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1.
Phys Chem Chem Phys ; 25(48): 32922-32930, 2023 Dec 13.
Artigo em Inglês | MEDLINE | ID: mdl-38018412

RESUMO

This work delves into the bonding nature of the pentagonal-pyramidal benzene and hexamethylbenzene dications, C6R62+ (R = H and CH3), which contain a hexacoordinate carbon. The study employs a range of methodologies to analyze a series of scalar fields, including electron density, electron localization function, local momentum representation, and the evaluation of the Coulomb hole through information theory-derived functions. The findings unveil that electron density undergoes transfer from the pentagonal ring to the apical group. As a result, the base of the complex accumulates the positive charge. Moreover, an extended electron density domain emerges between the carbon pentagon and the apical carbon atom. This phenomenon is related to the molecular orbitals with a dipolar character aligned with the principal axis of the molecule. The results also indicate an electron density polarization towards the apical carbon, coupled with an exclusion of electron density surrounding both the apical carbon and the lower portion of the pentagonal ring. These provide valuable insights into the complex bonding nature of hexacoordinate carbon and its implications for organic chemistry.

2.
Chemphyschem ; 23(1): e202100676, 2022 Jan 05.
Artigo em Inglês | MEDLINE | ID: mdl-34708497

RESUMO

The nature of the Na⋯B bond, in the recently synthesized NaBH 3 - adduct, is analyzed on the light of the Na- propensity to polarize along the bond axis as a consequence of the electric field produced by the BH3 fragment. The observed induced polarization has two consequences: (i) the energetic stabilization of the Na- , and (ii) the split of its valence electrons into two opposite lobes along the bond axis. Additionally, an analysis of the electron localization is presented using the information content of the correlated conditional pair density that reveals a significant delocalization between one lobe of the polarized Na- anion and the BH3 fragment at the equilibrium distance. Our findings reported here complement previous works on this system.

3.
Molecules ; 27(21)2022 Oct 26.
Artigo em Inglês | MEDLINE | ID: mdl-36364105

RESUMO

The C-X bond cleavage in different methyl halides (CH3X; X = Cl, Br, I) mediated by 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(II) (CoIICbx) was theoretically investigated in the present work. An SN2-like mechanism was considered to simulate the chemical process where the cobalt atom acts as the nucleophile and the halogen as the leaving group. The reaction path was computed by means of the intrinsic reaction coordinate method and analyzed in detail through the reaction force formalism, the quantum theory of atoms in molecules (QTAIM), and the calculation of one-electron density derived quantities, such as the source function (SF) and the spin density. A thorough comparison of the results with those obtained in the same reaction occurring in presence of 5,6-dimethylbenzimidazole-bis(dimethylglyoximate)cobalt(I) (CoICbx) was conducted to reveal the main differences between the two cases. The reactions mediated by CoIICbx were observed to be endothermic and possess higher activation energies in contrast to the reactions where the CoICbx complex is present. The latter was supported by the reaction force results, which suggest a relationship between the activation energy and the ionization potentials of the different nucleophiles present in the cleavage reaction. Moreover, the SF results indicates that the lower axial ligand (i.e., 5,6-dimethylbenzimidazole) exclusively participates on the first stage of the reaction mediated by the CoIICbx complex, while for the CoICbx case, it appears to have an important role along the whole process. Finally, the QTAIM charge analysis indicates that oxidation of the cobalt atom occurs in both cases; at the same time, it suggests the formation of an uncommon two-center one-electron bond in the CoIICbx case. The latter was confirmed by means of electron localization calculations, which resulted in a larger electron count at the Co-C interatomic region for the CoICbx case upon comparison with its CoIICbx counterpart.


