The electronic spectrum of AgCl2: ab initio benchmark versus density-functional theory calculations on the lowest ligand-field states including spin-orbit effects.

The X 2pi(g), 2sigma(g)+, and 2delta(g) states of AgCl2 have been studied through benchmark ab initio complete active space self-consistent field plus second-order complete active space multireference Moller-Plesset algorithm (CASSCF+CASPT2) and complete active space self-consistent field plus averaged coupled pair functional (CASSCF+ACPF) and density-functional theory (DFT) calculations using especially developed basis sets to study the transition energies, geometries, vibrational frequencies, Mulliken charges, and spin densities. The spin-orbit (SO) effects were included through the effective Hamiltonian formalism using the LambdaSSigma ACPF energies as diagonal elements. At the ACPF level, the ground state is 2pi(g) in contradiction with ligand-field theory, SCF, and large CASSCF; the adiabatic excitation energies for the 2sigma(g)+ and 2delta(g) states are 1640 and 18,230 cm(-1), respectively. The inclusion of the SO effects leads to a pure omega = 32(2pi(g)) ground state, a omega = 12 (66%2pi(g) and 34%2sigma(g)+) A state, a omega = 12 (34%2pi(g) and 66%2sigma(g)+) B state, a omega = 52(2delta(g))C state, and a omega = 32(99%2delta(g))D state. The X-A, X-B, X-C, and X-D transition energies are 485, 3715, 17 246, and 20 110 cm(-1), respectively. The B97-2, B3LYP, and PBE0 functionals overestimate by approximately 100% the X 2pi(g)-2sigma(g)+T(e) but provide a qualitative energetic ordering in good agreement with ACPF results. B3LYP with variable exchange leads to a 42% optimal Hartree-Fock exchange for transition energies but all equilibrium geometries get worsened. Asymptotic corrections to B3LYP do not provide improved values. The nature of the bonding in the X 2pi(g) state is very different from that of CuCl2 since the Mulliken charge on the metal is 1.1 while the spin density is only 0.35. DFT strongly delocalizes the spin density providing even smaller values of around 0.18 on Ag not only for the ground state, but also for the 2sigma(g)+ state.

Comparative studies of the spectroscopy of CuCl2: DFT versus standard ab initio approaches.

The X2Pi g-2Sigma g+, X2Pi g-2Delta g, X2Pi g-2Sigma u+, X2Pi g-2Pi u transitions on CuCl2 have been studied using several exchange-correlation functionals from the various types of density functional theory (DFT) approaches like local density approximation (LDA), generalized gradient approximation (GGA), hybrid and meta-GGA. The results are compared with the experience and with those coming from the most sophisticated nondynamic and dynamic electronic correlation treatments using the same relativistic effective core potentials and especially developed basis sets to study the electronic structure of the five lowest states and the corresponding vertical and adiabatic transition energies. The calculated transition energies for three of the hybrid functionals (B3LYP, B97-2, and PBE0) are in very good agreement with the benchmark ab initio results and experimental figures. All of the other functionals largely overestimate the X2Pi g-2Sigma g+ and X2Pi g-2Delta g transition energies, many of them even placing the 2Delta g ligand field state above the charge transfer 2Pi u and 2Sigma u+ states. The relative weight of the Hartree-Fock exchange in the definition of the functional used appears to play a key role in the accurate description of the LambdaSSigma density defined by the orientation of the 3d hole (sigma, pi, or delta) on Cu in the field of both chlorine atoms, but no simple connection of this weight with the quality of the spectra has been found. Mulliken charges and spin densities are carefully analyzed; a possible link between the extent of spin density on the metal for the X2Pi g state and the performance of the various functionals was observed, suggesting that those that lead to the largest values (close to 0.65) are the ones that best reproduce these four transitions. Most functionals lead to a remarkably low ionicity for the three ligand field states even for the best performing functionals, compared to the complete active space (SCF) (21, 14) ab initio values. These findings show that not only large variational ab initio calculations can produce reliable spectroscopic results for extremely complex systems where delicate electronic correlation effects have to be carefully dealt with. However, those functionals that were recently shown to perform best for a series of molecular properties [J. Chem. Phys. 121 3405 (2004)] are not the ones that produce the best transition energies for this complex case.

Ab initio study on the spectroscopy of CuCl2. II. Benchmark calculations on the X2Pi g-C2Deltag and X2Pi g-D2Deltag transitions.

