Inverse problems of vibrational spectroscopy /

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Yagola, A. G. (Autor)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Utrecht, the Netherlands : VSP, 1999.
Colección:Inverse and ill-posed problems series.
Temas:
Vibrational spectra.
Spectrum analysis.
Raman spectroscopy.
Infrared spectroscopy.
Inverse problems (Differential equations)
Spectre de vibration.
Spectroscopie Raman.
Spectroscopie infrarouge.
Problèmes inverses (Équations différentielles)
infrared spectroscopy.
Infrared spectroscopy
Raman spectroscopy
Spectrum analysis
Vibrational spectra
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Introduction
  • Chapter 1. Physical model of molecular vibrations
  • 1.1. Classical theory of small vibrations. Preliminary considerations
  • 1.2. Simplified quantum mechanical statement of the problem
  • Chapter 2. Full statement of the vibrational problem
  • 2.1. Vibrational-rotational interaction. Classical consideration
  • 2.2. Centrifugal distortion. Classical consideration
  • 2.2.1. Linear molecules
  • 2.3. Quantum mechanical model
  • 2.4. Adiabatic approximation
  • 2.5. Vibrational-rotational interaction. Quantum mechanical consideration
  • 2.6. Centrifugal distortion. Quantum mechanical consideration2.7. The adiabatic theory of perturbations
  • Chapter 3. Consideration of the mathematical model for molecular vibration analysis. Direct and inverse problems
  • 3.1. Introduction. Parameters of the model
  • 3.2. Ab initio methods
  • 3.3. Results and difficulties of using ab initio methods
  • 3.4. Semiempirical methods
  • 3.5. Empirical methods
  • Chapter 4. Vibrational problem in internal coordinates. Use of the redundant coordinate system
  • 4.1. Models of a molecular force field
  • 4.2. Choice of generalized coordinates4.3. Construction of the auxiliary matrices
  • 4.3.1. The matrix of kinematic coefficients
  • 4.3.2. Bond stretching
  • 4.3.3. Valence bond angle bending
  • 4.3.4. Angle between a bond and the plane of an atomic triple
  • 4.3.5. Angle between two planes (torsion coordinate)
  • 4.3.6. An example of constructing the matrix B for the torsional coordinate
  • 4.3.7. An example of constructing matrix G
  • 4.3.8. Construction of the matrix H
  • 4.3.9. The other matrices
  • 4.4. Use of redundant coordinates
  • Chapter 5. Vibrational problem in symmetry coordinates5.1. Use of molecular symmetry
  • 5.2. Use of symmetry in the calculation of molecular vibrations
  • 5.3. Calculation of the molecular constants in symmetry coordinates
  • Chapter 6. Ill-posed problems and the regularization method. Regularizing algorithms for constructing force fields of polyatomic molecules on the base of experimental data
  • 6.1. Well-posed and ill-posed problems
  • 6.2. Ill-posedness of the problem of constructing force field on the base of experimental data (inverse vibrational problem)
  • 6.3. Mathematical formulation of the inverse vibrational problem6.4. Ill-posedness of the problem of searching for a normal pseudosolution of the linear algebraic equation system (LAES)
  • 6.5. Regularizing algorithms for constructing a normal pseudosolution of LAES
  • 6.6. Nonlinear ill-posed problems
  • 6.7. Inverse vibrational problem for a single molecule
  • 6.8. Joint calculation of force field in a series of related molecules
  • Chapter 7. Numerical methods
  • 7.1. Searching for eigenvalues and eigenvectors
  • 7.2. Minimization of functional. Simple constraints

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