Assuntos
Cobalto , Teoria Quântica , Cobalto/química , Modelos Teóricos , Ligantes , Elétrons
4.
J Comput Chem ; 42(12): 818-826, 2021 05 05.
Artigo em Inglês | MEDLINE | ID: mdl-33590912

RESUMO

In the present work, the fast amide bond cleavage of [3-((1R,5S,7s)-3-azabicyclo[3.3.1]nonane-7-carbonyl)-3-azabicyclo[3.3.1]nonane-7-carboxylic acid (bi-ATDO)], through an intramolecular nucleophilic attack of an amine group is evaluated. First, six possible peptide bond cleavage mechanisms, two of them including a water molecule, are described at the ωB97XD/6-311 + G(d,p)//MP2/6-311 + G(d,p) level of theory. The reaction consisting of an intramolecular nitrogen nucleophilic attack followed by a proton transfer and the amide bond cleavage is determined as the most favorable mechanism. The activation free energy computed for the latter is 20.5 kcal mol-1 , which agrees with the reported experimental result of 24.8 kcal mol-1 . Inclusion of a water molecule to assist the first step of the reaction results in an activation free energy increase of about 17 kcal mol-1 . All the steps in the most favorable mechanism are studied more in detail employing intrinsic reaction coordinate as well as the reaction force and reaction electronic flux analysis.

5.
Int J Mol Sci ; 22(1)2021 Jan 05.
Artigo em Inglês | MEDLINE | ID: mdl-33466251

RESUMO

Recently, several studies have demonstrated that diaminodicyanoquinone derivatives (DADQs) could present interesting fluorescence properties. Furthermore, some DADQs under the solid state are capable of showing quantum yields that can reach values of 90%. Besides, the diaminodiacyanoquinone core represents a versatile building block propense either to modification or integration into different systems to obtain and provide them unique photophysical features. Herein, we carried out a theoretical study on the fluorescence properties of three different diaminodicyanoquinodimethane systems. Therefore, time-dependent density functional theory (TD-DFT) was used to obtain the values associated with the dipole moments, oscillator strengths, and the conformational energies between the ground and the first excited states of each molecule. The results suggest that only two of the three studied systems possess significant luminescent properties. In a further stage, the theoretical insights were confirmed by means of experimental measurements, which not only retrieved the photoluminescence of the DADQs, but also suggest a preliminary and promising antibacterial activity of these systems.


Assuntos
Benzoquinonas/química , Antibacterianos/química , Fluorescência , Luminescência , Conformação Molecular
6.
Int J Mol Sci ; 22(13)2021 Jun 26.
Artigo em Inglês | MEDLINE | ID: mdl-34206795

RESUMO

In this study, the degradation mechanism of chloroacetanilide herbicides in the presence of four different nucleophiles, namely: Br-, I-, HS-, and S2O3-2, was theoretically evaluated using the dispersion-corrected hybrid functional wB97XD and the DGDZVP as a basis set. The comparison of computed activation energies with experimental data shows an excellent correlation (R2 = 0.98 for alachlor and 0.97 for propachlor). The results suggest that the best nucleophiles are those where a sulfur atom performs the nucleophilic attack, whereas the other species are less reactive. Furthermore, it was observed that the different R groups of chloroacetanilide herbicides have a negligible effect on the activation energy of the process. Further insights into the mechanism show that geometrical changes and electronic rearrangements contribute 60% and 40% of the activation energy, respectively. A deeper analysis of the reaction coordinate was conducted, employing the evolution chemical potential, hardness, and electrophilicity index, as well as the electronic flux. The charge analysis shows that the electron density of chlorine increases as the nucleophilic attack occurs. Finally, NBO analysis indicates that the nucleophilic substitution in chloroacetanilides is an asynchronous process with a late transition state for all models except for the case of the iodide attack, which occurs through an early transition state in the reaction.


Assuntos
Acetamidas/química , Teoria da Densidade Funcional , Enxofre/química
7.
J Phys Chem A ; 124(2): 386-394, 2020 Jan 16.
Artigo em Inglês | MEDLINE | ID: mdl-31846329

RESUMO

We study the Shannon entropy and the Fisher information in a non-Born-Oppenheimer (nBO) regime, where these quantities are constructed from one-particle densities obtained from an exact nBO analytic wave function for a Coulomb-Hooke model of a four-particle system. This model consists of two electrons and two protons with Coulombic interactions between like particles and Hookean interactions otherwise [ Becerra , M. et al. Int. J. Quantum Chem 2013 , 113 ( 10 ), 1584 - 1590 ]. In the nBO case, there arise densities for both the nuclei and electrons. Furthermore, these densities vary with respect to a particular point of reference from which they are calculated. We consider, in the present work, electron and nuclear densities calculated from the following reference points: a global center of mass, the geometric center between the electrons, and the geometric center between the protons. A comparison of the nBO Shannon entropy and Fisher information, with respect to their counterparts computed from Born-Oppenheimer densities, suggests that the former quantities provide more insights into the chemical reactivity because of the nonuniqueness nature of the nBO electron density as well as the availability and access to the nBO nuclear density. Finally, some comments are made concerning the nBO vs the BO regimes in relation to this particular chemical reactivity indicator.

