Mercedes Alacid

Determination of highly excited rovibrational states for N2O using generalized internal coordinates

Generalized internal vibrational coordinates are optimized and used to describe highly excited vibrational motions in the N2O molecule. These coordinates are defined as the magnitudes of two vectors, which are expressed as linear combinations of the internal displacement vectors and the angle formed between them. They depend on two parameters and contain, as particular cases, valence and orthogonal (Jacobi, Radau, etc.) coordinate systems. The coordinates are optimized by minimizing unconverged variationally computed vibrational energies with respect to the external parameters. A comparison of the optimal internal coordinates derived for N2O with valence and hyperspherical normal coordinates is made. The optimal internal coordinates are also used to determine a new potential energy function for N2O from the observed vibrational frequencies up to 15 000 cm−1 using fully variational calculations. The quality of the adjusted potential energy function is checked by computing vibrational-rotation energy levels...

Matrix elements for the modified Pöschl—Teller potential

Analytical exact expressions are obtained for matrix elements of the modified Poeschl-Teller oscillator over different operators including powers of the hyperbolic functions sinh({alpha}x), cosh({alpha} x), and tanh({alpha} x) and the differential operators d/dx and d{sup 2}/dx{sup 2}. These expressions are derived using explicitly the Poschl-Teller eigenfunctions. In addition, several recursion relations connecting different Poschl-Teller matrix elements are obtained using the factorization and hypervirial techniques. It is shown that these relations can be used to make easier the computation of the matrix elements. 38 refs., 1 fig.

The role of rotation in the calculated ultraviolet photodissociation spectrum of ozone

We present exact quantum calculations of the photodissociation of ozone in the Hartley band. These calculations rely on an hyperspherical description of the system, including rotation. A pseudospectral approach has been used for an efficient implementation of this scheme. The autocorrelation function has been directly computed by means of a Lanczos scheme, augmented by a complex absorbing potential. Using a single excited potential energy surface (D 1B2), calculations up to J=17 are reported. It is shown that in these conditions rotation has only marginal effects over the first 500 fs. The origin of the observed experimental temperature dependence is discussed in this context.

Excited vibrational states and potential energy function for OCS determined using generalized internal coordinates

Variational calculations of excited vibrational states for the OCS molecule, using generalized internal coordinates properly optimized, are presented. The calculations are made for two empirical and one ab initio potential energy surfaces previously reported. It is shown that the computed vibrational frequencies differ considerably from the experimental values for the three potential surfaces employed. Consequently a new and much more accurate potential surface is determined for OCS by nonlinear least-squares fitting to the observed vibrational terms. The surface is expressed as a Morse-cosine expansion in valence coordinates and its quality is checked by computing the vibrational frequencies of three isotopic species of the molecule.

Bound and resonance states by a time-independent filter diagonalization method for large Hamiltonian systems

Abstract A new algorithm on the basis of Neuhauser–Mandelshtam–Taylor developments of the filter diagonalization method is proposed for calculating highly excited bound states and resonances for large Hamiltonian systems, even in the high-density-state part of the spectrum. This is a complementary method to the Lanczos procedure with no reorthogonalization which is widely used for calculating the low lying energy levels, i.e. the low-density part of the spectrum. An illustrative numerical example is given.

Two‐center matrix elements for Kratzer oscillators

An exact expression for two‐center Kratzer oscillator matrix elements of rβ (r is the internuclear distance) is derived. Using the hypervirial‐like theorem procedure, several recursion relations among these matrix elements are obtained. It is shown that these relations can be used to calculate recursively two‐center Kratzer oscillator matrix elements of rβ and rβd/dr in a very simple way.

Global potential energy surfaces for the CO2 and CS2 molecules

Abstract Global potential energy surfaces for the ground electronic states of the CO 2 and CS 2 molecules are determined. We use the many-body single-value surfaces previously constructed by Murrell and Guo (J. Chem. Soc. Faraday Trans. 2 (1987) 83, 683) and refine their parameters by the non-linear least-squares method in order to reproduce the observed vibrational frequencies of each molecule. The fits are made by computing variationally the vibrational frequencies using sets of optimal generalized internal coordinates. The quality of the potentials is checked by computing vibrational frequencies of isotopic species and highly excited vibrational energies nor included in the fits.

Rotational–vibrational matrix elements for Kratzer oscillators

Several recursion relations connecting Kratzer oscillator matrix elements of different operators are derived using the hypervirial theorem. These relations can be easily used to calculate such matrix elements, either numerically or by developing analytical expressions. In particular, analytical expressions for the matrix elements of the xα and xαd/dx operators, where x is an internuclear separation coordinate, are obtained.

Variational calculations of vibrational states of N2O using hyperspherical normal coordinates

Accurate variational calculations are presented for highly excited vibrational bound states of N2O using different recently proposed ab initio and empirical potential energy surfaces. All these potential surfaces are expressed as series expansions in terms of internal displacement coordinates. Transformations of them into Simons, Parr and Finlan (SPF) and Morse expansion are also considered. The vibrational state calculations are performed using a set of curvilinear hyperspherical normal coordinates derived from Radau coordinates. The vibrational energies are compared with experimental data and the quality of the potential energy surfaces used is discussed.

Optimal generalized internal vibrational coordinates for symmetrical linear triatomic molecules

Abstract The use of generalized internal vibrational coordinates to describe vibrational motions in symmetrical linear triatomic molecules is considered. These coordinates are defined as the magnitudes of two generalized internal vectors and the angle formed between them, and they depend on two parameters which can be properly optimized. We derive an analytical expression which provides the optimal values of these parameters for linear symmetrical triatomic molecules. The validity of this expression is checked by making variational calculations of vibrational energy levels for the CO 2 and CS 2 molecules.