Determination of Force Constants of Octahedral XY6 Molecules by the GF Matrix Method

2005 ◽  
Vol 60 (11-12) ◽  
pp. 819-822 ◽  
Author(s):  
Fatih Ucun ◽  
M. Gökhan Şengül
Keyword(s):  
Matrix Method ◽  
Molar Mass ◽  
Interaction Force ◽  
Force Constants ◽  
Complex Ions ◽  
Slowing Down ◽  
The Matrix ◽  
The Difference ◽  
Raphson Method

The force constants of the internal coordinates of octahedral XY6 molecules and complex ions were calculated by using the GF matrix method. The matrix solutions were found by means of a computer program using the Newton-Raphson method. From the calculations it has been observed that the bond stretch force constants of octahedral XF6 molecules and XY6 complex ions having the same centre X atom decrease with the increasing molar mass of the centre X atom for the former and the ligand Y atom for the latter, respectively. This was attributed to the slowing down of the molecule with increasing molar mass of the molecule as the whole. In addition we have concluded that the difference of squares of the vibration frequencies ν1 and ν2 of octahedral XY6 complex ions decreases with the increasing mass of the Y atom since the interaction force constant of these ions decreases with the increasing mass.

Determination of the Force Constants of Non-linear XY2 Molecules in the Gas-Phase by the GF Matrix Method

2004 ◽  
Vol 59 (9) ◽  
pp. 621-622 ◽  
Author(s):  
Fatih Ucun ◽  
Vesile Gūçlü
Keyword(s):  
Gas Phase ◽  
Condensed Phase ◽  
Matrix Method ◽  
Solid Phase ◽  
Force Constants ◽  
Matrix Solution ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of nonlinear XY2 molecules in the gas-phase were calculated by using the GF matrix method. The matrix solution was carried out by means a computer program built relative to the Newton-Raphson method and the calculations were listed in a table. The force constants of some molecules in the liquidand solid- phase were also found and compared with these ones, and it was seen that the force constants for more condensed phase are lower as in an agreement with having its lower frequency.

Determination of Force Constants of Planar XY3 and Tetrahedral XY4 Molecules by the GF Matrix Method

2005 ◽  
Vol 60 (3) ◽  
pp. 183-186 ◽  
Author(s):  
Vesile Güçlü ◽  
Fatih Ucun
Keyword(s):  
Computer Program ◽  
Matrix Method ◽  
Force Constants ◽  
Internal Coordinates ◽  
The Matrix ◽  
Newton Raphson ◽  
Raphson Method

The force constants of the internal coordinates of planar XY3 and tetrahedral XY4 molecules were calculated using the GF matrix method. The matrix solutions were carried out by means of a computer program built relative to the Newton-Raphson method, and the calculations were listed in tables. For tetrahedral XY4 molecules having the same Y atom it was found that the force constants decrease with the increasing mass of the X atom, and this was attributed to the slowing of the molecule with increasing mass of the centre X atom.

scholarly journals A computer program for the algebraic determination of control coefficients in Metabolic Control Analysis

1993 ◽  
Vol 292 (2) ◽  
pp. 351-360 ◽  
Author(s):  
S Thomas ◽  
D A Fell
Keyword(s):  
Computer Program ◽  
Metabolic Control ◽  
Matrix Method ◽  
Metabolic Control Analysis ◽  
Control Analysis ◽  
Point Distribution ◽  
Algebraic Expressions ◽  
The Matrix ◽  
Control Coefficients

A computer program (MetaCon) is described for the evaluation of flux control, concentration control and branch-point distribution control coefficients of a metabolic pathway. Requiring only the reaction scheme as input, the program produces algebraic expressions for the control coefficients in terms of elasticity coefficients, metabolite concentrations and pathway fluxes. Any of these variables can be substituted by numeric or simple algebraic expressions; the expressions will then be automatically rearranged in terms of the remaining unknown variables. When all variables have been substituted, numeric values will be obtained for the control coefficients. The program is a computerized implementation of the matrix method for the determination of control coefficients. The features of MetaCon are compared with those of other programs available to workers in Metabolic Control Analysis. Potential benefits of, and methods of using, MetaCon are discussed. The mathematical background and validity of the matrix method rules are discussed, and the algorithm used by MetaCon is described. The matrix method is shown to be a specific case of a previously described general formalism for calculating control coefficients.

The potentiometric determination of stability constants of sulfite and cobalt(II) in ionic strength 2.0 M (NaClO4). Use of the matrix method

Polyhedron ◽  
1987 ◽  
Vol 6 (9) ◽  
pp. 1717-1719 ◽  
Author(s):  
Éder Tadeu Gomes Cavalheiro ◽  
Ana Maria De Guzzi Plepis ◽  
Gilberto Orivaldo Chierice ◽  
Eduardo F.A. Neves
Keyword(s):  
Ionic Strength ◽  
Stability Constants ◽  
Matrix Method ◽  
Potentiometric Determination ◽  
The Matrix

scholarly journals Determination of stoichiometric coefficients by the matrix method

2007 ◽  
Vol 61 (1) ◽  
pp. 18-22
Author(s):  
Goran Tadic ◽  
Branko Pejovic ◽  
Miladin Gligoric ◽  
Vladan Micic
Keyword(s):  
Matrix Equation ◽  
Matrix Method ◽  
Chemical Compounds ◽  
New Approach ◽  
Standard Methods ◽  
Vector Algebra ◽  
Chemical Equations ◽  
The Matrix ◽  
Chemical Equation

The problem of calculating stoichiometric coefficients in a chemical equation can be solved by standard methods and the method of multidimensional vector space, but good knowledge of vector algebra is required. In this paper, the authors proposed a matrix method and other treatment of the problem was given as the authors' own interpretation. A matrix was formed in the form of base using all the elements which take place in a chemical reaction, after which the matrixes of all the chemical compounds were determined based on numerical indexes and element symbols. This approach enables the setting of a principal matrix equation based on a mathematical approach. The solutions of this matrix equation are the desired stoichiometric coefficients that form a balanced equation. A new approach to tabular solving is presented. This method, compared to existing standard methods, is faster, simpler, and more effective, especially for complex chemical equations. The method was tasted on examples from inorganic chemistry and metallurgy.

Struktur und Schwingungsspektren von Titan(III)-halogeno-Komplexverbindungen / Structure and Vibrational Spectra of Titanium (III) -halo-complexes

1970 ◽  
Vol 25 (10) ◽  
pp. 1087-1089 ◽  
Author(s):  
H. P. Fritz ◽  
W. P. Griffith ◽  
G. Stefaniak ◽  
R. S. Tobias
Keyword(s):  
Infrared Spectra ◽  
Vibrational Spectra ◽  
Force Constants ◽  
Complex Ions ◽  
Bond Lengths ◽  
Regular Octahedron ◽  
The Difference

The infrared spectra of polycrystalline pyridinium hexahalo titanates (III), (C5H6N) 3 [TiX6] (X = Cl, Br), show a slight deviation of the complex ions from the form of a regular octahedron, as previously found for K2Na [TiF6]. The spectra can be interpreted by assuming D4h symmetry. The difference between the axial and the equatorial TiX bond lengths is estimated by calculation of the force constants; it is in the order of about 0,01 A.

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