Multiphoton Ionization Spectroscopy of AlAr_N Clusters

Abstract

Experimental and theoretical studies are reported of the multiphoton ionization spectroscopy of selected AlAr N clusters (N ) 2-54). Resonantly enhanced 1 uv + 1 vis and 2 vis + 1 vis ionization spectra are recorded of neutral clusters employing a laser-ablation/pulsed supersonic expansion source and time-of-flight mass spectrometric cluster-ion detection. The spectra are dominated by broad red-and blue-shifted asymmetric bands in the neighborhood of the 308 and 303 nm atomic Al 3p f 3d and 4p lines. The detailed structures of these bands and the observed degree of their spectral shifts with increasing cluster size are attributed on the basis of concomitant ab initio theoretical calculations to interplay among a number of factors, including (i) the comparable strengths of spin-orbit-split anisotropic ( 2 P 1/2 )Al-( 1 S 0 )Ar interactions and Ar-Ar mutual attractions, responsible for predicted external-site Al atom locations on distorted icosahedral Ar N structures, (ii) avoided crossings in the nearly degenerate AlAr N potential energy surfaces accessed by one-and twophoton atomic Al 3p f 3d and 4p excitations, giving rise to the red-and blue-shifted spectral profiles, and (iii) significant dynamical rearrangement and parent cluster-ion fragmentation following ionization, resulting in Al + Ar M signals that generally reflect the absorption cross sections of an ensemble of larger prior clusters (AlAr N , N > M). Additionally, nonuniformity in the cluster-size distribution of the incident molecular beam is inferred from the calculated and measured spectra and must be incorporated in the development for a completely satisfactory accounting between theory and experiment. Comparisons with the results of earlier experimental studies of the ionization potentials of AlAr N clusters also underscore the importance of dynamical parent-ion rearrangement and fragmentation, consequent of the increased Ar solvation of the Al + radical in the equilibrium Al + Ar M cluster-ion structures. The reported multiphoton ionization cluster-ion spectra are evidently highly sensitive to the details of the atomic Ar arrangements around the Al chromophore and accordingly provide a spectroscopic probe of the nature and evolution of the Al trapping sites and cluster geometries with increasing cluster size when the complex electronic and vibrational phenomena underlying the measurements are appropriately interpreted.

Atomic Spectral Methods for Ab Initio Molecular Electronic Energy Surfaces: Transitioning From Small-Molecule to Biomolecular-Suitable Approaches

“…The subscript O indicates adoption of an odometer ordering convention for the sequence of N-term atomic spectral products in the row vector Φ ( r : R ), in which the enumeration of the atomic eigenstates appearing later in eq is advanced prior to those appearing earlier. This convention has a number of consequences, including particularly the specific forms of matrix representatives of Hamiltonian operators in the spectral-product basis, with additional aspects of notational conventions described in the sequel and reported in great detail elsewhere. − …”

“…Equation is seen to be a generalization of the familiar pairwise van der Waals expression, now also including overlap interactions. Retaining the n = 3 term in eq provides both two- and three-body interaction terms, the latter in a form similar to the familiar Casimir–Polder expression, providing a simple and easily evaluated approximation to aggregate energies which has been found to be highly accurate in calculations on large neat and doped inert-gas clusters. ,, …”

“…An attractive alternative approach, potentially capable of overcoming the aforementioned limitations, is based on enforcing the antisymmetry requirements of Pauli’s principle “ex-post-facto” by unitary transformation of a Hamiltonian matrix which is considerably simpler to evaluate than those of conventional developments, also offering additional flexibility in choice of forms of product representations employed for this purpose. − In the case of simple atomic- or molecular-orbital representations in Hartree-product forms, for example, it has been shown that results identical with conventional use of Slater determinants are obtained, employing either finite or arbitrarily large orbital basis sets, and adding confidence to the approach, but not providing any particular computational advantage in orbital-product cases. By contrast, use of Hartree-like products of universal many-electron atomic eigenstates as an orthonormal representation for purposes of analysis and for support suitable for molecular computations, as described in the original formulation of the method, , has led to a continuing series of investigations in clarification of aspects of the theory, ,,− , and for purposes of implementation. ,,,, These developments also incorporate in a unified ab initio formalism earlier attempts to employ atomic-based representations in combined descriptions of van der Waals and chemical forces, semiempirical “atoms-in-molecules” calculations of chemical bond strengths, adoption of atomic-pair energies in semiempirical “diatomics-in-molecules” approximations to potential energy surfaces, and clarification of the role of electron permutation symmetry in long-range atomic interactions. , …”

“…By contrast, use of Hartreelike products of universal many-electron atomic eigenstates as an orthonormal representation for purposes of analysis and for support suitable for molecular computations, as described in the original formulation of the method, 36,37 has led to a continuing series of investigations in clarification of aspects of the theory, 39,40,[42][43][44]46 and for purposes of implementation. 38,41,45,47,48 These developments also incorporate in a unified ab initio formalism earlier attempts to employ atomicbased representations in combined descriptions of van der Waals and chemical forces, 49 semiempirical "atoms-in-molecules" calculations of chemical bond strengths, 50 adoption of atomic-pair energies in semiempirical "diatomics-in-molecules" approximations to potential energy surfaces, 51 and clarification of the role of electron permutation symmetry in long-range atomic interactions. 52,53 The present contribution to this J. Andrew McCammon Festschrift describes the ex-post-facto methodology in the "atomic spectral-product" form, and a computer code suite for implementation of electronic structure calculations potentially suitable for applications to biomolecules and other large aggregates.…”

Molecular Slater Integrals for Electronic Energy Calculations

“…The SMILES methodology in present form is largely applicable to the orbital principal quantum numbers required for accurate descriptions of the valence shells of atoms and molecules, and is therefore highly suitable largely for studies of ground-state molecular structure and low-lying valence excited electronic states. Highly excited molecular electronic states, however, are of considerable interest in a great many connections, including optical spectroscopic diagnostics for identification and characterization of newly synthesized chemical compounds for propulsion and energetics [3], studies of photochemical potential energy surfaces for atmospheric and related reactions [4], descriptions of molecular Rydberg and continuum states required in photon and electron-impact excitation processes [5], and in calculations which require spectral closure over electronic states, such as the long-range interactions required in atomic and molecular cluster studies [6], to mention some representative examples. Extension of SMILES methodology to higher principal quantum numbers would open the way to development of a great many new computational applications suites which can provide concomitant support to on-going DoD materials, chemical physics, and aeronautical and propulsion sciences research programs.…”