Force field for out-of-plane vibrations of pyrazine

1986 ◽  
Vol 51 (12) ◽  
pp. 2656-2664 ◽  
Author(s):  
Juan F. Arenas ◽  
Juan I. Marcos ◽  
Juan T. Lopez-Navarrete ◽  
Juan C. Otero
Keyword(s):  
Force Field ◽  
Theoretical Data ◽  
Force Constants ◽  
Second Derivatives ◽  
Out Of Plane ◽  
Quadratic Force Field ◽  
Derivatives Of ◽  
Theory And Experiment

A general quadratic force field has been calculated for the out-of-plane vibrations of pyrazine by the MINDO/3 method. The first derivatives of the energy were computed analytically and the second derivatives of energy numerically. The force constants so obtained have been refined to fit the observed frequencies of -h4, -d4 and cis-pyrazine-d2. The calculations proved our assignment suggested previously, though the disagreement between theory and experiment for the Au vibrations of pyrazine needs additional experimental and theoretical data for clarification.

A general quadratic force field for the out-of-plane vibrations of the s-tetrazine molecule

1987 ◽  
Vol 43 (7) ◽  
pp. 873-878 ◽  
Author(s):  
I.Lorite Villacreces ◽  
M.Fernandez Gomez ◽  
J.J.Lopez Gonzalez ◽  
A.Cardenete Espinosa
Keyword(s):  
Force Field ◽  
Out Of Plane ◽  
Quadratic Force Field

A general quadratic force field for the pyridazine molecule: out-of-plane B1 normal modes

1986 ◽  
Vol 142 ◽  
pp. 33-36 ◽  
Author(s):  
M. Fernandez ◽  
J.J. Lopez ◽  
A. Cardenete ◽  
J.F. Arenas
Keyword(s):  
Force Field ◽  
Normal Modes ◽  
Out Of Plane ◽  
Quadratic Force Field

Vibrational spectra and force field studies of [PtCl3(CO)]− anion labelled with 13C16O, 12C18O, and radioactive 14C16O

1991 ◽  
Vol 69 (11) ◽  
pp. 1855-1863 ◽  
Author(s):  
J. Mink ◽  
P. L. Goggin
Keyword(s):  
Force Field ◽  
Vibrational Spectra ◽  
Approximate Calculation ◽  
Field Studies ◽  
Force Constants ◽  
Carbonyl Complexes ◽  
Valence Force Field ◽  
Square Planar ◽  
Out Of Plane ◽  
Bending Modes

Detailed infrared and Raman studies are reported for [PtCl3(12C16O)]−, [PtCl3(13C16O)]−, [PtCl3(12C18O)]−, and [PtCl3(14C16O)]− together with assignments. Bands observed for the 14C16O species at 2005, 483, 507, and 466 cm−1 are assigned to CO and PtC stretching, PtCO in-plane and out-of-plane linear bending modes, respectively. Force constants have been calculated using a modified valence force field, with constrained off-diagonal force constants based on [PtCl4]2− and [PtX3(CO)]− (X = Br, I). The effective G-matrix method (EGM) has been used for approximate calculation of CO and PtC stretching force constants for some other square-planar platinum–carbonyl complexes. The results are discussed with the assistance of stretching force constants for some of the simpler complexes. Key words: vibrational spectra, force constant calculation, 13C, 14C, and 18O labelled [PtCl3(CO)]−.

Theoretical study of spectroscopic constants and anharmonic force field of formaldehyde

2014 ◽  
Vol 13 (06) ◽  
pp. 1450049 ◽  
Author(s):  
Xuejun Wang ◽  
Meishan Wang ◽  
Chuanlu Yang ◽  
Jing Li ◽  
Dianmin Tong
Keyword(s):  
Force Field ◽  
Theoretical Data ◽  
Dft Method ◽  
Force Constants ◽  
Coupling Constants ◽  
Basis Set ◽  
Basis Sets ◽  
Spectroscopic Constants ◽  
Equilibrium Geometries ◽  
Anharmonic Force

The equilibrium geometries of formaldehyde are optimized with B3LYP, B3PW91 and MP2 methods employing three basis sets 6-311++G(2d,2p), aug-cc-pVTZ and cc-pVTZ, respectively, which agree well with the corresponding experimental and previous theoretical data. The best optimized geometries are obtained at the theoretical level B3LYP/6-311++G(2d,2p) basis set. Basing on the calculated equilibrium geometries, the spectroscopic constants and anharmonic force field of H 2 CO are investigated. The results show that DFT method is superior to MP2 method at the calculation of spectroscopic constants and force constants of H 2 CO . The vibration–rotation interaction constants and fundamental vibrational wave numbers of H 2 CO are firstly theoretically calculated. The Coriolis coupling constants, cubic force constants and most of quartic force constants are firstly theoretically predicted.

