Ian Hamilton

Potential energy surface for large‐amplitude motion and vibrational spacings for FH+2

Multireference configuration interaction calculations have been carried out on the ground electronic state of the fluoronium ion FH+2 . Both local (expansion about equilibrium geometry) and global (expansion about linear equidistant geometry) surface fits are obtained. The equilibrium geometry occurs at Re=1.812 35 bohr and ∠HFH=112.30 deg. The proton affinity is 116.5 kcal/mol and the inversion barrier height is 19.25 kcal/mol. The surface is suitable for the study of large‐amplitude motion, and we obtain vibrational energies up to 2 eV, which is well above the barrier height. For higher vibrational levels, we note the effect of the potential energy barrier on the vibrational spacing. The minimum in vibrational spacing for the bending progression is found to be in excellent agreement with the calculated barrier height.

Vibrational spacings for H+3

Vibrational spacings for H+3 are calculated for two different fits to the potential energy surface of Dykstra and Swope. We use a variational calculation with a distributed Gaussian basis (DGB); the calculation is shown to be simple and efficient.

The Rydberg states of FH2

The ground and first few excited electronic states of FH2 have been calculated by the MRD‐CI method, in an effort to make predictions on the Rydberg spectrum of this molecule. The results show that the excited Rydberg states, up to the 4p levels (in the united atom notation), are bound and have minima at geometries similar to that of the cation FH+2 except the first excited state, which is also found to be bound but with minimum energy at a considerably longer bond length. The most intense bound–bound transitions are predicted to occur from the 3d, 4p, and 4s states to the first excited state 1 2B2(3p).

Theoretical investigation involving electronic and vibrational calculations of the 2 2A1(3p)→1 2B2(3p) and the 3 2A1(4s)→1 2B2(3p) transitions in FH2 and FD2

Theoretical calculations have been carried out on the X 2A1, 1 2B2(3p), 2 2A1(3p), and 3 2A1(4s) electronic states of FH2. Equilibrium geometries and rotational constants as well as the first few vibrational levels of the excited states have been calculated, in order to obtain theoretical information on the 2 2A1(3p)→1 2B2(3p) and the 3 2A1(4s)→1 2B2(3p) transitions in FH2, which might be relevant to the observed spectra at about 7500 and 8000 A. The results show that the equilibrium geometry of the first excited state of FH2, 1 2B2(3p), is quite different from those of the other excited states. The estimated transition energies (ΔE0) in FH2 are 1.68 and 1.97 eV for the transitions 2 2A1(3p)→1 2B2(3p) and 3 2A1(4s)→1 2B2(3p), respectively, while in FD2 the corresponding quantities are 1.65 and 1.95 eV, respectively. A search for a minimum on the ground state surface of FH2, which has been carried out near two saddle point geometries, has not found one. Thus the present calculations do not find a metastabl...

Complicated and dissociative dynamics for the weakly forced and weakly damped morse oscillator

We examine the dynamics of a Morse oscillator which is weakly forced and weakly damped with initial conditions close to the dissociation energy. We calculate higher derivatives of the phase of the Morse oscillator with respect to time and use these to construct higher‐order phase plots. We use the higher‐order phase plots to visualize the higher harmonics of the phase which are essential for complicated and dissociative dynamics. We focus on topological changes in the higher‐order phase‐space structures and show that the higher‐order phase plots provide information regarding the dissociation process that is not easily obtained from the usual phase plot.

Energy level statistics for the regular energy spectrum of nonlinear triatomics: Nongeneric aspects and quantum chaos

We examine the regular energy spectrum of a nonlinear triatomic using model systems for which there is no coupling between the vibrational modes. We calculate the second and third moments of the successive spacing distribution and show that these may differ from those found for a generic regular energy spectrum in an energy range above the potential energy barrier for going through the linear geometry. Consequently, for nonlinear triatomics, caution must be exercised in using energy level statistics as evidence for the existence and degree of quantum chaos.

Thermal dissociation of diatomics in inert gases: A Nosé equation approach

The thermal dissociation of diatomics in inert gases has been the subject of numerous experimental and theoretical studies. There is excellent agreement between the measured and calculated bimolecular rate constants for H2, and this has become a test case for master‐equation and other approaches. In this paper we consider a Nose equation approach, which is appropriate if the inert gas simply acts as a heat bath, as may be the case in the limit of infinite dilution of H2. We examine the extent to which the Nose equation can thermalize the H2 dynamics for the temperature range 4000–10 000 K. We show that we can calculate meaningful pseudo‐unimolecular rate constants for the temperature range 7000–10 000 K and, for this temperature range, we obtain an activation energy of 3.7±0.5 eV, which is compatible with the experimental value.