8.
Mol Divers ; 24(4): 913-932, 2020 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-31659696

RESUMO

In this report, we introduce a set of aggregation operators (AOs) to calculate global and local (group and atom type) molecular descriptors (MDs) as a generalization of the classical approach of molecular encoding using the sum of the atomic (or fragment) contributions. These AOs are implemented in a new and free software denominated MD-LOVIs ( http://tomocomd.com/md-lovis ), which allows for the calculation of MDs from atomic weights vector and LOVIs (local vertex invariants). This software was developed in Java programming language and employed the Chemical Development Kit (CDK) library for handling chemical structures and the calculation of atomic weights. An analysis of the complexities of the algorithms presented herein demonstrates that these aspects were efficiently implemented. The calculation speed experiments show that the MD-LOVIs software has satisfactory behavior when compared to software such as Padel, CDKDescriptor, DRAGON and Bluecal software. Shannon's entropy (SE)-based variability studies demonstrate that MD-LOVIs yields indices with greater information content when compared to those of popular academic and commercial software. A principal component analysis reveals that our approach captures chemical information orthogonal to that codified by the DRAGON, Padel and Mold2 software, as a result of the several generalizations in MD-LOVIs not used in other programs. Lastly, three QSARs were built using multiple linear regression with genetic algorithms, and the statistical parameters of these models demonstrate that the MD-LOVIs indices obtained with AOs yield better performance than those obtained when the summation operator is used exclusively. Moreover, it is also revealed that the MD-LOVIs indices yield models with comparable to superior performance when compared to other QSAR methodologies reported in the literature, despite their simplicity. The studies performed herein collectively demonstrated that MD-LOVIs software generates indices as simple as possible, but not simpler and that use of AOs enhances the diversity of the chemical information codified, which consequently improves the performance of traditional MDs.


Assuntos
Modelos Químicos , Bibliotecas de Moléculas Pequenas/química , Algoritmos , Modelos Lineares , Análise Multivariada , Relação Quantitativa Estrutura-Atividade , Software
9.
Molecules ; 25(3)2020 Jan 25.
Artigo em Inglês | MEDLINE | ID: mdl-31991810

RESUMO

In the present work, a number of R-X⋯NH3 (X = Cl, Br, and I) halogen bonded systems were theoretical studied by means of DFT calculations performed at the ωB97XD/6-31+G(d,p) level of theory in order to get insights on the effect of the electron-donating or electron-withdrawing character of the different R substituent groups (R = halogen, methyl, partially fluorinated methyl, perfluoro-methyl, ethyl, vinyl, and acetyl) on the stability of the halogen bond. The results indicate that the relative stability of the halogen bond follows the Cl < Br < I trend considering the same R substituent whereas the more electron-withdrawing character of the R substituent the more stable the halogen bond. Refinement of the latter results, performed at the MP2/6-31+G(d,p) level showed that the DFT and the MP2 binding energies correlate remarkably well, suggesting that the Grimme's type dispersion-corrected functional produces reasonable structural and energetic features of halogen bond systems. DFT results were also observed to agree with more refined calculations performed at the CCSD(T) level. In a further stage, a more thorough analysis of the R-Br⋯NH3 complexes was performed by means of a novel electron localization/delocalization tool, defined in terms of an Information Theory, IT, based quantity obtained from the conditional pair density. For the latter, our in-house developed C++/CUDA program, called KLD (acronym of Kullback-Leibler divergence), was employed. KLD results mapped onto the one-electron density plotted at a 0.04 a.u. isovalue, showed that (i) as expected, the localized electron depletion of the Br sigma-hole is largely affected by the electron-withdrawing character of the R substituent group and (ii) the R-X bond is significantly polarized due to the presence of the NH3 molecule in the complexes. The afore-mentioned constitutes a clear indication of the dominant character of electrostatics on the stabilization of halogen bonds in agreement with a number of studies reported in the main literature. Finally, the cooperative effects on the [Br-CN]n system (n = 1-8) was evaluated at the MP2/6-31+G(d,p) level, where it was observed that an increase of about ~14.2% on the complex stability is obtained when going from n = 2 to n = 8. The latter results were corroborated by the analysis of the changes on the Fermi-hole localization pattern on the halogen bond zones, which suggests an also important contribution of the electron correlation in the stabilization of these systems.


