Chapter
Chapter 2. Full statement of the vibrational problem
2.1. Vibrational-rotational interaction. Classical consideration
2.2. Centrifugal distortion. Classical consideration
2.3. Quantum mechanical model
2.4. Adiabatic approximation
2.5. Vibrational-rotational interaction. Quantum mechanical consideration
2.6. Centrifugal distortion. Quantum mechanical consideration
2.7. 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
3.3. Results and difficulties of using ab initio methods
3.4. Semiempirical 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 coordinates
4.3. Construction of the auxiliary matrices
4.3.1. The matrix of kinematic coefficients
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 coordinates
5.1. 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 problem
6.4. 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
7.3. The linearization method
7.4. Calculation of the functional gradients
7.5. Estimate of operator error
7.6. Estimate of the measure of incompatibility
7.7. Choice of the regularization parameter
7.8. Projection of gradients in symmetry coordinates
Chapter 8. Analysis of band intensities in vibrational spectra of polyatomic molecules
8.1. Classical and quantum mechanical consideration of intensities in molecular vibrational spectra
8.2. The mathematical model
8.3. Statements of the inverse electrooptical problem
8.4. Computational aspects
Chapter 9. Numerical implementation of algorithms for solving problems of vibrational spectroscopy
9.1. Principles of construction of the software package
9.2. Structure of the input file
9.3. Detailed structure and description of the software package of programs
9.4. Symmetry analysis package
9.5. Some other useful options
Chapter 10. Examples of molecular force field calculations on the basis of experimental data
10.1. Some preliminary remarks
10.2. Force field of the water molecule
10.3. Force fields of the transition metal oxotetrafluorides
10.4. Force field of fiuoroform
10.5. Example of joint treatment of force fields of two molecules
Chapter 11. Joint treatment of ab initio and experimental data in molecular force field calculations with Tikhonov's method of regularization
11.1. Ab initio force fields in regularizing procedures
11.2. Computational details and practical aspects of calculations
11.3. Examples of using ab initio data in force field calculations
11.4. Regularization procedure for empirical scaling of quantum mechanical force constants
Appendix A. Systems of units used in vibrational spectroscopy
A.l. International System (SI)
A.2. Measurement of frequencies in spectroscopy
A.4. Measuring force field in frequency units
A.5. Measuring force field in atomic units
A.6. Conversion between different systems
A.7. Electrooptical parameters
Inverse Problems of Vibrational Spectroscopy
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