the coordinate system. The formal advantages of a Geertsen approach to third- and fourth-rank mixed-multipole susceptibilities are discussed.


2004 - The vibrational spectrum of camphor from ab initio and density functional theory and parity violation in the C-C*-CO bending mode [Articolo su rivista]
P., Schwerdtfeger; A., Kuehn; R., Bast; J. K., Laerdahl; Faglioni, Francesco; Lazzeretti, Paolo
abstract

The C-C*-CO bending mode in camphor (C* denotes a chiral carbon) as originally investigated for parity violation effects by Arimondo et al. [Opt. Commun. 23 (1977) 369] lies in the CO2 laser frequency range with the most intense transition at 1045 cm(-1). The vibrational spectrum of camphor is, therefore, reinvestigated by ab initio and density functional calculations and compared with experimental results. This provides the basis for a local mode analysis which reveals that the C-C*-CO bending mode has only minute parity violation contributions (<10(-5) Hz) to vibrational transitions far below the current detection limit of high resolution spectroscopy.


2003 - Magnetic response of dithiin molecules: is there anti-aromaticity in nature? [Articolo su rivista]
S., Pelloni; Faglioni, Francesco; A., Soncini; Ligabue, Andrea; Lazzeretti, Paolo
abstract

Ab initio current density formalism is used to investigate the response to external magnetic fields of the only knownnaturally occurring moieties which are formally anti-aromatic, i.e., dithiines. Magnetic susceptibility, nuclear shieldingconstants, and the topology of induced current densities indicate that although these molecules satisfy H€uckels rule forbeing anti-aromatic, they are not. In chiral dithiines, the multipolar expansion of the response contains non-vanishinganapole terms associated with spinning cuff current lines.


2003 - Parity Violating Contributions to Nuclear Magnetic Shielding. [Articolo su rivista]
A., Soncini; Faglioni, Francesco; Lazzeretti, Paolo
abstract

A gauge-invariant formalism is developed to describe the effect of parity-violating weak-nuclear interactionson nuclear magnetic chemical shift in molecules. Such effect is computed for two molecules with ab initiotechniques and it is found to be orders of magnitude smaller than experimental resolution for the moleculesconsidered.


2003 - Parity-Violation Effect on Vibrational Spectra [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo
abstract

Weak nuclear coupling between the nucleons of a molecule and its electrons causes the energy and electronic wave function to be different for two enantiomers of a chiral molecule, i.e., for two molecules which are the specular image of each other. Although this effect has been known for some time, its magnitude is so small that all attempts made so far at measuring it experimentally have failed. We report in this paper computational estimates of vibrational frequency shifts due to parity-violation energy near or above current experimental resolution. Our findings indicate that an experimental evidence of parity-violation effects in molecular systems is within reach.


2002 - Heterogeneous Inhibition of Homogeneous Reactions: Karstedt Catalyzed Hydrosilylation [Articolo su rivista]
Faglioni, Francesco; M., Blanco; W. A., GODDARD III; D., Saunders
abstract

The Karstedt-catalyzed hydrosilylation reaction used in curing of silicone release coatings was investigated using first-principle quantum mechanical techniques (density functional theory) as well as semiempirical methods to estimate solubility parameters. The results we obtain for the catalytic cycle indicate, in agreement with experimental results, that hydrosilylation occurs easily at room temperature. The detailed mechanism we suggest contains the key features of the models previously proposed in the literature by Lewis and Chalk-Harrod and adds quantitative estimates of reaction energies and barriers. On the basis of the energy profile for the catalytic cycle in the presence of inhibitor molecules and on solubility parameters for the species involved in the reaction, we conclude that the role of the inhibitors we considered is to phase-separate the catalyst from the substrate. The reaction is thus quenched by introducing a microscopic second phase that interferes with the homogeneous reaction.


