Accurateabinitiocalculations which demonstrate a3Πuground state for Al2

Ab initio characterization of the aluminum dimer in its X 3 Π u $$ {}^3{\Pi}_u $$ and A 3 Σ g - $$ {}^3{\Sigma}_g^{-} $$ electronic states

The potential energy functions of the aluminum dimer, Al₂ , in its lowest-energy electronic states, X 3 Π u $$ {}^3{\Pi}_u $$ and A 3 Σ g - , $$ {}^3{\Sigma}_g^{-}, $$ have been determined from ab initio calculations using the multi-reference averaged coupled-pair functional method in conjunction with the correlation-consistent basis sets up to septuple-zeta quality. The core-electron correlation, scalar relativistic, and spin-orbit effects were taken into account. The vibration-rotation energy levels for both the states of Al₂ were calculated to near the "spectroscopic" accuracy. The 3 Π u $$ {}^3{\Pi}_u $$ state was unequivocally confirmed to be the electronic ground state of Al₂ , and the electronic term value T 0 $$ {T}_0 $$ of the 3 Σ g - $$ {}^3{\Sigma}_g^{-} $$ state was predicted to be 247 cm^-1 . The energies and intensities of direct electronic-vibration transitions X 3 Π u $$ {}^3{\Pi}_u $$  ↔ A 3 Σ g - $$ {}^3{\Sigma}_g^{-} $$ were predicted.

Term rules for simple metal clusters

Hund’s term rules are only valid for isolated atoms, but have no generalization for molecules or clusters of several atoms. We present a benchmark calculation of Al₂ and Al₃, for which we find the high and low-spin ground states ³Π_u and , respectively. We show that the relative stabilities of all the molecular terms of Al₂ and Al₃ can be described by simple rules pertaining to bonding structures and symmetries, which serve as guiding principles to determine ground state terms of arbitrary multi-atom clusters.

Large-scale first principles configuration interaction calculations of optical absorption in aluminum clusters

Optical absorption in Al clusters.

Half-sandwich structure of cyclopentadienyl dialuminum [Al2(eta5-C5H5)] from pulsed-field ionization electron spectroscopy and ab initio calculations

Cyclopentadienyl dialuminum [Al2Cp, Cp = C5H5] was prepared in a pulsed laser ablation cluster beam source and identified with a time-of-flight photoionization mass spectrometer. The high-resolution electron spectrum of this complex was obtained using pulsed-field ionization zero electron kinetic energy (ZEKE) photoelectron spectroscopy. Three isomeric structures with two Al atoms residing on the same or opposite sites of the Cp plane were predicted by second-order Møller-Plesset perturbation theory. A half-sandwich structure with an aluminum dimer perpendicular to the Cp plane was identified by the experiment. The ground electronic states of the neutral and ionized species are 2A' ' in Cs symmetry and 1A1 in C5v symmetry, respectively. In both the neutral and ionic states, one of the Al2 atoms binds with five carbons, and the metal-ligand bonding consists of orbital and electrostatic contributions. Ionization of the 2A' ' neutral state enhances the metal-ligand bonding but weakens the metal-metal interaction.

Theoretical Study of Alnand AlnO (n= 2−10) Clusters

The stable structures, energies, and electronic properties of neutral, cationic, and anionic clusters of Al(n) (n = 2-10) are studied systematically at the B3LYP/6-311G(2d) level. We find that our optimized structures of Al5(+), Al9(+), Al9(-), Al10, Al10(+), and Al10(-) clusters are more stable than the corresponding ones proposed in previous literature reports. For the studied neutral aluminum clusters, our results show that the stability has an odd/even alternation phenomenon. We also find that the Al3, Al7, Al7(+), and Al7(-) structures are more stable than their neighbors according to their binding energies. For Al7(+) with a special stability, the nucleus-independent chemical shifts and resonance energies are calculated to evaluate its aromaticity. In addition, we present results on hardness, ionization potential, and electron detachment energy. On the basis of the stable structures of the neutral Al(n) (n = 2-10) clusters, the Al(n)O (n = 2-10) clusters are further investigated at the B3LYP/6-311G(2d), and the lowest-energy structures are searched. The structures show that oxygen tends to either be absorbed at the surface of the aluminum clusters or be inserted between Al atoms to form an Al(n-1)OAl motif, of which the Al(n-1) part retains the stable structure of pure aluminum clusters.

