Rosendo Valero

Consistent van der Waals Radii for the Whole Main Group

Atomic radii are not precisely defined but are nevertheless widely used parameters in modeling and understanding molecular structure and interactions. The van der Waals radii determined by Bondi from molecular crystals and data for gases are the most widely used values, but Bondi recommended radius values for only 28 of the 44 main-group elements in the periodic table. In the present Article, we present atomic radii for the other 16; these new radii were determined in a way designed to be compatible with Bondis scale. The method chosen is a set of two-parameter correlations of Bondis radii with repulsive-wall distances calculated by relativistic coupled-cluster electronic structure calculations. The newly determined radii (in A) are Be, 1.53; B, 1.92; Al, 1.84; Ca, 2.31; Ge, 2.11; Rb, 3.03; Sr, 2.49; Sb, 2.06; Cs, 3.43; Ba, 2.68; Bi, 2.07; Po, 1.97; At, 2.02; Rn, 2.20; Fr, 3.48; and Ra, 2.83.

On the Performances of the M06 Family of Density Functionals for Electronic Excitation Energies

We assessed the accuracy of the four members of the M06 family of functionals (M06-L, M06, M06-2X, and M06-HF) for the prediction of electronic excitation energies of main-group compounds by time-dependent density functional theory. This is accomplished by comparing the predictions both to high-level theoretical benchmark calculations and some experimental data for gas-phase excitation energies of small molecules and to experimental data for midsize and large chromogens in liquid-phase solutions. The latter comparisons are carried out using implicit solvation models to include the electrostatic effects of solvation. We find that M06-L is one of the most accurate local functionals for evaluating electronic excitation energies, that M06-2X outperforms BHHLYP, and that M06-HF outperforms HF, although in each case, the compared functionals have the same or a similar amount of Hartree-Fock exchange. For the majority of investigated excited states, M06 emerges as the most accurate functional among the four tested, and it provides an accuracy similar to the best of the other global hybrids such as B3LYP, B98, and PBE0. For 190 valence excited states, 20 Rydberg states, and 16 charge transfer states, we try to provide an overall assessment by comparing the quality of the predictions to those of time-dependent Hartree-Fock theory and nine other density functionals. For the valence excited states, M06 yields a mean absolute deviation (MAD) of 0.23 eV, whereas B3LYP, B98, and PBE0 have MADs in the range 0.19-0.22 eV. Of the functionals tested, M05-2X, M06-2X, and BMK are found to perform best for Rydberg states, and M06-HF performs best for charge transfer states, but no single functional performs satisfactorily for all three kinds of excitation. The performance of functionals with no Hartree-Fock exchange is of great practical interest because of their high computational efficiency, and we find that M06-L predicts more accurate excitation energies than other such functionals.

Performance of the M06 family of exchange-correlation functionals for predicting magnetic coupling in organic and inorganic molecules

The performance of the M06 family of exchange-correlation potentials for describing the electronic structure and the Heisenberg magnetic coupling constant (J) is investigated using a set of representative open-shell systems involving two unpaired electrons. The set of molecular systems studied has well defined structures, and their magnetic coupling values are known experimentally. As a general trend, the M06 functional is about equally as accurate as B3LYP or PBE0. The performance of local functionals is important because of their economy and convenience for large-scale calculations; we find that M06-L local functional of the M06 family largely improves over the local spin density approximation and the generalized gradient approximation.

Verdict: Time-Dependent Density Functional Theory "Not Guilty" of Large Errors for Cyanines.

We assess the accuracy of eight Minnesota density functionals (M05 through M08-SO) and two others (PBE and PBE0) for the prediction of electronic excitation energies of a family of four cyanine dyes. We find that time-dependent density functional theory (TDDFT) with the five most recent of these functionals (from M06-HF through M08-SO) is able to predict excitation energies for cyanine dyes within 0.10-0.36 eV accuracy with respect to the most accurate available Quantum Monte Carlo calculations, providing a comparable accuracy to the latest generation of CASPT2 calculations, which have errors of 0.16-0.34 eV. Therefore previous conclusions that TDDFT cannot treat cyanine dyes reasonably accurately must be revised.