2002 - Methane Activation by Transition-Metal Oxides, MOx (M=Cr, Mo, W; x=1,2,3) [Articolo su rivista]
X., Xu; Faglioni, Francesco; W. A., GODDARD III
abstract

Recent experiments on the dehydrogenation-aromatization of methane (DHAM) to form benzene using a MoO3/HZSM-5 catalyst stimulated us to examine methane activation by the transition-metal oxide molecules, MOx (M = Cr, Mo, W; x = 1, 2, 3). The present studies use hybrid density functional theory (B3LYP). The reactivity trend is rationalized in terms of changes in the electrophilicity of MO,, the strength of the M-O pi bond, and the bonding properties of MQ(x) to methyl or hydrogen as M and x are varied, It is found that or-bond metathesis to the metal hydride product (H-MOx-1-OCH3) occurs preferentially over the high oxidation state form (MO3) of the heavier metals, as well as all chromium oxides (CrOx). Instead, oxidative addition of MOx leading to methyl metal hydride (H-M(O-x)-CH3) is more favorable over the low oxidation state of MOx (M = Mo, W, x = 2, 1). In particular, it is found that WO2 can undergo oxidative addition with negligible activation barrier and is predicted to be the most reactive compound of this class toward methane activation. Our finding that MO2 (M = W, Mo) is the best oxidation state for this class of metal oxides toward methane activation suggests that the MO3/HZSM-5 catalysts active in the DHAM reaction may be W and Mo oxycarbides (MO2C2). The formation of such intermediates may be the reason that the experiments find an induction period before the catalyst is active for the desired reaction.


2002 - Understanding Parity violation in molecular systems [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo
abstract

Parity-violation energy (EPV) due to weak nuclear interactions between nucleons and electrons in chiralmolecular systems provides a fundamental tool to verify our understanding of electronic behavior in complexsystems. We used both a relativistic and a nonrelativistic approach to study a number of simple molecules andanalyze the corresponding EPV in terms of intuitive electrodynamic concepts. We developed a qualitativemodel to predict the sign of EPV and its behavior against selected geometric distortions. Our model provides avaluable tool to screen large sets of molecules and select interesting candidates for more expensive investigations.


2001 - Reactivity of methane mono-oxygenase, insights from quantum mechanic studies on synthetic iron model complexex [Articolo su rivista]
KNOPS GERRITS, P. P.; P. A., Jacobs; A., Fukuoka; M., Ichikawa; Faglioni, Francesco; W. A., GODDARD III
abstract

Methane mono-oxygenase (MMO) and deoxyhemerythrin (DHr) are examples of di-iron enzymes that catalyze the dissociative and non-dissociative binding of molecular oxygen. To mimic the MMO active site with a finite cluster, we chose to study the binuclear heptapodate coordinated iron(III)-complexes of N,N,N,N'-tetrakis(2-benzimidazolylmethyl)-2-hydroxy-1,3-diamino-propane (HPTB) and N,N,N',N'-tetrakis(2-pyridylmethyl)-2-hydroxy-1,3-diamino-propane (HPTP). These have active sites of the form [Fez (HPTP)(mu -OH)](4+) (1) and [Fe-2(HPTB)(mu -OH)](4+) (2). Quantum mechanics structures are compared with the experimental data obtained from the EXAFS analysis. For the O-2 binding on the reduced active site. the mu-eta (1):eta (1)-O-2 mode seems the slightly more stable precursor to the O=Fe-O-Fe=O bis-ferryl (re)active site. The nature of the ferryl groups are these of a reactive two center three electron bond. (C) 2001 Elsevier Science B.V. All rights reserved.


2001 - Scanning Tunneling Microscopy of Functional Groups: Substituted Alkanes and Alkanols on Graphite [Articolo su rivista]
N. S., Lewis; C. L., Claypool; W. A., GODDARD III; Faglioni, Francesco; H. B., Gray; R. A., Marcus
abstract

Scanning Tunneling Microscopy of Functional Groups: Substituted Alkanes and Alkanols on Graphite


2000 - Investigations of heterogeneous and homogeneous transition metal catalysis using density functional theory. [Articolo su rivista]
Goddard, Wa; Muller, R; Kua, J; Faglioni, Francesco; Philipp, D.
abstract

Investigations of heterogeneous and homogeneous transition metal catalysis using density functional theory.