Assuntos
Compostos de Amônio/química , Halogênios/química , Modelos Teóricos , Algoritmos , Elétrons , Modelos Moleculares , Eletricidade Estática
10.
J Phys Chem A ; 123(45): 9721-9728, 2019 Nov 14.
Artigo em Inglês | MEDLINE | ID: mdl-31638808

RESUMO

High-spin lithium clusters, n+1Lin (n = 2-21), have been systematically studied by using density functional theory. Although these high-spin clusters have no bonding electron pairs, they are stable with respect to isolated atoms. A set of 42 density functional theory functionals were benchmarked against CCSD(T)/cc-pVQZ results for clusters from the dimer to the hexamer. For these clusters, the strong non-additivity on the binding energy is analyzed employing a many-body energy decomposition scheme, concluding that most of the binding energy is due to a balance between the three- and four-body contributions. After a quality parameter had been defined, the LC-BP86 functional was identified as the most promising one for the description of high-spin lithium clusters. We employ the dependence of the second energy difference on cluster size to predict the formation of a higher-stability cluster.

11.
Proc Natl Acad Sci U S A ; 112(14): 4245-50, 2015 Apr 07.
Artigo em Inglês | MEDLINE | ID: mdl-25831544

RESUMO

The Sample Analysis at Mars (SAM) investigation on the Mars Science Laboratory (MSL) Curiosity rover has detected oxidized nitrogen-bearing compounds during pyrolysis of scooped aeolian sediments and drilled sedimentary deposits within Gale crater. Total N concentrations ranged from 20 to 250 nmol N per sample. After subtraction of known N sources in SAM, our results support the equivalent of 110-300 ppm of nitrate in the Rocknest (RN) aeolian samples, and 70-260 and 330-1,100 ppm nitrate in John Klein (JK) and Cumberland (CB) mudstone deposits, respectively. Discovery of indigenous martian nitrogen in Mars surface materials has important implications for habitability and, specifically, for the potential evolution of a nitrogen cycle at some point in martian history. The detection of nitrate in both wind-drifted fines (RN) and in mudstone (JK, CB) is likely a result of N2 fixation to nitrate generated by thermal shock from impact or volcanic plume lightning on ancient Mars. Fixed nitrogen could have facilitated the development of a primitive nitrogen cycle on the surface of ancient Mars, potentially providing a biochemically accessible source of nitrogen.


Assuntos
Meio Ambiente Extraterreno/química , Sedimentos Geológicos/análise , Marte , Nitrogênio/análise , Nitratos/química , Óxido Nítrico/química , Nitrogênio/química , Temperatura , Água/química , Vento
12.
J Chem Phys ; 144(24): 244104, 2016 Jun 28.
Artigo em Inglês | MEDLINE | ID: mdl-27369494

RESUMO

In the present work, the information gained by an electron for "knowing" about the position of another electron with the same spin is calculated using the Kullback-Leibler divergence (DKL) between the same-spin conditional pair probability density and the marginal probability. DKL is proposed as an electron localization measurement, based on the observation that regions of the space with high information gain can be associated with strong correlated localized electrons. Taking into consideration the scaling of DKL with the number of σ-spin electrons of a system (N(σ)), the quantity χ = (N(σ) - 1) DKLfcut is introduced as a general descriptor that allows the quantification of the electron localization in the space. fcut is defined such that it goes smoothly to zero for negligible densities. χ is computed for a selection of atomic and molecular systems in order to test its capability to determine the region in space where electrons are localized. As a general conclusion, χ is able to explain the electron structure of molecules on the basis of chemical grounds with a high degree of success and to produce a clear differentiation of the localization of electrons that can be traced to the fluctuation in the average number of electrons in these regions.

