efei Xu

Perspectives on Basis Sets Beautiful: Seasonal Plantings of Diffuse Basis Functions

We present a perspective on the use of diffuse basis functions for electronic structure calculations by density functional theory and wave function theory. We especially emphasize minimally augmented basis sets and calendar basis sets. We base our conclusions on our previous experience with commonly computed quantities, such as bond energies, barrier heights, electron affinities, noncovalent (van der Waals and hydrogen bond) interaction energies, and ionization potentials, on Stephens et al.s results for optical rotation and on our own new calculations (presented here) of polarizabilities and of potential energy curves of van der Waals complexes. We emphasize the benefits of partial augmentation of the higher-zeta basis sets in preference to full augmentation at a lower ζ level. Benefits and limitations of the use of fully, partially, and minimally augmented basis sets are reviewed for different electronic structure methods and molecular properties. We have found that minimal augmentation is almost always enough for density functional theory (DFT) when applied to ionization potentials, electron affinities, atomization energies, barrier heights, and hydrogen-bond energies. For electric dipole polarizabilities, we find that augmentation beyond minimal has an average effect of 8% at the polarized triple-ζ level and 5% at the polarized quadruple-ζ level. The effects are larger for potential energy curves of van der Waals complexes. The effects are also larger for wave function theory (WFT). Even for WFT though, full augmentation is not needed for most purposes, and a level of augmentation between minimal and full is optimal for most problems. The calendar basis sets named after the months provide a convergent sequence of partially augmented basis sets that can be used for such calculations. The jun-cc-pV(T+d)Z basis set is very useful for MP2-F12 calculations of barrier heights and hydrogen bond strengths.

How Well Can Modern Density Functionals Predict Internuclear Distances at Transition States

We introduce a new database called TSG48 containing 48 transition state geometrical data (in particular, internuclear distances in transition state structures) for 16 main group reactions. The 16 reactions are the 12 reactions in the previously published DBH24 database (which includes hydrogen transfer reactions, heavy-atom transfer reactions, nucleophilic substitution reactions, and association reactions plus one unimolecular isomerization) plus four H-transfer reactions in which a hydrogen atom is abstracted by the methyl or hydroperoxyl radical from the two different positions in methanol. The data in TSG48 include data for four reactions that have previously been treated at a very high level in the literature. These data are used to test and validate methods that are affordable for the entire test suite, and the most accurate of these methods is found to be the multilevel BMC-CCSD method. The data that constitute the TSG48 database are therefore taken to consist of these very high level calculations for the four reactions where they are available and BMC-CCSD calculations for the other 12 reactions. The TSG48 database is used to assess the performance of the eight Minnesota density functionals from the M05-M08 families and 26 other high-performance and popular density functionals for locating transition state geometries. For comparison, the MP2 and QCISD wave function methods have also been tested for transition state geometries. The MC3BB and MC3MPW doubly hybrid functionals and the M08-HX and M06-2X hybrid meta-GGAs are found to have the best performance of all of the density functionals tested. M08-HX is the most highly recommended functional due to the excellent performance for all five subsets of TSG48, as well as having a lower cost when compared to doubly hybrid functionals. The mean absolute errors in transition state internuclear distances associated with breaking and forming bonds as calculated by the B2PLYP, MP2, and B3LYP methods are respectively about 2, 3, and 5 times larger than those calculated by MC3BB and M08-HX.

Do Practical Standard Coupled Cluster Calculations Agree Better than Kohn–Sham Calculations with Currently Available Functionals When Compared to the Best Available Experimental Data for Dissociation Energies of Bonds to 3d Transition Metals?

