RESUMO
The anion-water bonds and hydrogen bonds between water molecules in X(-)(H(2)O)(n) (X = F and Cl, n = 3-7) clusters are analyzed by evaluating the charge-transfer (CT) and dispersion terms for every pair of ions and molecules with the perturbation theory based on the locally projected molecular orbitals. In particular, the relative stabilities and the bond strengths in all 11 distinct cubic X(-)(H(2)O)(7) isomers are analyzed by classifying the ligand water (L) with the numbers of the donating (n) and accepting (m) OHs as LD(n)A(m). The number of LD(0)A(2) waters determines the relative stability. It is demonstrated that the strengths of the anion-ligand bonds are strongly influenced by two other hydrogen bonds of the water molecules adjacent to the ligand. When the model theory of Mulliken's charge-transfer interaction is applied to the anion-ligand and water-water hydrogen bonds, the dependence of the bond strengths on the chains of the hydrogen bonds is explained.
RESUMO
The geometric and electronic structures of the ground and low-lying states for the Al(12)Cs(-), Al(11)Cs(2) (-), and Al(10)Cs(3) (-) clusters were examined using the density functional theory. Semi-icosahedral structures of the Al(12)Cs(-) and Al(11)Cs(2) (-) clusters were found as the ground state. The most stable structure of the Al(10)Cs(3) (-) cluster is a distorted icosahedron structure. The vertical detachment energy of these clusters and the anion photoelectron spectra (PES) were compared. The peaks of the anion PES were assigned on the basis of the shell model. The single peak of 3.1-3.2 or 2.5-2.7 eV for the Al(12)Cs(-) or Al(11)Cs(2) (-) cluster, respectively, is observed due to the electron detachment from the 2p or 1f or 1f+2p shells. Two large peaks of 2.1 eV and 3.1-3.3 eV correspond to the electron detachments from the 1f+2p and 2p, and 1d+1f shells, respectively. It was found that a second peak appears with the hybridization of the 1d and 1f shells due to the distortion from the icosahedral structure in the Al(10)Cs(3) (-) cluster.
RESUMO
The stable geometries and formation processes of the AlmNan (m = 2-4; n = 1-8) clusters were investigated using the density functional theory (DFT). The Alm (m = 2-4) structures are maintained in the clusters. The Na atoms are attached to the Al-Al bond or Al plane for less than n = 4 in the AlmNan (m = 2-4) clusters. The odd electron of the attached Na atom is transferred to the Alm part for n ≤ 4 or 5 in the AlmNan (m = 2-4) clusters since the Alm part becomes stable. The Na-Na bonding is formed by the attached Na atom after saturation of the Al-Al bonds or Al atoms. The Al2Na5, Al3Na5, Al3Na6, Al3Na7, and Al3Na8 clusters have a characteristic structure. The Na wing is formed in the Al3Nan (n = 5-8) clusters. The 2S shell containing the 3s orbital of the Na atom and the 3p orbital of the Al atom becomes stable before the occupation of the 1D shell because the electrons are delocalized on the Na plane for n ≥ 5 in the AlmNan (m = 2-4) clusters. The stability of the AlmNan (m = 2-4; n = 1-8) clusters was evaluated by comparison of the vertical ionization potential (IP), HOMO-LUMO gap, adsorption energy of the Na atom, and binding energy per atom.
RESUMO
PURPOSE: In addition to a description of our three previously developed one-dimensional (1D) methods from the viewpoint of shear modulus reconstruction using the strain ratio, two new methods for stabilizing the 1D methods are described, together with their limitations. As confirmed using human in vivo breast tissues, method 1 for evaluating the strain ratio itself is useful when the measurement accuracy of the strain distribution is high. However, because tissues having high shear moduli, such as scirrhous carcinoma, often form singular points/regions, both methods 2 and 3 using the strain ratio (initial estimate) and a regularization method are effective for realizing a unique, stable, useful shear modulus reconstruction. Because method 3 carries out implicit integration only at singular points/regions, whereas method 2 carries out implicit integration throughout the region of interest (ROI), the smaller number of singular points enables more rapid shear modulus reconstruction by method 3 than by method 2. Like method 1, method 3 is also useful when the measurement accuracy of the strain distribution is high. However, when evaluating strain distribution in an ROI with a high spatial resolution to obtain a shear modulus reconstruction having a high spatial resolution, shear modulus reconstructions obtained by methods 1, 2, and 3 often become laterally unstable due to the instability and low accuracy of the strains in the reference regions (reference strains), i.e., regularization in methods 2 and 3 cannot reduce the instability in the initial estimate. METHODS: To cope with this instability, (i) the reconstruction obtained by calculating the strain ratio should be low-pass filtered; for breast tissues, in particular, the reconstruction of the inverse shear modulus should be low-pass filtered, not the reconstruction of the shear modulus. (ii) Otherwise, when using homogeneous regions as a reference, such as a block of reference material, fatty tissue, or parenchyma, evaluation of the reference strains with a low spatial resolution is effective. RESULTS: Although such evaluation yields a stable reconstruction with a high spatial resolution compared with that obtained by the low-pass filtering of the strain ratio, we confirmed through simulations that, when reducing artifacts due to a 1D reconstruction of the shear modulus, the evaluation yields a low-accuracy reconstruction value of inhomogeneity. In contrast, in such a case the low-pass filtering of the strain ratio yields a more accurate reconstruction value. CONCLUSION: All the above-mentioned methods using the strain ratio realize real-time shear modulus reconstruction and should be selected appropriately in conventional ultrasonic imaging equipment by considering the application of the reconstruction (i.e., in accordance with the measurement accuracy of the strains and the occurrence of artifacts).
