An analysis of two local measures of the electronic localization: a comparison with the ELF and the exchange-correlation density results

In this work we have explored the performance of two functions, recently proposed by Ayers [J. Chem. Sci., 2005, 117, 441], with the purpose of quantifying local electron localization. The first function, ζ(h), measures the total fluctuation per electron in the number of electrons at a given position r(1), while the second one, ζ(R), is a local representation of the minimum fluctuation criterion for electron localization. The study is carried out through a set of diatomic molecules that covers a wide range of covalent/polar character. Additionally, we have also calculated the electron localization function and the exchange-correlation hole along the internuclear axis. We have found that, for all the studied molecules, the numerical integration involved in computing ζ(h) did not converge. We think that this is so because the hole correlation calculations are not able to yield its correct asymptotic decaying behavior for large absolute values of the internuclear distances. On the other hand, the calculation of ζ(R) has proved to be feasible, and the information obtained from it has been concluded to be compatible to that rendered by the electron localization function (ELF) and the exchange-correlation density. Moreover, it has been also found that the results for ζ(R) allow to quantify the relative degree of electron localization within different molecular regions.     

Performance of the M11 and M11-L density functionals for calculations of electronic excitation energies by adiabatic time-dependent density functional theory

Adiabatic time-dependent density functional theory is a powerful method for calculating electronic excitation energies of complex systems, but the quality of the results depends on the choice of approximate density functional. In this article we test two promising new density functionals, M11 and M11-L, against databases of 214 diverse electronic excitation energies, and we compare the results to those for 16 other density functionals of various kinds and to time-dependent Hartree-Fock. Charge transfer excitations are well known to be the hardest challenge for TDDFT. M11 is a long-range-corrected hybrid meta-GGA, and it shows better performance for charge transfer excitations than any of the other functionals except M06-HF, which is a specialized functional that does not do well for valence excitations. Several other long-range-corrected hybrid functionals also do well, and we especially recommend M11, ωB97X, and M06-2X for general spectroscopic applications because they do exceptionally well on ground-state properties as well as excitation energies. Local functionals are preferred for many applications to extended systems because of their significant cost advantage for large systems. M11-L is a dual-range local functional and-unlike all previous local functionals-it has good performance for Rydberg states as well as for valence states. Thus it is highly recommended for excitation energy calculations on extended systems.     

Communication: A global hybrid generalized gradient approximation to the exchange-correlation functional that satisfies the second-order density-gradient constraint and has broad applicability in chemistry

We extend our recent SOGGA11 approximation to the exchange-correlation functional to include a percentage of Hartree-Fock exchange. The new functional, called SOGGA11-X, has better overall performance for a broad chemical database than any previously available global hybrid generalized gradient approximation, and in addition it satisfies an extra physical constraint in that it is correct to second order in the density-gradient.     

The performance of time-dependent density functional theory based on a noncollinear exchange-correlation potential in the calculations of excitation energies

In the present work we have studied the accuracy of excitation energies calculated from spin-flip transitions with a formulation of time-dependent density functional theory based on a noncollinear exchange-correlation potential proposed in a previous study. We compared the doublet-doublet excitation energies from spin-flip transitions and ordinary transitions, calculated the multiplets splitting of some atoms, the singlet-triplet gaps of some diradicals, the energies of excited quartet states with a doublet ground state. In addition, we attempted to calculate transition energies with excited states as reference. We compared the triplet excitation energies and singlet-triplet separations of the excited state from spin-flip and ordinary transitions. As an application, we show that using excited quartet state as reference can help us fully resolve excited states spin multiplets. In total the obtained excitation energies calculated from spin-flip transitions agree quite well with other theoretical results or experimental data.     

Density functional LCAO calculations for solids: Comparison among Hartree–Fock,DFT local density approximation,and DFT generalized gradient approximation structural properties

In this article, the results of a recently implemented DFT a posteriori and Kohn-Sham (KS ) linear combination of atomic orbital computational scheme for solids are presented. The equilibrium lattice parameters, bulk moduli, and lattice energies are calculated for eight crystallized systems. Local density approximation (LDA ) and generalized gradient approximation (GCA ) functionals and potentials are used. The maps of the Hartree-Fock (HF ) and Ks electronic densities and band structures are depicted. The KS results confirm the trend of the a posteriori scheme. Very good agreement between calculated and experimental lattice energies has been found for GGA potentials. © 1995 John Wiley & Sons, Inc.     

The reduced density matrix method for electronic structure calculations and the role of three-index representability conditions

The variational approach for electronic structure based on the two-body reduced density matrix is studied, incorporating two representability conditions beyond the previously used P, Q, and G conditions. The additional conditions (called T1 and T2 here) are implicit in the work of Erdahl [Int. J. Quantum Chem. 13, 697 (1978)] and extend the well-known three-index diagonal conditions also known as the Weinhold-Wilson inequalities. The resulting optimization problem is a semidefinite program, a convex optimization problem for which computational methods have greatly advanced during the past decade. Formulating the reduced density matrix computation using the standard dual formulation of semidefinite programming, as opposed to the primal one, results in substantial computational savings and makes it possible to study larger systems than was done previously. Calculations of the ground state energy and the dipole moment are reported for 47 different systems, in each case using an STO-6G basis set and comparing with Hartree-Fock, singly and doubly substituted configuration interaction, Brueckner doubles (with triples), coupled cluster singles and doubles with perturbational treatment of triples, and full configuration interaction calculations. It is found that the use of the T1 and T2 conditions gives a significant improvement over just the P, Q, and G conditions, and provides in all cases that we have studied more accurate results than the other mentioned approximations.     

