Brian T. Sutcliffe

The ab initio calculation of the vibrational‐rotational spectrum of triatomic systems in the close‐coupling approach, with KCN and H2Ne as examples

A Hamiltonian for the vibration‐rotation motions of atom–diatom systems is derived in body‐fixed coordinates and a method for its solution as a close‐coupled secular problem is formulated. The radial coordinate is expanded in Morse oscillator functions. Calculations on KCN and H2Ne are presented. For KCN the neglect of Coriolis interactions is found to have little effect. Extensions of the method to problems in more dimensions are suggested.

A GENERALIZED-APPROACH TO THE CALCULATION OF RO-VIBRATIONAL SPECTRA OF TRIATOMIC-MOLECULES

A generalization of the well known atom-diatom scattering hamiltonian to a coordinate system of two lengths and an angle is derived, another special case of which is a previously known bond angle-bond length hamiltonian. Different axis embeddings are also considered. The formalism is applied to the ro-vibrational levels of D2H+, CH+ 2 and HDHe (A 1 A′) and the advantage of a judicious choice of coordinates demonstrated. The vibrational band origins for HDHe*, the first predictions for this system for which previous calculations had failed, are obtained using a new geometrically defined coordinate system. It is suggested that these coordinates might be used to represent isotopically substituted van der Waals complexes.

On the rovibrational levels of the H3 ÷ and H2D ÷ molecules

Variationally exact rovibrational levels for the H3 + and H2D+ molecules are calculated using a recently published accurate potential. Vibrational fundamentals are v A 1 = 3191 cm-1 and vE = 2494 (2521·6) cm-1 for H3 + and v 1 = 3000 cm-1, v 2 = 2184 cm-1 and v 3 = 2310 cm-1 for H2D+. For H3 + calculated ground state rotational constants are B 0 = 43·51 (43·57) cm-1, C 0 = 20·59 (20·71) cm-1, DJ 0 = 0·04 (0·05) cm-1, DJ K 0 = -0·07 (-0·10) cm-1 and DK = 0·04 (0·04) cm-1 (where experimental results are given in parenthesis). An attempt is made to stabilize many vibrational states. We thus reassess the results of Carney and Porter. The implications for astrophysics, the interpretation of the infrared spectrum of H3 + near its dissociation limit and the unassigned spectrum of H2D+ are discussed.

Highly rotationally excited states of floppy molecules: H2D+ with J ⩽ 20

A partitioning of the generalized triatomic hamiltonian of the preceding paper is developed which allows the calculation of highly-excited rotational states, without approximation, in a two-step variational procedure. Iterative diagonalization techniques are found to be particularly useful for the second variational step. The rotationally-excited states of H2D+ are studied with J ⩽ 20, well into the region where the ground and excited state manifolds overlap. Comparison of results for two different ab initio potentials and convergence considerations suggest that pure rotational transition frequencies obtained from our results should be accurate to about 1 cm-1 for J ∼ 15.

Molecular structure and the born—Oppenheimer approximation

Abstract A discussion is attempted of the validity of the Born—Oppenheimer approximation which is characterized as an asymptotic analysis leading to a semiclassical theory of molecular structure. It is suggested that there are inherent defects in the resulting semiclassical theory which will limit its utility in the explanation of highly accurate experiments involving molecules.

Vibrational energy levels with arbitrary potentials using the Eckart-Watson Hamiltonians and the discrete variable representation

An effective and general algorithm is suggested for variational vibrational calculations of N-atomic molecules using orthogonal, rectilinear internal coordinates. The protocol has three essential parts. First, it advocates the use of the Eckart-Watson Hamiltonians of nonlinear or linear reference configuration. Second, with the help of an exact expression of curvilinear internal coordinates (e.g., valence coordinates) in terms of orthogonal, rectilinear internal coordinates (e.g., normal coordinates), any high-accuracy potential or force field expressed in curvilinear internal coordinates can be used in the calculations. Third, the matrix representation of the appropriate Eckart-Watson Hamiltonian is constructed in a discrete variable representation, in which the matrix of the potential energy operator is always diagonal, whatever complicated form the potential function assumes, and the matrix of the kinetic energy operator is a sparse matrix of special structure. Details of the suggested algorithm as well as results obtained for linear and nonlinear test cases including H(2)O, H(3) (+), CO(2), HCNHNC, and CH(4) are presented.

Variationally exact ro-vibrational levels of the floppy CH2+ molecule

Abstract Ro-vibrational calculations are performed on the CH 2 + radical using a method recently developed for atom-diatom systems. The vibrational fundamentals obtained are 2998.8, 718.3, and 3270.7 cm −1 , in good agreement with recent results. Band origins for several higher vibrational levels are also obtained. Calculations with J = 1 show that the Coriolis interaction play a significant role and two alternative embeddings are discussed. Use of correlation parameters confirms that CH 2 + belongs to no idealized class of molecules in keeping with its “floppy” nature.

On the use of variational wavefunctions in calculating vibrational band intensities

It is shown that vibrational band intensities calculated using variational wavefunctions and dipole surfaces give results which depend on how the Cartesian axes of the dipole surface are defined. It is suggested that the most consistent definition of these axes uses the rules proposed by Eckart for separating rovibrational motion. The consequences of this choice of axis system for the calculated band intensities of H2S, LiNC and H3 +, and the apparent validity of Honl-London factors are discussed. Computed band intensities are presented for H2S, HDS and D2S which correct previous literature values.

Matrix Elements between Bonded Functions

Formulas are given for the spinless one‐ and two‐particle density matrices and for certain other density functions in terms of bonded function wavefunctions.

All the bound vibrational states of H3+ : a reappraisal

The 3D discrete variable representation (DVR) calculations of Henderson and Tennyson [Chem. Phys. Lett. 173, 133 (1990)] are reanalyzed to find the source of the nonvariational behavior highlighted by Carter and Meyer [J. Chem. Phys. 96, 2424 (1992)]. The discrepancy is found to be caused not by the use of incorrect boundary conditions, but by a failure of the quadrature approximation commonly used in DVR calculations. Corrected DVR calculations show variational but slow convergence. Calculations using the same intermediate vectors as the nonvariational calculations and a corrected final Hamiltonian show greatly enhanced convergence. The vibrational band origins computed with this method are converged to within 2 cm−1 up to 35 000 cm−1. A complete list of these is presented and comparisons made with previous predictions.