Ellinger Y., Defranceschi M. (eds.) Strategies and applications in quantum chemistry (Kluwer, 200

In Table 5, we show the calculated magnetic susceptibilities for A1H and , and the Lipscomb et al. [7] obtained values for A1H using an extended basis set of field independent Slater type orbitals.

Our results are in close agreement with the values obtained by Lipscomb et al. [7]; this confirm the validity of our approach. Note that, A1H is predicted to be weakly diamagnetic

susceptibility of this anion is strongly depending on the inclusion of diffuse orbitals in the basis set. We notice that the basis set II permits to obtain reliable results, its further extension by extra diffuse functions (basis set III) leading approximately to the same

results. should be diamagnetic, and its mean susceptibility is of the order of -22.

It should be noted that diffuse functions which are necessary for a good description of the magnetic properties of anions, have been found needless when computing the susceptibilities of the neutral molecules.

In Table 7, we reported the mean magnetic susceptibilities of the BH and molecules, obtained by G. Berthier et al. [3], using the same SCF ab initio method, employing a triple-zeta basis set augmented by a s-type bond function. We produce also in

comparison. We note, that the magnetic susceptibilities exhibit the same features in the two analogous series of molecules, namely that diamagnetism decreases when the heavy atom nuclear charge increases.

3. Conclusion

The good agreement between our results and those obtained by Lipscomb and al. [7],

the introduction of several diffuse orbitals in the basis set. In both series of compounds, diamagnetism decreases with the increase of the heavy atom nuclear charge.

References

1.R.M. Stevens, R.M. Pitzer and W.N. Lipscomb, J. Chem. Phys. 42, 3666 (1965)

2.R.A. Hegstrom and W.N. Lipscomb, J. Chem. Phys. 45, 2378 (1966).

3.G. Boucekkine-Yaker, A. Boucekkine, A. Zaucer and G. Berthier, Int. J. Quant.

Chem.. 23, 365 (1983).

4.G. Boucekkine-Yaker, A. Boucekkine, and G. Berthier, Int. J. Quant. Chem.. 18,

369 (1984).

[6]. The technology of astrophysical measurements on excited states for molecules such as

PN is still in its infancy and, to the best of our knowledge, no results have been reported.

2. Procedure

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. CI wave functions were obtained with the MELDF suite of programs

[9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals.

All three states were described by a single set of SCF molecular orbitals based on the

space known as "K-orbitals" [10] which , among other properties, approximate the set of natural orbitals. Transition moments within orthogonal basis functions are easier to derive. For the X state the composition of the reference space was obtained by performing two

Hartree-Fock single and double excitations (HFSD-CI) calculations at two typical internuclear distances, i.e. (equilibrium geometry) and about and adding to the HF

configuration all those configurations whose coefficients in either of these CIs were

. The resulting list of 44 configurations constituted the occupancy of the reference space for Multi-Reference Single and Double CI (MRSD-CI) calculations in the region The energy threshold value, hereafter referred to as ETHRESH, used in the

perturbation theory selection procedure of the configurations was set equal to

HFSD-CIs, two MRSD-CI calculations at the above internuclear distances were next performed, keeping in either case all configurations with expansion coefficients

combined space spanned by all configurations whose coefficients equalled or exceeded

should ensure that the overwhelming majority of the correlation energy was recovered via the variational CI calculation.

For the state, this procedure led to still much larger reference spaces and larger CI wave functions because of the still larger number of configurations possessing expansion

able to compute properties in the neighbourhood of the potential curve's minimum with acceptable accuracy, this wavefunction should still be adequate. This will be illustrated by comparing our lifetime results with those of CO obtained by a different CI approach as well as a set of spectroscopic constants with those obtained by similar CI calculations based on another algorithm.

Estimates of the energy contributions from higher than double excitations out of the reference space were obtained by means of one form of the "Davidson correction" [11,7]. More details can be found in references [7,8].

3.1.1. Potential energy curve; one-electron properties; spectroscopic constants

The potential energy curve including the Davidson correction is shown in Figure 1. Among the calculated one-electron properties [7] only a few ones did show sizeable correlation effects (Table 1). The calculated and experimental values of the electric dipole moment are unexpectedly yet in good agreement although multiple bonded systems are known to require the use of a large number of higher angular momentum basis functions [ 12J. The rather large theoretical difference found for the nuclear coupling remains at the present time an open question: if the experimental value is accurate, this difference is due to a too small value of the electric field gradient. It should be pointed out this observable is neither easy to measure with precision nor to compute accurately, especially for multiple bonded systems involving third period atoms.

3.1.2. Spectroscopic constants

Selected spectroscopic constants (Table 2), derived by the well-known Dunham polynomial fit expansion method [13,14] were calculated from both the variational MRSDCI energies and the estimated full CI energies, i.e. including the Davidson correction. In general, the effects of the Davidson correction appear to be small. A very good agreement,

Davidson correction. For the calculations of lifetimes within a single state ,in contrast to two distinct states , the vibrational/rovibrational decays occuring via a cascade mode, the electric dipole moment function replaces the usual electric dipolar transition moment function required in case of transitions between states. More details can be found in [7,8] as well as the references quoted therein.

A remarkable agreement with experiment had been found for pure rotational excitations (Table 3). The calculated values are systematically a little smaller because the theoretical internuclear distance is slightly larger than the experimental one, i.e.

(expt), (theor.) and this deviation affects the parameter values

leading to our previous observation. A slight deviation with respect to the expected effect of the anharmonicity on the vibrorotational transitions is observed in contrast to the same effect noted on the pure rotational excitations.

To the best of our knowledge, pure rotational transition calculations for the PN X state are reported for the first time.

The calculated lifetimes (Table 4) are several powers of ten larger then those corresponding

which require special techniques of measurements that were available only in recent years.

Molecular lifetimes corresponding to pure vibrational (v =0-4) and rovibrational (v =0-4, j=l-5) levels - derived for the first time - were found to be eight to ten powers of ten larger

than those corresponding to an electric dipolar transition state above state). In the latter case large transition moments for non-orthogonal off-diagonal vibrational states are also responsible for the resulting magnitude of these lifetimes. In this case, the

off-diagonal elements of the dipole moment for orthogonal vibrational states are several powers of ten smaller compared to their transition moment counterparts, leading to much smaller values of the transition probabilities and Einstein spontaneous emission coefficients and therefore very large lifetimes. A very important rotational effect on the lifetime for v'=0, becoming rather weak for v'=l and being not existent for higher v's considered in this study is noted.

MR SD-CI potential curves including the Davidson corrections are presented in Figure 1.