Coupled-cluster (CC) methods have been extensively used as the high-level approach in quantum electronic structure theory to predict various properties of molecules when experimental results are unavailable. It is often assumed that CC methods, if they include at least up to connected-triple-excitation quasiperturbative corrections to a full treatment of single and double excitations (in particular, CCSD(T)), and a very large basis set, are more accurate than Kohn-Sham (KS) density functional theory (DFT). In the present work, we tested and compared the performance of standard CC and KS methods on bond energy calculations of 20 3d transition metal-containing diatomic molecules against the most reliable experimental data available, as collected in a database called 3dMLBE20. It is found that, although the CCSD(T) and higher levels CC methods have mean unsigned deviations from experiment that are smaller than most exchange-correlation functionals for metal-ligand bond energies of transition metals, the improvement is less than one standard deviation of the mean unsigned deviation. Furthermore, on average, almost half of the 42 exchange-correlation functionals that we tested are closer to experiment than CCSD(T) with the same extended basis set for the same molecule. The results show that, when both relativistic and core-valence correlation effects are considered, even the very high-level (expensive) CC method with single, double, triple, and perturbative quadruple cluster operators, namely, CCSDT(2)Q, averaged over 20 bond energies, gives a mean unsigned deviation (MUD(20) = 4.7 kcal/mol when one correlates only valence, 3p, and 3s electrons of transition metals and only valence electrons of ligands, or 4.6 kcal/mol when one correlates all core electrons except for 1s shells of transition metals, S, and Cl); and that is similar to some good xc functionals (e.g., B97-1 (MUD(20) = 4.5 kcal/mol) and PW6B95 (MUD(20) = 4.9 kcal/mol)) when the same basis set is used. We found that, for both coupled cluster calculations and KS calculations, the T1 diagnostics correlate the errors better than either the M diagnostics or the B1 DFT-based diagnostics. The potential use of practical standard CC methods as a benchmark theory is further confounded by the finding that CC and DFT methods usually have different signs of the error. We conclude that the available experimental data do not provide a justification for using conventional single-reference CC theory calculations to validate or test xc functionals for systems involving 3d transition metals.

Photodissociation Dynamics of Phenol: Multistate Trajectory Simulations including Tunneling

We report multistate trajectory simulations, including coherence, decoherence, and multidimensional tunneling, of phenol photodissociation dynamics. The calculations are based on full-dimensional anchor-points reactive potential surfaces and state couplings fit to electronic structure calculations including dynamical correlation with an augmented correlation-consistent polarized valence double-ζ basis set. The calculations successfully reproduce the experimentally observed bimodal character of the total kinetic energy release spectra and confirm the interpretation of the most recent experiments that the photodissociation process is dominated by tunneling. Analysis of the trajectories uncovers an unexpected dissociation pathway for one quantum excitation of the O-H stretching mode of the S1 state, namely, tunneling in a coherent mixture of states starting in a smaller ROH (∼0.9-1.0 Å) region than has previously been invoked. The simulations also show that most trajectories do not pass close to the S1-S2 conical intersection (they have a minimum gap greater than 0.6 eV), they provide statistics on the out-of-plane angles at the locations of the minimum energy adiabatic gap, and they reveal information about which vibrational modes are most highly activated in the products.

Performance of Effective Core Potentials for Density Functional Calculations on 3d Transition Metals

The performance of popular Hartree-Fock-based effective core potentials in Hartree-Fock and density functional calculations of 3d transition metals has been evaluated by basis-set convergence studies for ten cases: the equilibrium bond dissociation energy (De) for dissociation of ground-state Ti2 to ground and excited atoms, the ground-state dissociation energies of FeO, Cu2, ScH, TiH, Sc2, Fe2, and TiV(+), and the first excitation energy (Ex) of Ti atom. Each case is studied with 11 or 13 density functionals. For comparison, the accuracy of the all-electron def2-TZVP basis set is tested with both relativistic and nonrelativistic treatments. Convergence and accuracy are assessed by comparing to relativistic all-electron calculations with a nearly complete relativistic basis set (NCBS-DK, which denotes the cc-pV5Z-DK basis set for 3d metals and hydrogen and the ma-cc-pV5Z-DK basis set for oxygen) and to nonrelativistic all-electron calculations with a nearly complete nonrelativistic basis set (NCBS-NR, which denotes the cc-pV5Z basis set for 3d metals and hydrogen and the ma-cc-pV5Z basis set for oxygen). As compared to NCBS-DK results, all ECP calculations perform worse than def2-TZVP all-electron relativistic calculations when averaged over all 130 data (13 functionals and ten test cases). The compact effective potential (CEP) relativistic effective core potential (RECP) combined with a valence basis set developed for the many-electron Dirac-Fock (MDF10) RECP performs best in effective core potential calculations and has an average basis-set incompleteness error of 3.7 kcal/mol, which is much larger than that (0.9 kcal/mol) of def2-TZVP relativistic all-electron results. Hence, the def2-TZVP relativistic all-electron calculations are recommended for accurate DFT calculations on 3d transition metals. In addition to our general findings, we observed that all kinds of density functionals do not show the same trends. For example, when ECPs are used with hybrid functionals, which sometimes are not recommended for calculations of transition metal systems, they are found to perform better at achieving the basis-set limit than when used with local functionals and meta-GGA functionals. The most successful combination of RECP and basis set has a basis-set incompleteness error of 1.7-2.4 kcal/mol for hybrid generalized gradient approximations, which is smaller than that of nonrelativistic NCBS calculations (whose average basis-set incompleteness error for hybrid functionals is 2.7-2.9 kcal/mol). The average basis-set incompleteness error in Hartree-Fock calculations is 1.0-4.4 kcal/mol for five of the ECP basis sets but is 5.8-10.8 kcal/mol for six others.