Earth's gravity field parameters determination by the space geodesy dynamical approach

2017 ◽  
Vol 919 (1) ◽  
pp. 7-12
Author(s):  
N.A Sorokin
Keyword(s):  
Coordinate System ◽  
Gravitational Potential ◽  
Coefficient Matrix ◽  
Measured Quantity ◽  
Second Derivative ◽  
Measured Variable ◽  
Second Derivatives ◽  
Rectangular Coordinates ◽  
Cartesian Coordinate ◽  
Derivatives Of

The method of the geopotential parameters determination with the use of the gradiometry data is considered. The second derivative of the gravitational potential in the correction equation on the rectangular coordinates x, y, z is used as a measured variable. For the calculated value of the measured quantity required for the formation of a free member of the correction equation, the the Cunningham polynomials were used. We give algorithms for computing the second derivatives of the Cunningham polynomials on rectangular coordinates x, y, z, which allow to calculate the second derivatives of the geopotential at the rectangular coordinates x, y, z.Then we convert derivatives obtained from the Cartesian coordinate system in the coordinate system of the gradiometer, which allow to calculate the free term of the correction equation. Afterwards the correction equation coefficients are calculated by differentiating the formula for calculating the second derivative of the gravitational potential on the rectangular coordinates x, y, z. The result is a coefficient matrix of the correction equations and corrections vector of the free members of equations for each component of the tensor of the geopotential. As the number of conditional equations is much more than the number of the specified parameters, we go to the drawing up of the system of normal equations, from which solutions we determine the required corrections to the harmonic coefficients.

Some new generalizations for GA-convex functions

Filomat ◽  
2017 ◽  
Vol 31 (4) ◽  
pp. 1009-1016 ◽  
Author(s):  
Ahmet Akdemir ◽  
Özdemir Emin ◽  
Ardıç Avcı ◽  
Abdullatif Yalçın
Keyword(s):  
Convex Functions ◽  
Integral Identity ◽  
Integral Inequalities ◽  
General Integral ◽  
Second Derivatives ◽  
Derivatives Of

In this paper, firstly we prove an integral identity that one can derive several new equalities for special selections of n from this identity: Secondly, we established more general integral inequalities for functions whose second derivatives of absolute values are GA-convex functions based on this equality.

System of thermodynamic quantities in the McMillan-Mayer solution theory

1985 ◽  
Vol 50 (4) ◽  
pp. 791-798 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Generating Function ◽  
Simple Form ◽  
Unit Volume ◽  
Thermodynamic Quantities ◽  
Solution Theory ◽  
Pure Solvent ◽  
Second Derivatives ◽  
Definition Of ◽  
Derivatives Of

The McMillan-Mayer (MM) free energy per unit volume of solution AMM, is employed as a generating function of the MM system of thermodynamic quantities for solutions in the state of osmotic equilibrium with pure solvent. This system can be defined by replacing the quantities G, T, P, and m in the definition of the Lewis-Randall (LR) system by AMM, T, P0, and c (P0 being the pure solvent pressure). Following this way the LR to MM conversion relations for the first derivatives of the free energy are obtained in a simple form. New relations are derived for its second derivatives.

Force field for in-plane vibrations of terephthalonitrile

1989 ◽  
Vol 54 (1) ◽  
pp. 18-27 ◽  
Author(s):  
Juan F. Arenas ◽  
Juan I. Marcos ◽  
Francisco J. Ramírez
Keyword(s):  
Experimental Data ◽  
Force Field ◽  
Normal Coordinates ◽  
Internal Coordinates ◽  
Isotopic Shifts ◽  
Quadratic Force Field ◽  
Semi Empirical

The general quadratic force field for the in-plane vibrations of terephthalonitrile was calculated by the semi-empirical MINDO/3 method. This force field was refined to the frequencies observed experimentally for terephthalonitrile and isotopic shifts of terephthalonitrile-[15N2]. The refined frequencies reproduce the experimental data with errors less than 0.5%. The normal coordinates and the force field in internal coordinates were also calculated from the refined field.

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