2000 - Thermochemistry for hydrocarbon intermediates chemisorbed on metal surfaces: CH{n-m}(CH3)m with n=1, 2, 3 and m >= n on Pt, Ir, Os, Pd, Ph, and Ru [Articolo su rivista]
J., Kua; Faglioni, Francesco; W. A., Goddard
abstract

To provide insight and understanding of the thermochemistry underlying hydrocarbon rearrangements on transition metal surfaces, we report systematic studies of hydrocarbon radicals chemisorbed on metal clusters representing the closest packed surfaces of the six second and third row group VIII transition metals. Using first principles quantum mechanics [nonlocal density functional theory with exact HF exchange (B3LYP)], we find that (i) CH3-m(CH3)(m) forms one bond to the surface, preferring the on-top site (eta(1)), (ii) CH2-m(CH3)(m) forms two bonds to the surface, preferring the bridge site (eta(2)), and (iii) CH1-m(CH3)(m) forms three bonds to the surface, preferring the 3-fold site (eta(3)). For all six metals, the adiabatic bond energy is nearly proportional to the number of bonds to the surface, but there are dramatic decreases in the bond energy with successive methyl substitution. Thus from CH3 to CH2CH3, CH(CH3)(2), and C(CH3)(3), the binding energy decreases by 6, 14, and 23 kcal/mol, respectively (out of similar to 50). From CH2 to CHCH3 and C(CH3)(2), the binding energy decreases by 8 and 22 kcal/mol, respectively (out of similar to 100). These decreases due to methyl substitution can be understood in terms of steric repulsion with the electrons of the metal surface. For CH to C(CH3), the bond energy decreases by 13 kcal/mol (out of similar to 160), which is due to electronic promotion energies. These results are cast in terms of a thermochemical group additivity framework for hydrocarbons on metal surfaces similar to the Benson scheme so useful for gas-phase hydrocarbons. This is used to predict the chemisorption energies of more complex adsorbates.


2000 - Tutorial: Case studies in the use of density functional theory for transition metal systems, with an emphasis on heterogeneous and homogeneous catalysis, metal alloys, and transition metal oxides. [Articolo su rivista]
Goddard, Wa; Muller, R; Strachan, A; Kua, J; Faglioni, F; Philipp, D; Feldmann, M; Chakraborty, D; Jang, Yh; Xu, X; Blanco, M; Tang, Y; Cagin, T
abstract

Tutorial: Case studies in the use of density functional theory for transition metal systems, with an emphasis on heterogeneous and homogeneous catalysis, metal alloys, and transition metal oxides.


1999 - Effects of molecular geometry on the STM image contrast of methyl- and bromo-substituted alkanes and alkanols on graphite [Articolo su rivista]
C. L., Claypool; Faglioni, Francesco; A. J., Matzger; W. A., Goddard; N. S., Lewis
abstract

Scanning tunneling microscopy (STM) images have been collected for a series of substituted alkanes and alkanols that form ordered overlayers at room temperature on highly ordered pyrolytic graphite surfaces. Molecules that have been imaged possess an internal bromide, with or without terminal alcohol groups (HO(CH2)(9)CHBr(CH2)(10)OH and H3C(CH2)(16)CHBr(CH2)(16)CH3), an internal -OH group (H3C(CH2)(16)CHOH(CH2)(16)CH3), and an internal methyl group (H3C(CH2)(16)CHCH3(CH2)(16)CH3). These data allow comparison to the STM image contrast reported previously for molecules in which -OH, -Br, and -CH3 groups were located in terminal positions of alkane chains adsorbed onto graphite surfaces. When the functional groups were in gauche positions relative to the alkyl chain, and thus produced molecular features that protruded toward the tip, the functional groups were observed to produce bright regions in a constant current STM image, regardless of the STM contrast behavior observed for these same functional groups when they were in terminal positions of adsorbed alkyl chains. These observations are in excellent agreement with theoretical predictions of the STM behavior of such systems. Additionally, several interesting packing structures have been observed that have yielded insight into the intermolecular forces that control the packing displayed by these overlayers.


1999 - Energetic Stabilization of d-Camphor via Weak Neutral Currents [Articolo su rivista]
Lazzeretti, Paolo; R., Zanasi; Faglioni, Francesco
abstract

It is shown via a series of numerical tests on the camphor molecule, C10H16O, that the naturally occurringd-enantiomer is energetically stabilized with respect to its mirror image by electroweak force. The calculatedenergy difference between enantiomers, about 1.5310219 hartree, is roughly eight orders of magnitude smallerthan the upper bound suggested by available spectroscopic investigations on the frequency of a spectroscopictransition. However, such a difference is about ten times larger than previous estimates of parity-violatingenergy contributions reported in the literature for other chiral molecules, which makes the idea of electroweakstabilization of one enantiomer more reliable than expected before.