Structures and stability of B-doped Al clusters: AlnB and AlnB2 (n=1–7)

Various structural possibilities for Al(n)B(m) (n=1-7, m=1-2) neutral isomers were investigated using B3LYP6-311G(d) and CCSD(T)6-311G(d) methods. Our calculations predicted the existence of a number of previously unknown isomers. The B atom favors to locate over/inside of all clusters in this series. All structures of the Al(n)B (n=2-7) may be derived from capping/putting a B atom over/inside the Al(n) cluster. All Al(n)B(2) (n=1-5) may be understood as two substitutions of Al atoms by B atoms in the Al(n+2) molecule. The strong B-B bond is a dominant factor in the building-up principle of mixed Al(n)B(2) neutral clusters. The second difference in energy showed that the Al(n)B(m) clusters with even n+m are more stable than those with odd n+m. Our results and analyses revealed that the mixed Al-B clusters exhibit aromatic behaviors.

Electron affinities of Al(n) clusters and multiple-fold aromaticity of the square Al4(2-) structure

The concept of aromaticity was first invented to account for the unusual stability of planar organic molecules with 4n + 2 delocalized pi electrons. Recent photoelectron spectroscopy experiments on all-metal MAl(4)(-) systems with an approximate square planar Al(4)(2-) unit and an alkali metal led to the suggestion that Al(4)(2-) is aromatic. The square Al(4)(2-) structure was recognized as the prototype of a new family of aromatic molecules. High-level ab initio calculations based on extrapolating CCSD(T)/aug-cc-pVxZ (x = D, T, and Q) to the complete basis set limit were used to calculate the first electron affinities of Al(n)(), n = 0-4. The calculated electron affinities, 0.41 eV (n = 0), 1.51 eV (n = 1), 1.89 eV (n = 3), and 2.18 eV (n = 4), are all in excellent agreement with available experimental data. On the basis of the high-level ab initio quantum chemical calculations, we can estimate the resonance energy and show that it is quite large, large enough to stabilize Al(4)(2-) with respect to Al(4). Analysis of the calculated results shows that the aromaticity of Al(4)(2-) is unusual and different from that of C(6)H(6). Particularly, compared to the usual (1-fold) pi aromaticity in C(6)H(6), which may be represented by two Kekulé structures sharing a common sigma bond framework, the square Al(4)(2-) structure has an unusual "multiple-fold" aromaticity determined by three independent delocalized (pi and sigma) bonding systems, each of which satisfies the 4n + 2 electron counting rule, leading to a total of 4 x 4 x 4 = 64 potential resonating Kekulé-like structures without a common sigma frame. We also discuss the 2-fold aromaticity (pi plus sigma) of the Al(3)(-) anion, which can be represented by 3 x 3 = 9 potential resonating Kekulé-like structures, each with two localized chemical bonds. These results lead us to suggest a general approach (applicable to both organic and inorganic molecules) for examining delocalized chemical bonding. The possible electronic contribution to the aromaticity of a molecule should not be limited to only one particular delocalized bonding system satisfying a certain electron counting rule of aromaticity. More than one independent delocalized bonding system can simultaneously satisfy the electron counting rule of aromaticity, and therefore, a molecular structure could have multiple-fold aromaticity.

Quantum Mechanical Calculations to Chemical Accuracy

Full configuraton-interaction (FCI) calculations have given an unambiguous standard by which the accuracy of theoretical approaches of incorporating electron correlation into molecular structure calculations can be judged. In addition, improvements in vectorization of programs, computer technology, and algorithms now permit a systematic study of the convergence of the atomic orbital (or so-called one-particle) basis set. These advances are discussed and some examples of the solution of chemical problems by quantum mechanical calculations are given to illustrate the accuracy of current techniques.