Validation study of the ability of density functionals to predict the planar-to-three-dimensional structural transition in anionic gold clusters

As gold clusters increase in size, the preferred structure changes from planar to three-dimensional and, for anionic clusters, Au(n)-, the two-dimensional(2D)-->three-dimensional (3D) transition is found experimentally to occur between n=11 and n=12. Most density functionals predict that planar structures are preferred up to higher n than is observed experimentally, an exception being the local spin density approximation. Here we test four relatively new functionals for this feature, in particular, M05, M06-L, M06, and SOGGA. We find that M06-L, M06, and SOGGA all predict the 2D-->3D transition at the correct value of n. Since the M06-L and M06 functionals have previously been shown to be reasonably accurate for transition metal bond energies, main group atomization energies, barrier heights, and noncovalent interaction energies, and, since they are here shown to perform well for the s-d excitation energy and ionization potential of Au atoms and for the size of Au(n)- clusters at which the 2D-->3D transition occurs, they are recommended for simulating processes catalyzed by gold clusters.

Good performance of the M06 family of hybrid meta generalized gradient approximation density functionals on a difficult case: CO adsorption on MgO(001)

The adsorption of CO on Mg(001) constitutes a challenge for current density functional approximations because of its weak interaction character. In the present work we show that the M06-2X and M06-HF exchange-correlation functionals are the first ones to provide a simultaneously satisfactory description of adsorbate geometry, vibrational frequency shift, and adsorption energy of CO on MgO(001). For a sufficiently large embedded cluster model, the three functionals of the M06 family-which contain a nonzero percentage of Hartree-Fock exchange (M06, M06-2X, and M06-HF)-all predict positive C-O vibrational shifts, in agreement with the experimental findings, while the local M06-L functional gives large negative shifts. Moreover, the shifts computed with the M06-2X and M06-HF potentials are in good agreement with the experimental shift of +14 cm(-1). The interaction energy (D(e)) calculated with M06-2X and M06-HF is approximately 6.0 kcal/mol, which agrees well with the D(e) value ( approximately 4 kcal/mol) deduced from the D(0) obtained in thermal desorption measurements on single-crystal surfaces.

Density functional study of CO and NO adsorption on Ni-doped MgO(100)

The adsorption of small molecules such as NO or CO on surfaces of magnetic oxides containing transition metals is difficult to model by current density functional approximations. Two such oxides are NiO(100) and Ni-doped MgO(100). Here we compare the results of a theoretical model of the Ni-doped MgO(100) surface with experimental results on NiO(100), which introduces some uncertainty into a quantitative theory-experiment comparison. In the present work, we tested seven meta-GGA and hybrid metafunctionals, in particular, three developed by the Minnesota group (M05, M06-L, and M06), and TPSS, TPSSh, TPSSKCIS, and B1B95; six GGA functionals, including BP86, PBE, and four other functionals that are modifications of PBE (PBEsol, SOGGA, revPBE, and RPBE); five hybrid GGA functionals (B3LYP, PBE0, B97-2, B97-3, and MPWLYP1M); and one unconventional functional of the generalized gradient type with scaled correlation called MOHLYP. The Minnesota meta-GGA functionals were found in the past to be very good choices when transition metal atoms were present; the other functionals chosen are a selection from the most currently used and most promising sets of functionals for bulk solids and surfaces and for transition metals. The difficulty is due to the charge transfer between open shells in the case of NO and to the weak character of the interaction in the case of CO. It is shown that the M06 hybrid meta functional applied to NO or CO on a model of the Ni-doped MgO(100) surface is able to provide a good description of both adsorbate geometries and binding energies. The M06 vibrational frequency shifts are more accurate than for other functionals, but there is still room for improvement.

Density functional study of multiplicity-changing valence and Rydberg excitations of p-block elements: Delta self-consistent field, collinear spin-flip time-dependent density functional theory (DFT), and conventional time-dependent DFT