1999 - GVB-RP: A reliable MCSCF wave function for large systems [Articolo su rivista]
Faglioni, Francesco; W. A., Goddard
abstract

We have developed a version of generalized valence bond (GVB) that overcomes the major weakness of the perfect pairing approximation without requiring a full transformation of the integrals at each step of the self-consistent orbital optimization. The method, called generalized valence bond-restricted pairing (GVB-RP), describes properly the dissociation of up to triple bonds and provides smooth potential energy surfaces for most chemical reactions. The wave functions obtained are a good starting point for more sophisticated computational techniques. The applicability of the method is illustrated with a few simple examples including multiple-bond dissociations, transition states for symmetry allowed, symmetry forbidden, and radical reactions, as well as reactions at a transition-metal center. The cost of the method compares well with other self-consistent correlated techniques.


1999 - MSC/Caltech Collaborations with Industry an Catalysis Technologies [Articolo su rivista]
W. A., GODDARD III; Faglioni, Francesco; J., Kua; D., Phillip; M., Feldmann
abstract

MSC/Caltech Collaborations with Industry an Catalysis Technologies


1999 - Tunneling mechanism implications from an STM study of H3C(CH2)15HC=C=CH(CH2)15CH3 on graphite and C14H29OH on MoS2 [Articolo su rivista]
C. L., Claypool; Faglioni, Francesco; W. A., Goddard; N. S., Lewis
abstract

The observations reported herein confirm that the bright spots in high-resolution STM images of adsorbed alkanes and alkanols are predominantly due to the electronic and topographic structure of the molecule, and not predominantly due to the substrate. STM images of a monolayer of 17,18-pentatriacontadiene, H3C(CH2)(15)-HC=C=CH(CH2)(15)CH3, adsorbed on graphite were obtained to evaluate whether changes in the orientation of the exposed methylene hydrogen atoms relative to the STM tip produced changes in the observed pattern of bright spots in a STM image. STM images of this system showed a pattern of bright spots within individual molecules that appears to change on either side of the allene -C=C=C- functionality. STM images were also obtained for tetradecanol overlayers on graphite and MoS2 surfaces. The angles and distances observed in the images of tetradecanol on MoS2 were nearly identical to those measured previously in our laboratories for alkanol and alkane monolayers on graphite despite that fact that the separation between bright spots in an STM image of graphite is 2.46 Angstrom, while the separation between bright spots in STM images of MoS2 is 3.16 Angstrom.


1998 - Transition states for homogeneous and heterogeneous catalysis, including stereoselective polymerizations and for metathesis. [Articolo su rivista]
W. A., Goddard; C., Brandow; C., Kankel; J., Sefcik; Faglioni, Francesco
abstract

Transition states for homogeneous and heterogeneous catalysis, including stereoselective polymerizations and for metathesis.


1998 - Why molecules look the way they do in STM: A systematic functional group approach. [Articolo su rivista]
C. L., Claypool; N. S., Lewis; Faglioni, Francesco; W. A., Goddard; H. B., Gray; R. A., Marcus
abstract

Why molecules look the way they do in STM: A systematic functional group approach.


1997 - Source of Image Contrast in STM Images of Functionalized Alkanes on Graphite: A Systematic Functional Group Approach [Articolo su rivista]
C. L., Claypool; Faglioni, Francesco; W. A., Goddard; H. B., Gray; N. S., Lewis; R. A., Marcus
abstract

