Physics

We present a study on differen)al photometric observa)ons of the Delta Scu) star GSC 4464-0924 in the Lower-upper-middle (LUM) filter band captured over a 6.2 hour period in 2012 from a site in Athens, Greece. A comprehensive analysis has been conducted to achieve our main goals for this project which were to investigate a new ephemeris and light curve, calculate oscillation modes using Fourier analysis, obtain an observed minus calculated (O−C) analysis, and identify physical parameters of the star that result in determination of harmonic and pulsation modes. High Amplitude Delta Scuti (HADS) stars are very important as standard candles that can be used to measure galactic distances.

At first, we introduce basic methods used to find exoplanets. Then we focus on TTV method, which is less popular in comparison to other methods, but very efficient. It's main concept and properties will be discussed. Besides, what TTV has discovered using small telescopes is introduced.

In this paper, aspects of observable and non-observable based models are discussed. A survey of recent literature was done to show how using non-observable-based language carelessly may cause disagreement, even in professional research programs and incorrect assertions, even in prestigious journals. The relation between physical measurements and observables is discussed and it is shown that, in contrast to general belief, this relation may be complicated and not always straightforward. The decomposition of the system into basic subsystems (physical or conceptual) is traced as the origin of non-observable-based languages. The possibility of defining new quantum mechanical observables for open quantum subsystems and of replacing them with non observable-based concepts has been mentioned and the AIM theory is explained as an example. An account of some current non-observable-based models for molecular geometry is discussed and it is shown that not all non-observable-based languages possess the same effectiveness. In the end, the need to develop a clear chemical language is stressed.

A rigorous mathematical procedure is proposed in order to employ the variational apparatus in “Quantum theory of atoms in molecules.” This mathematical procedure is free from the previously reported mathematical obstacles. Although it is possible to apply the Schro¨dinger’s variational procedure to derive the putative net zero-flux condition, no claim has been made to derive the equation of motion (Schro¨dinger equation) from subsystem variational procedure. In this regard, the problem of admissible and general neighborhoods and their relevance to the subsystem variational procedure has been discussed thoroughly in this article. In the end, a brief discussion has been offered to emphasize the difference between the net and local zeroflux conditions with particular emphasize on its logical consequences.

In this letter, a comprehensive ab initio post-HF study was conducted on the geometry and vibrational spectrum of cyclic, hypercoordinate carbon containing (B6C)-2 dianion. The analysis reveals extraordinary sensitivity of out-of-plane bending mode of this molecule to the diffuse functions of Pople-type basis sets. Accordingly, this molecule seems to be another example of the set of recently described planar molecules that exhibit spurious (but artificial) “imaginary” out-of-plane bending frequencies at post-HF levels. The analysis eventually comes to the conclusion that this anion is indeed stable with regard to nuclear distortions, but unstable in regard to electron auto-detachment.

An explicit classification of consistent variational constraints within context of the “Quantum Theory of Proper Open Subsystems” (QTPOS) as well as the “Quantum Theory of Atoms in Molecules” (QTAIM) was presented.  It is demonstrated that the general variational procedure is not sensitive enough to discriminate between mathematically consistent variational conditions.  The uniqueness of the regional kinetic energy is employed to derive the net zero-flux condition and the regions satisfying this condition are named as Quantum Divided Basins.  A modified form of the local zero-flux is proposed in order to define topological atoms within context of the orthodox QTAIM.

The role of finite nuclear models is scrutinized within the context of the Quantum Theory of Atoms in Molecules.  It is demonstrated that the newly proposed analytic-algebraic definition of the topological atoms is consistently extendable to the cases where a finite nuclear model is employed to construct the molecular hamiltonian.  The whole variational procedure is reconsidered, and the insensitivity of final results relative to the employed finite nuclear models is explicitly demonstrated.  The analysis once again clearly demonstrates that the analytic-algebraic condition is an independent axiom that must be added to the subsystem variational procedure in order to construct the Quantum Theory of Atoms in Molecules.

