Monte Carlo Simulations of the Structures and Optical Absorption Spectra of AlAr(sub N) Clusters

Multiphoton Ionization Spectroscopy of AlArN Clusters

“…The two avoided-crossing interactions are also indicated in Figure 7 by the dot-dashed curves giving the nonadiabatic coupling matrix elements of eq 4 obtained from the unitary transformation connecting the adiabatic and atomic-product states. 25,33 In fact, the (3d) 2 Σ + and (4p) 2 Σ + curves evidently undergo two distinct avoided-crossing and recrossing interactions, as revealed by the variation of the associated moments and interaction matrix elements in Figure 7. The repulsive or attractive behaviors of the excited-state potential curves and moments of Figures 6 and 7 can be understood qualitatively on the basis of the spatial characteristics of the atomic Al 3d and 4p orbitals contributing to the individual molecular states, which allow closer approach in Π configurations than in Σ configurations.…”

“…The predicted AlAr 6 absorption cross section, for example, bears no resemblance by itself to the experimental spectrum of Figure 16, and the calculated cross sections generally do not include the broad flat blue bands evident in Figure 4. 33 Although all of the cross sections show red bands in approximately the same spectral interval and in one or two cases there is a hint of agreement between theory and experiment in this interval (cf. the N ) 12 results of Figures 14 and 16), the predicted blue bands appear as isolated features in the individual cross sections.…”

“…Note in this connection that some care must be exercised in employing phase-or sign-consistent electronic dipole transition moments in constructing the U d (Al,Ar) and U ∞ (Al,Ar) matrices. 33 Diagonalization of the many-body Hamiltonian matrix of eq 2 provides energy surfaces and eigenstates that include spinorbit splittings and nonpairwise-additive anisotropic Al-Ar interactions and that incorporate the avoided crossings and other interactions required for a satisfactory representation of the excited electronic states of the clusters. Although the Ar atoms are formally assumed to remain in their ground 1 S 0 state in this approach (D (Ar) f I), their charge distortions due to interactions with the Al and Ar atom are included in the diatomic and atomic-product states and are thereby incorporated in the calculated many-body cluster electronic states.…”

“…The method is seen to be a logical extension to avoided crossing situations of previously described perturbative methods for employing atomic pair-interaction potentials in cluster and other aggregate calculations 34,35 and is an alternative computational implementation of a recently developed more general spectral theory of chemical interactions. 36,37 Optical absorption cross sections are obtained from the calculated MRCI energies and dipole transition moments and classical Monte Carlo simulations of the vibrational motions on the calculated potential energy surfaces at 10-30 K. 26,33 The ground-state geometries of the clusters, which are employed only for visualization purposes, are provided by the lowest-…”

“…Nonadiabatic coupling matrix elements between the atomic-product states are also obtained from the unitary transformation matrix U ( Al,Ar ) in the form 31 where U ( Al,Ar ) is generally constructed to ensure the equivalence of the invariant one-electron transition density matrix in the two representations. , In the case of the relatively weak dispersion interactions of interest here, however, it is judged sufficient to employ the matrix of dipole transition moments calculated in the two representations (diatomic and atomic-product) to construct the required transformation matrix, a procedure that corresponds to use of a dipole-operator-weighed integral over the transition density matrix in place of the more complicated transition density matrix itself. This approximation provides the simple expression U ( Al,Ar ) = · , where is the matrix that diagonalizes the molecular dipole transition moment matrix and diagonalizes its asymptotic ( R AlAr → ∞) atomic-product limit.…”