A series of functionalized alkanes and/or alkyl alcohols have been prepared and imaged by scanning tunneling microscopy (STM) methods on graphite surfaces. The stability of these ordered overlayers has facilitated reproducible collection of STM images at room temperature with submolecular resolution, in most cases allowing identification of individual hydrogen atoms in the alkane chains, but in all cases allowing identification of molecular length features and other aspects of the image that can be unequivocally related to the presence of functional groups in the various molecules of concern. Functional groups imaged in this study include halides (X = F, Cl, Br, I), amines, alcohols, nitriles, alkenes, alkynes, ethers, thioethers, and disulfides. Except for -Cl and -OH, all of the other functional groups could be distinguished from each other and from -Cl or -OH through an analysis of their STM metrics and image contrast behavior. The dominance of molecular topography in producing the STM images of alkanes and alkanols was established experimentally and also was consistent with quantum chemistry calculations. Unlike the contrast of the methylene regions of the alkyl chains, the STM contrast produced by the various functional groups was not dominated by topographic effects, indicating that variations in local electronic coupling were important in producing the observed STM images of these regions of the molecules. For molecules in which electronic effects overwhelmed topographic effects in determining the image contrast, a simple model is presented to explain the variation in the electronic coupling component that produces the contrast between the various functional groups observed in the STM images. Additionally, the bias dependence of these STM images has been investigated and the contrast vs bias behavior is related to factors involving electron transfer and hole transfer that have been identified as potentially being important in dominating the electronic coupling in molecular electron transfer processes.


1997 - Theoretical Description of the STM Images of Alkanes and Substituted Alkanes Adsorbed on Graphite [Articolo su rivista]
Faglioni, Francesco; C. L., Claypool; N. S., Lewis; W. A., Goddard
abstract

A theoretical model based on perturbation theory has been developed to predict the scanning tunneling microscopy (STM) images of molecules adsorbed on graphite, The model is applicable to a variety of different molecules with reasonable computational effort and provides images that are in qualitative agreement with experimental results. The model predicts that topographic effects will dominate the STM images of alkanes on graphite surfaces. The computations correlate well with the STM data of functionalized alkanes and allow assessment of the structure and orientation of most of the functionalized alkanes that have been studied experimentally. In addition, the computations suggest that the highly diffuse virtual orbitals of the adsorbed molecules, despite being much farther in energy from the Fermi level of the graphite than the occupied orbitals, may play an important role in determining the STM image contrast of such systems.


1996 - Theoretical-studies of Metallocene Polymerization Catalysts [Articolo su rivista]
W. A., Goddard; C., Brandow; Faglioni, Francesco; E. P., Bierwagen
abstract

Theoretical-studies of Metallocene Polymerization Catalysts


1994 - Simulation and Design of Materials - Applications to Polymers, Ceramics, Semiconductors, and Catalysis [Articolo su rivista]
W. A., Goddard; K. T., Lim; M., Belmares; Y., Guo; X., Chen; Faglioni, Francesco
abstract

SIMULATION AND DESIGN OF MATERIALS - APPLICATIONS TO POLYMERS, CERAMICS, SEMICONDUCTORS, AND CATALYSIS


1993 - CALCULATION OF INFRARED AND VIBRATIONAL CIRCULAR-DICHROISM INTENSITIES VIA NUCLEAR ELECTROMAGNETIC SHIELDINGS [Articolo su rivista]
Faglioni, Francesco; Lazzeretti, Paolo; Malagoli, M; Zanasi, Roberto; Prosperi, T.
abstract

Infrared and vibrational circular dichroism intensities have been evaluated theoretically for trans-(1S,2S)-dideuteriooxirane, trans-(1S,2S)-dideuteriocyclopropane, (S)-propylene oxide, and trans-(1R,2R)-dimethyl-cyclopropane molecules, via electric and electromagnetic nuclear shielding tensors determined by random-phase approximation within the framework of 6-31g, 6-31g**, 6-31gext, and 6-31gpol Gaussian basis sets. Differentiation of matrix elements is avoided by the procedure adopted in this work. By comparing the results provided by several numerical tests it is found that reliable force fields of Hartree-Fock quality can be obtained at the 6-31g** and 6-31gex level; 6-31gpol basis provides the most accurate polar and axial atomic tensors. The nuclear shieldings are to be calculated with great accuracy in order to achieve a good prediction of the intensity patterns, as they bias the overall quality of theoretical oscillator strengths and rotational strengths. Comparison with available experimental data and previous ab initio calculations demonstrates the practicality of the present method for small and medium size molecules. The Hartree-Fock accuracy of the theoretical estimates of vibrational intensities is also proven by analyzing constraints for translational and rotational invariance which should be exactly fulfilled in the limit of complete basis sets. These results document the competitivity of the nuclear shielding method with the analytic derivative procedure.