13.
Int J Mol Sci ; 17(6)2016 May 27.
Artigo em Inglês | MEDLINE | ID: mdl-27240357

RESUMO

This report examines the interpretation of the Graph Derivative Indices (GDIs) from three different perspectives (i.e., in structural, steric and electronic terms). It is found that the individual vertex frequencies may be expressed in terms of the geometrical and electronic reactivity of the atoms and bonds, respectively. On the other hand, it is demonstrated that the GDIs are sensitive to progressive structural modifications in terms of: size, ramifications, electronic richness, conjugation effects and molecular symmetry. Moreover, it is observed that the GDIs quantify the interaction capacity among molecules and codify information on the activation entropy. A structure property relationship study reveals that there exists a direct correspondence between the individual frequencies of atoms and Hückel's Free Valence, as well as between the atomic GDIs and the chemical shift in NMR, which collectively validates the theory that these indices codify steric and electronic information of the atoms in a molecule. Taking in consideration the regularity and coherence found in experiments performed with the GDIs, it is possible to say that GDIs possess plausible interpretation in structural and physicochemical terms.


Assuntos
Preparações Farmacêuticas/química , Algoritmos , Gráficos por Computador , Desenho de Fármacos , Entropia
14.
J Phys Condens Matter ; 34(19)2022 Mar 07.
Artigo em Inglês | MEDLINE | ID: mdl-35144254

RESUMO

In the present work, resorting to linear response theory, we examine the plausibility of postulating Kohn-Sham (KS)-type equations which contain, by definition, an effective hybrid potential made up by some arbitrary mixture of local and non-local terms. In this way a general justification for the construction of hybrid functionals is provided without resorting to arguments based on the adiabatic connection, the generalized KS theory or the Levy's constrained search (or its variations). In particular, we examine the cases of single-hybrid functionals, derived from non-local exchange and of double-hybrid functionals, emerging from non-local second-order expressions obtained from the KS perturbation theory. A further generalization for higher-order hybrid functionals is also included.

15.
ACS Omega ; 7(5): 4185-4193, 2022 Feb 08.
Artigo em Inglês | MEDLINE | ID: mdl-35155912

RESUMO

The modification of the rutile TiO2(110) surface with dopamine represents the best example of the functionalization of TiO2-based nanoparticles with catecholamines, which is of great interest for sunlight harvesting and drug delivery. However, there is little information on the dopamine-TiO2(110) adsorption complex in terms of thermodynamic properties and structural parameters such as bond coordination and orientation of the terminal ethyl-amino group. Here, we report a density functional theory (DFT) investigation of dopamine adsorption on the TiO2(110) surface using the optB86b-vdW functional with a Hubbard-type correction to the Ti 3d orbitals, where U eff = 3 eV. Guided by available X-ray photoelectron spectroscopy (XPS) and near-edge X-ray absorption fine structure (NEXAFS) data, our simulations identify enolate species with bidentate coordination at a submonolayer coverage, which are bonded to two neighboring 5-fold-coordinated Ti atoms at the TiO2(110) surface through both deprotonated oxygen atoms of the dopamine, i.e., in a bridging fashion. The process is highly exothermic, involving an adsorption energy of -2.90 eV. Calculated structural parameters suggest that the molecule sits approximately upright on the surface with the amino group interacting with the π-like orbitals of the aromatic ring, leading to a gauche-like configuration. The resulting NH···π hydrogen bond in this configuration can be broken by overcoming an energy barrier of 0.22 eV; in this way, the amino group rotation leads to an anti-like conformation, making this terminal group able to bind to other biomolecules. This mechanism is endothermic by 0.07 eV. Comparison of existing spectroscopic data with DFT modeling shows that our computational setup can reproduce most experimentally determined parameters such as tilt angles from NEXAFS and chemical shifts in XPS, which allows us to identify the preferred mode of adsorption of dopamine on the TiO2(110) surface.

16.
Sci Rep ; 12(1): 6326, 2022 04 19.
Artigo em Inglês | MEDLINE | ID: mdl-35440687

RESUMO

Mercury (Hg(II)) has been classified as a pollutant and its removal from aqueous sources is considered a priority for public health as well as ecosystem protection policies. Oxidized graphenes have attracted vast interest in water purification and wastewater treatment. In this report, a partially reduced graphene oxide is proposed as a pristine adsorbent material for Hg(II) removal. The proposed material exhibits a high saturation Hg(II) uptake capacity of 110.21 mg g-1, and can effectively reduce the Hg(II) concentration from 150 mg L-1 to concentrations smaller than 40 mg L-1, with an efficiency of about 75% within 20 min. The adsorption of Hg(II) on reduced graphene oxide shows a mixed physisorption-chemisorption process. Density functional theory calculations confirm that Hg atom adsorbs preferentially on clean zones rather than locations containing oxygen functional groups. The present work, therefore, presents new findings for Hg(II) adsorbent materials based on partially reduced graphene oxide, providing a new perspective for removing Hg(II).