The X (2)Pi(g)-C (2)Delta(g) and X (2)Pi(g)-D (2)Delta(g) transitions on CuCl(2) have been studied using the most sophisticated nondynamic and dynamic electronic correlation treatments. We report here ab initio benchmark calculations using especially developed basis sets to study, at the complete active space self-consistent field plus second-order Møller-Plesset algorithm (CASSCF+CASPT2) and CASSCF+ACPF levels, the transition energies as well as the corresponding equilibrium geometries (ACPF-averaged coupled pair functional). The spin-orbit (SO) effects of both atoms were included in a second step through the effective Hamiltonian formalism, using the calibrated SO effective potentials developed by the Stuttgart group. Without SO at the CASSCF+ACPF level, the vertical excitation energy for the (2)Delta(g) state is 6711 cm(-1) and the symmetric stretching equilibrium Cu-Cl distance is 4.04 a.u. The inclusion of the SO effects leads to a pure (2)Delta(g) Omega=5/2C state and a Omega=3/2 (0.7% (2)Pi(g),99.3% (2)Delta(g))D state. The calculated transition energies for the C and D states are 6340 and 8020 cm(-1), in good agreement with the spin-orbit splitting recent values from gas-phase and rare-gas matrix isolation laser induced fluorescence experiments. The present benchmark results show, as was recently done for the X (2)Pi(g)-(2)Sigma(g) transition, the rather poor performance of all the density functional theory-based descriptions for the (2)Delta(g) state, which largely overestimate its T(e), systematically placing it around 19 000 cm(-1). The CASSCF+CASPT2 method also overestimates, by around 50%, the X (2)Pi(g)-(2)Delta(g) transition energy, showing that only large variational calculations can produce reliable spectroscopic results for this kind of complex systems where delicate electronic correlation effects have to be carefully dealt with.

Theoretical study of Ln(III) complexes with polyaza-aromatic ligands: geometries of [LnL(H2O)n]3+ complexes and successes and failures of TD-DFT.

The accuracy and the usefulness of density functional theory (DFT) and time-dependent density functional theory (TD-DFT) calculations for the theoretical study of Ln (La, Eu, Lu) complexes have been investigated. The geometries calculated at the DFT level for [Ln(H2O)nL]3+ complexes have been successfully compared with crystallographic data. TD-DFT is able to offer valuable insights into VUV spectra of lanthanide complexes. However, the results obtained on the largest ligand (i.e., 2,4,6-tri-(pyridin-2-yl)-1,3,5-triazine (Tptz)) have to be considered as a failure of TD-DFT.

Ab initio study on the spectroscopy of CuCl2. I. Benchmark calculations on the X2Pig - 2Sigmag+ transition.

The modern theoretical predictions on the LambdaSSigma nature of the ground state of CuCl2 have led to different answers, depending on the type (DFT-based or ab initio) and the quality of the electronic correlation treatment; for this reason the X2Pig - 2Sigmag+ transition energy has been predicted to range from -1856 to +5887 cm(-1). The physical problem at hand lies in the difficulty of accurately describing the orientation of the 3d hole on the central Cu2+(3d9)/Cu+(3d94s1) ion (in the field of both chlorine ions), which implies the need of the most sophisticated nondynamic and dynamic electronic correlation treatments. We report here ab initio benchmark calculations using especially developed basis sets to study, at the CASSCF + CASPT2 and CASSCF + ACPF levels, the transition energy as well as the corresponding equilibrium geometries. The spin-orbit (SO) effects of both atoms were included in a second step through the effective Hamiltonian formalism, using the calibrated SO effective potentials developed by the Stuttgart group. Without SO at the CASSCF + ACPF level, the ground state is X2Pig but the vertical transition energy to the 2Sigmag+ is only 99 cm(-1) at 3.95 a.u. The inclusion of the SO effects leads to a Omega = 1/2 (59% 2Pig,41% 2Sigmag+) ground state, in contradiction with the Omega experimental value of 3/2. In a last step we show that the SO effects (and therefore the final Omega ordering) are critically dependent on the LambdaSSigma electronic energies, so that it is not impossible that the Omega ordering is actually changed. For theoreticians interest in this matter is not purely academic, since many properties of organometallic complexes are linked to such delicate physical effects.