| Description |
1 online resource (206 p.) |
| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Notes |
Description based upon print version of record |
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5.5. RESOLUTION OF SINGULARITIES AT LINEAR GEOMETRIES: NON-RECTILINEAR COORDINATES |
| Genre/Form |
Electronic books
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| Form |
Electronic book
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| ISBN |
9780429531835 |
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0429531834 |
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