Assuntos
Mercúrio , Poluentes Químicos da Água , Purificação da Água , Adsorção , Ecossistema , Grafite , Concentração de Íons de Hidrogênio , Cinética , Mercúrio/análise , Água , Poluentes Químicos da Água/análise
17.
Comput Biol Med ; 142: 105245, 2022 03.
Artigo em Inglês | MEDLINE | ID: mdl-35077937

RESUMO

Cellular susceptibility to SARS-CoV-2 infection in the respiratory tract has been associated with the ability of the virus to interact with potential receptors on the host membrane. We have modeled viral dynamics by simulating various cellular systems and artificial conditions, including macromolecular crowding, based on experimental and transcriptomic data to infer parameters associated with viral growth and predict cell susceptibility. We have accomplished this based on the type, number and level of expression of the angiotensin-converting enzyme 2 (ACE2), transmembrane serine 2 (TMPRSS2), basigin2 (CD147), FURIN protease, neuropilin 1 (NRP1) or other less studied candidate receptors such as heat shock protein A5 (HSPA5) and angiotensin II receptor type 2 (AGTR2). In parallel, we studied the effect of simulated artificial environments on the accessibility to said proposed receptors. In addition, viral kinetic behavior dependent on the degree of cellular susceptibility was predicted. The latter was observed to be more influenced by the type of proteins and expression level, than by the number of potential proteins associated with the SARS CoV-2 infection. We predict a greater theoretical propensity to susceptibility in cell lines such as NTERA-2, SCLC-21H, HepG2 and Vero6, and a lower theoretical propensity in lines such as CaLu3, RT4, HEK293, A549 and U-251MG. An important relationship was observed between expression levels, protein diffusivity, and thermodynamically favorable interactions between host proteins and the viral spike, suggesting potential sites of early infection other than the lungs. This research is expected to stimulate future quantitative experiments and promote systematic investigation of the effect of crowding presented here.


Assuntos
COVID-19 , Células HEK293 , Humanos , SARS-CoV-2 , Internalização do Vírus
18.
Nanomaterials (Basel) ; 12(17)2022 Aug 31.
Artigo em Inglês | MEDLINE | ID: mdl-36080061

RESUMO

Graphene oxide (GO) and its reduced form, reduced graphene oxide (rGO), are among the most predominant graphene derivatives because their unique properties make them efficient adsorbent nanomaterials for water treatment. Although extra-functionalized GO and rGO are customarily employed for the removal of pollutants from aqueous solutions, the adsorption of heavy metals on non-extra-functionalized oxidized graphenes has not been thoroughly studied. Herein, the adsorption of mercury(II) (Hg(II)) on eco-friendly-prepared oxidized graphenes is reported. The work covers the preparation of GO and rGO as well as their characterization. In a further stage, the description of the adsorption mechanism is developed in terms of the kinetics, the associated isotherms, and the thermodynamics of the process. The interaction between Hg(II) and different positions of the oxidized graphene surface is explored by DFT calculations. The study outcomes particularly demonstrate that pristine rGO has better adsorbent properties compared to pristine GO and even other extra-functionalized ones.

20.
J Phys Chem B ; 113(15): 5059-71, 2009 Apr 16.
Artigo em Inglês | MEDLINE | ID: mdl-19317470

RESUMO

The full vibrational spectra of the gamma, delta, and epsilon crystalline phases of syndiotactic polystyrene (sPS), i.e., phases presenting the s(2/1)2 helical conformation, have been experimentally determined and compared with that calculated at the B3LYP/6-31G(d,p) level of theory for an infinite helix. The assignment of the different modes was highly facilitated and validated by the experimental evaluation of the direction of the transition moment vector of most IR peaks, which was made possible for the first time by measurements on sPS films with different uniplanar orientations of the crystalline phase. The normal vibration analysis of most representative modes of the periodic model allowed for a general description of each one to be obtained, which was further confirmed by the direct inspection of mode animations.

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