A database containing 17 multiplicity-changing valence and Rydberg excitation energies of p-block elements is used to test the performance of density functional theory (DFT) with approximate density functionals for calculating relative energies of spin states. We consider only systems where both the low-spin and high-spin state are well described by a single Slater determinant, thereby avoiding complications due to broken-symmetry solutions. Because the excitations studied involve a spin change, they require a balanced treatment of exchange and correlation, thus providing a hard test for approximate density functionals. We test three formalisms for predicting the multiplicity-changing transition energies. First is the ΔSCF method; we also test time-dependent density functional theory (TDDFT), both in its conventional form starting from the low-spin state and in its collinear spin-flip form starting from the high-spin state. Very diffuse basis functions are needed to give a qualitatively correct description of the Rydberg excitations. The scalar relativistic effect needs to be considered when quantitative results are desired, and we include it in the comparisons. With the ΔSCF method, most of the tested functionals give mean unsigned errors (MUEs) larger than 6 kcal/mol for valence excitations and MUEs larger than 3 kcal/mol for Rydberg excitations, but the performance for the Rydberg states is much better than can be obtained with time-dependent DFT. It is surprising to see that the long-range corrected functionals, which have 100% Hartree-Fock exchange at large inter-electronic distance, do not improve the performance for Rydberg excitations. Among all tested density functionals, ΔSCF calculations with the O3LYP, M08-HX, and OLYP functionals give the best overall performance for both valence and Rydberg excitations, with MUEs of 2.1, 2.6, and 2.7 kcal/mol, respectively. This is very encouraging since the MUE of the CCSD(T) coupled cluster method with quintuple zeta basis sets is 2.0 kcal/mol; however, caution is advised since many popular density functionals give poor results, and there can be very significant differences between the ΔSCF predictions and those from TDDFT.

Magnetic Coupling in Transition-Metal Binuclear Complexes by Spin-Flip Time-Dependent Density Functional Theory.

Spin-flip time-dependent density functional theory (SF-TDDFT) has been applied to predict magnetic coupling constants for a database of 12 spin-1/2 homobinuclear transition-metal complexes previously studied by Phillips and Peralta employing spin-projected broken-symmetry density functional theory (Phillips, J. J.; Peralta, J. E. J. Chem. Phys.2011, 134, 034108). Several global hybrid density functionals with a range of percentages of Hartree-Fock exchange from 20% to 100% have been employed within the collinear-spin formalism, and we find that both the high-spin reference state and low-spin state produced by SF-TDDFT are generally well adapted to spin symmetry. The magnetic coupling constants are calculated from singlet-triplet energy differences and compared to values arising from the popular broken-symmetry approach. On average, for the density functionals that provide the best comparison with experiment, the SF-TDDFT approach performs as well as or better than the spin-projected broken-symmetry strategy. The constrained density functional approach also performs quite well. The SF-TDDFT magnetic coupling constants show a much larger dependence on the percentage of Hartree-Fock exchange than on the other details of the exchange functionals or the nature of the correlation functionals. In general, SF-TDDFT calculations not only avoid the ambiguities associated with the broken-symmetry approach, but also show a considerably reduced systematic deviation with respect to experiment and a larger antiferromagnetic character. We recommend MPW1K as a well-validated hybrid density functional to calculate magnetic couplings with SF-TDDFT.

Coupled-surface investigation of the photodissociation of NH3(Ã): Effect of exciting the symmetric and antisymmetric stretching modes

Using previously developed potential energy surfaces and their couplings, non-Born-Oppenheimer trajectory methods are used to study the state-selected photodissociation of ammonia, prepared with up to six quanta of vibrational excitation in the symmetric (nu(1)) or antisymmetric (nu(3)) stretching modes of NH(3)(A). The predicted dynamics is mainly electronically nonadiabatic (that is, it produces ground electronic state amino radicals). The small probability of forming the excited-state amino radical is found, for low excitations, to increase with total energy and to be independent of whether the symmetric or antisymmetric stretch is excited; however some selectivity with respect to exciting the antisymmetric stretch is found when more than one quantum of excitation is added to the stretches, and more than 50% of the amino radical are found to be electronically excited when six quanta are placed in the antisymmetric stretch. These results are in contrast to the mechanism inferred in recent experimental work, where excitation of the antisymmetric stretch by a single quantum was found to produce significant amounts of excited-state products via adiabatic dissociation at total energies of about 7.0 eV. Both theory and experiment predict a broad range of translational energies for the departing H atoms when the symmetric stretch is excited, but the present simulations do not reproduce the experimental translational energy profiles when the antisymmetric stretch is excited. The sensitivity of the predicted results to several aspects of the calculation is considered in detail, and the analysis leads to insight into the nature of the dynamics that is responsible for mode selectivity.