In this account a detailed computational study is conducted in order to verify the geometric, energetic and electronic properties of planar cyclic (B6C)-2 (as the simplest carrier of hexacoordinate carbon) within some metal complexes.  The [M(B6C)](-) (M=Li, Na, K) and [M(B6C)] (M=Be, Mg, Ca) series are employed for this purpose.  Relevant ab initio calculations at both DFT and Post-HF levels vividly demonstrate that this dianion is stabilized considerably in the electric field generated by cations whereas the geometrical and electronic properties of this ring remain almost intact in these complexes. The complementary topological analysis of charge densities confirms that cyclic (B6C)-2 within these complexes exhibits the same topological patterns like the naked dianion so confirming the presence of an unusual charge density distribution in this dianion. An electrostatic model is proposed which not only qualitatively but also quantitatively explains the observed computational trends in these complexes.  This model is successful to trace the polarization of central carbon atom of the ring in presence of a hard, multiply charged cation.  To facilitate experimental detection, the photoelectron spectra of [M(B6C)](-) (M=Li, Na, K) series are computed and the dominant features are extracted. Although considered species are not global minima on their potential energy hyper-surfaces, but their kinetic stabilities are verified and demonstrated unequivocally.

"In this paper the convergence pattern of correlationconsistent
(cc-pVxZ) and polarized-consistent (PC-n) hierarchies relative to the complete basis set limit have been considered in a small set of diatomic molecules. Using the sequence of these basis sets it was demonstrated that potential energy surfaces derived from basis-set-dependent solution of the Hartree–Fock equations achieves the exact numerical derived potential energy surfaces (PESs) in an ordered manner. So it was possible to compute the spectroscopic parameters in the complete basis set limit with considerable accuracy using the most extended members of both hierarchies. On the other hand, for the first time the detailed convergence patterns of total energies in three separate inter-nuclear distances have been considered in these molecules and it was demonstrated that the total energies arrive at microhartree accuracy at a considerable rate. Possible performance of extrapolation schemes is discussed and it was demonstrated that reliable extrapolation procedures indeed exist. A successful test of the proposed extrapolation method, using the three most extended members of polarized-consistent basis sets, has been accomplished on selected polyatomic molecules."

"In a recent paper (Shahbazian and Zahedi, 2006), we have
discussed our viewpoint on the inherent conceptual problems
regarding the role and also use and misuse of non-observables
in chemical language. Although our treatment in that paper
was by no means a comprehensive analysis of chemical language and at the best could be viewed as a preliminary account, the response of the respected referees and also some of our colleagues, who read the manuscript before publication, surprised us. Some questions and even criticism of our statements in that paper come from a central (and it seems nontrivial) attitude toward the nature of the concept of chemical bond (CCB) in present day chemical language: Is it concrete or a fuzzy concept?"

In this account the relationship between the topological analysis of electronic charge densities and the general theory of dynamical systems is considered in detail.  It is shown that the main theorems of structural stability are best appreciated within the context of the general theory of dynamical systems.  On the other hand, it is demonstrated that this theory may set the stage for a generalized topological analysis.  This general framework could be applied easily to various scalar functions.  In the end, it is emphasized that the very concepts of structure and structural stability are not intrinsically tied to the nuclear coordinates.  Accordingly, by employing new variables like temperature or pressure it is possible to construct novel control spaces.

A selected group of sulfur diimides with the general formula SN2H(X) has been considered using DFT methods. Detailed study of the general geometrical features demonstrates that there is an intricate interaction between the (N=S=N) core and X derivatives possessing lone pairs and π-electrons. No simple resonance structures seem to be capable of describing the electronic structure of these molecules. A comparison of the energetic values computed by DFT methods predicts ZZ conformer general stability in the absence of deviation from planar geometry and 1,5 non-bonded steric interactions. The presence of a positive charge seems to affect stability, making EZ more stable than ZZ. In all cases studied, EE is the least stable conformer.

Using various theoretical methods, the complexation of BF3 as a Lewis acid with free base porphine has been investigated. It has been shown that addition of a BF3 molecule to porphine in the first step produces a stable 1:1 complex, and addition of a second BF3 to the 1:1 intermediate forms even more stable 1:2 complex. Generation of both of these complexes are exothermic but formation of the 1:2 adduct is around 2–6 kcal mol−1 more exothermic than the 1:1 species. Calculation results demonstrate that the most stable species obtained from the interaction of free porphine and BF3 must be trans-por · (BF3)2 complex, in which BF3 molecules are located on opposite porphine faces, each coordinated to a pyrrolenine nitrogen donor and hydrogen bonded to a pyrrole N–H group. The B–N bond distances of ∼1.6 Å in all the complexes indicate that a strong donor–acceptor interaction takes place between boron atom of BF3 and pyrrolenine nitrogen atom of porphine. Formation of new B–N chemical bonds accompanied by F–H intermolecular hydrogen bonds of ∼1.7 Å length fairly justify molecular complexes stability. This novel complexation and bonding interaction between a single porphine and two BF3 molecules seem to promise the development of a possibly new class of porphine complexes.