Diabatic Molecular Orbitals, Potential Energies, and Potential Energy Surface Couplings by the 4-fold Way for Photodissociation of Phenol

Complete-active-space self-consistent-field (CASSCF) calculations provide useful reference wave functions for configuration interaction or perturbation theory calculations of excited-state potential energy surfaces including dynamical electron correlation. However, the canonical molecular orbitals (MOs) of CASSCF calculations usually have mixed character in regions of strong interaction of two or more electronic states; therefore, they are unsuitable for diabatization using the configurational uniformity approach. Here, CASSCF diabatic MOs for phenol have been obtained by the 4-fold way, and comparison to the CASSCF canonical MOs shows that they are much smoother. Using these smooth CASSCF diabatic MOs, we performed direct diabatization calculations for the three low-lying states ((1)ππ, (1)ππ*, and (1)πσ*) and their diabatic (scalar) couplings at the dynamically correlated multiconfiguration quasidegenerate perturbation theory (MC-QDPT) level. We present calculations along the O-H stretching and C-C-O-H torsion coordinates for the nonadiabatic photodissociation of phenol to the phenoxyl radical and hydrogen atom. The seams of (1)ππ*/(1)πσ* and (1)ππ/(1)πσ* diabatic crossings are plotted as functions of these coordinates. We also present diabatization calculations for displacements along the out-of-plane ring distortion modes 16a and 16b of the phenyl group. The dominant coupling modes of the two conical intersections ((1)ππ*/(1)πσ* and (1)ππ/(1)πσ*) are discussed. The present diabatization method is confirmed to be valid even for significantly distorted ring structures by diabatization calculations along a reaction path connecting the planar equilibrium geometry of phenol to its strongly distorted prefulvenic form. The present work provides insight into the mode specificity of phenol photodissociation and shows that diabatization at the MC-QDPT level employing CASSCF diabatic MOs can be a good starting point for multidimensional dynamics calculations of photochemical reactions.

Ligand- and anion-controlled formation of silver alkynyl oligomers from soluble precursors

Novel silver(I) alkynyl cluster complexes ([Ag5(bpy)4(C [triple bond] CBu(t))2](3+), [Ag8(bpy)6(C [triple bond] CBu(t))4](4+), and [Ag 12(bpy)4(C [triple bond] CBu(t))6(CF3CO2)6]) have been synthesized by reacting soluble polymeric precursors with bipyridine ligands, and control of the nuclearity can be achieved by varying the molar ratio of the reactants and using different types of anions.

Diabatization based on the dipole and quadrupole: The DQ method

In this work, we present a method, called the DQ scheme (where D and Q stand for dipole and quadrupole, respectively), for transforming a set of adiabatic electronic states to diabatic states by using the dipole and quadrupole moments to determine the transformation coefficients. It is more broadly applicable than methods based only on the dipole moment; for example, it is not restricted to electron transfer reactions, and it works with any electronic structure method and for molecules with and without symmetry, and it is convenient in not requiring orbital transformations. We illustrate this method by prototype applications to two cases, LiH and phenol, for which we compare the results to those obtained by the fourfold-way diabatization scheme.

Combined Self-Consistent-Field and Spin-Flip Tamm–Dancoff Density Functional Approach to Potential Energy Surfaces for Photochemistry

We present a new approach to calculating potential energy surfaces for photochemical reactions by combining self-consistent-field calculations for single-reference ground and excited states with symmetry-corrected spin-flip Tamm-Dancoff approximation calculations for multireference electronic states. The method is illustrated by an application with the M05-2X exchange-correlation functional to cis-trans isomerization of the penta-2,4-dieniminium cation, which is a model (with three conjugated double bonds) of the protonated Schiff base of retinal. We find good agreement with multireference configuration interaction-plus-quadruples (MRCISD+Q) wave function calculations along three key paths in the strong-interaction region of the ground and first excited singlet states.

Methanol triggered ligand flip isomerization in a binuclear copper(I) complex and the luminescence response

Methanol drives the blue emissive complex, [Cu(2)(dppy)(3)(MeCN)](BF(4))(2) (dppy = diphenylphosphino-pyridine), with a head-to-tail arrangement of the three bridging phosphine ligands to convert to its linkage isomer (head-to-head, green emissive) in the solid state, and the transformation could be reversibly realized through recrystallization in different solvents.