Computational Spectroscopy of Polyatomic Molecules

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
CHAPTER 1: Introduction
CHAPTER 2: Coordinates choice
	2.1. MOLECULAR FRAME
	2.2. COORDINATE TRANSFORMATION
		2.2.1. Three translational conditions
		2.2.2. Three rotational conditions
	2.3. MOLECULAR FRAMES
		2.3.1. Bond frame
		2.3.2. Eckart frame
		2.3.3. Principal axes frame
	2.4. VIBRATIONAL COORDINATES
		2.4.1. Geometrically defined, valence coordinates
		2.4.2. Z-matrix
		2.4.3. Jacobi frames
		2.4.4. Derivatives of the geometrically defined coordinates with respect to the Cartesian coordinates
	2.5. LINEARISED COORDINATES
		2.5.1. Normal modes
		2.5.2. Vibrational coordinates for linear molecules
	2.6. OTHER MOLECULES
		2.6.1. Rigid tetratomics of the XY3-type (phosphine)
		2.6.2. Non-rigid XY3 (ammonia)
	2.7. NON-LINEAR RIGID TETRATOMIC MOLECULES: H2CO TYPE
	2.8. NON-RIGID CHAIN MOLECULE HOOH
	2.9. METHANE AS AN EXAMPLE OF AN XY4-TYPE TETRAHEDRAL MOLECULE
CHAPTER 3: Kinetic energy operator: Coordinate transformation
	3.1. MOLECULAR KEO
	3.2. TRANSFORMATIONS OF COORDINATES AND MOMENTA
		3.2.1. The t–s formalism
		3.2.2. An alternative, g-matrix method to derive KEO
	3.3. NORMAL MODES AND WATSON HAMILTONIAN
	3.4. SØRENSEN APPROACH FOR THE ROTATIONAL S-MATRIX
		3.4.1. Example of derivation of Sørensen vectors for H2CO
	3.5. NUMERICAL EVALUATION OF KEO AT ANY INSTANTANEOUS GEOMETRY
		3.5.1. KEO in geometrically defined coordinates
	3.6. JACOBI COORDINATES KEOS
	3.7. KEO AS A TAYLOR-TYPE EXPANSION
		3.7.1. Recursive expansion scheme
		3.7.2. Taylor-expanded s-vectors in the linearised coordinates using the t–s algorithm and its Sørensen\'s derivative
		3.7.3. Non-rigid reference configuration and linearised coordinates
CHAPTER 4: KEO: Triatomic molecules
	4.1. KEO OF XY2 IN VALENCE COORDINATES
		4.1.1. Eckart frame
		4.1.2. Sørensen\'s solution
		4.1.3. PAS frame
		4.1.4. Radau frame
	4.2. XYZ MOLECULE
	4.3. LINEARISED COORDINATES FOR XY2
	4.4. SINGULARITIES IN KEO OF TRIATOMICS
		4.4.1. Method 1: 3N – 5 case or four rectilinear coordinates
CHAPTER 5: Basis sets
	5.1. MATRIX ELEMENTS OF HAMILTONIAN
	5.2. RO-VIBRATIONAL BASIS SET
	5.3. VIBRATIONAL BASIS SETS
		5.3.1. Product-form basis sets
		5.3.2. Two-dimensional basis functions for doubly degenerate vibrations
		5.3.3. 3D vibrational basis functions
		5.3.4. Basis set pruning: polyad and energy thresholds
		5.3.5. Basis set bookkeeping
	5.4. BASIS SET CONTRACTION
		5.4.1. The J = 0 representation
		5.4.2. ‘Contracted’ representation of Hamiltonian
		5.4.3. Another layer of contraction
		5.4.4. Basis set contraction with the vibrational angular momentum
		5.4.5. Assignment: vibrational quantum numbers
	5.5. RESOLUTION OF SINGULARITIES AT LINEAR GEOMETRIES: NON-RECTILINEAR COORDINATES
		5.5.1. Formulation
		5.5.2. Associated Laguerre polynomials
	5.6. ROTATIONAL BASIS SET
		5.6.1. Rigid rotor wavefunctions
		5.6.2. Rotational matrix elements
CHAPTER 6: Symmetry-adapted basis sets
	6.1. INTRODUCTION
	6.2. MOLECULAR SYMMETRY: SOME THEORY
	6.3. AUTOMATIC SYMMETRISATION
	6.4. NUMERICAL EXAMPLES
		6.4.1. Symmetry-adapted vibrational basis set for an XY2-type molecule
		6.4.2. Symmetrisation of the XY3 vibrational basis set
	6.5. SYMMETRY SAMPLING OF EIGENFUNCTIONS
		6.5.1. Sampling symmetrisation of a XY3 vibrational basis set, the C3v-symmetry
		6.5.2. Reduction of a product
		6.5.3. Symmetry properties of rigid rotor wavefunctions
	6.6. SYMMETRISATION OF THE RIGID ROTOR BASIS FUNCTIONS: SPECIAL CASE
	6.7. MATERIALS USED
CHAPTER 7: Applications
	7.1. INTENSITY CALCULATIONS
		7.1.1. General formulation of ro-vibrational intensities
		7.1.2. Calculating the line strength
	7.2. REFINEMENT OF PES
		7.2.1. Fitting using Newton\'s minimisation method
		7.2.2. Correlated parameters and constrained fit
Bibliography
Index