Multilevel and density functional electronic structure calculations of proton affinities and gas-phase basicities involved in biological phosphoryl transfer

Five multilevel model chemistries (CBS-QB3, G3B3, G3MP2B3, MCG3/3, and MC-QCISD/3) and seven hybrid density functional methods (PBE0, B1B95, B3LYP, MPW1KCIS, PBE1KCIS, and MPW1B95) have been applied to the calculation of gas-phase basicity and proton affinity values for a series of 17 molecules relevant to the study of biological phosphoryl transfer. In addition, W1 calculations were performed on a subset of molecules. The accuracy of the methods was assessed and the nature of systematic errors was explored, leading to the introduction of a set of effective bond enthalpy and entropy correction terms. The multicoefficient correlation methods (MCG3/3 and MC-QCISD), with inclusion of specific zero-point scale factors, slightly outperform the other multilevel methods tested (CBS-QB3, G3B3, and G3MP2B3), with significantly less computational cost, and in the case of MC-QCISD, slightly less severe scaling. Four density functional methods, PBE1KCIS, MPW1B95, PBE0, and B1B95 perform nearly as well as the multilevel methods. These results provide an important set of benchmarks relevant to biological phosphoryl transfer reactions.     

A local density functional—LCAO method with effective potentials for obtaining the electronic structure of molecules and clusters

The introduction of effective core potentials into the Xα LCAO method can greatly expand the size of the molecular system which may be feasibly treated. Therefore, we have incorporated norm-conserving effective potentials into this framework, using a gaussian basis set, for calculations of the electronic structure of molecules and cluster models of solids and surfaces. This combined methodology makes possible the determination of equilibrium geometries and certain aspects of potential surfaces required for a large class of electronic structure problems.     

Metal complexes of allyl derivatives of C60 fullerene: molecular and electronic structure prediction from density functional calculations

The problem of existence of ³—-complexes of C₆₀ fullerene with transition metal atoms is discussed. The complexes C₆₀R₃Co(CO)₃ (R = H, F, Cl, Br), C₆₀H₃NiCp, and C₆₀H₃Fe(CO)Cp, where C₆₀R₃ is an allyl derivative of C₆₀ fullerene, were shown to be sufficiently stable. In these complexes the metal atoms are ³—-bound to the fullerene cage. In contrast to this, the metal atoms in the C₆₀H₃Li and C₆₀H₃FeCp complexes are ⁵—-coordinated to the carbon cage. Density functional calculations were carried out with the Perdew—Burke—Ernzerhof exchange-correlation potential (PBE). It was concluded that the type of bonding in the complexes of allyl derivatives of C₆₀ fullerene depends on the nature of the species attached. Among the systems studied, the maximum energy of the ³—-bond was obtained for the C₆₀H₃NiCp complex. The results obtained can be useful in the design of synthesis of new fullerene derivatives with the ³—-coordination of the transition metal atoms to the carbon cage.     

Load balancing by work–stealing in quantum chemistry calculations: Application to hybrid density functional methods

Parallel implementations of quantum chemistry programs targeting supercomputers are challenging applications of dynamic load balancing algorithms. The implementation of work stealing (WS) algorithms is discussed and their usefulness is demonstrated. Evaluation of the four‐center integrals of a Cu₁₀ cluster requires 25 core‐hours overall, achieving 88% efficiency with simple WS for 2048 cores, and 97% with task presorting based on a cost estimate. Limitations of cost sorting become noticeable for larger systems. When spatial symmetry is exploited together with integral screening, bundling the original tasks yields an efficiency of 98% for Cu₇₉ in O_h symmetry on 512, 1204, and 2048 cores. The advantage of WS algorithms described in this work is not limited to the evaluation of four‐center integrals. © 2014 Wiley Periodicals, Inc.     

The relative performance of the local density approximation and gradient-corrected density functional theory for computing metal–ligand distances in Werner-type and organometallic complexes

Optimized metal-ligand (M-L) bond lengths for 17 classical Werner-type transition-metal complexes were calculated using the local density approximation (LDA) and a gradient-corrected (GC) extension. GCs lengthen the bonds by between 0.02 and 0.09 Å relative to the LDA results. The latter range from 0.02 Å shorter than observed to 0.05 Å longer, while the GC data range from exact agreement with experiment to some 0.12 Å too long. The LDA rms deviation is 0.025 Å compared to the GC error of 0.070 Å. In contrast, data from the literature for organometallic species show that the LDA gives systematically too short M-L distances and GCs lead to a better agreement with experiment. The relative performance of LDA and GC functionals reflects the qualitatively different chemistries of organometallic and Werner-type complexes. The magnitude of the GC bond-length expansion for the latter correlates with the ionicity of the M-L interaction. © 1997 John Wiley & Sons, Inc.     

On the electronic structure of MoO: Spin-polarized density functional calculations of spectroscopic properties of low-lying quintet,triplet, and septet states

Density functional theory (DFT ) calculations for the ground state and four excited quintet, two septet, and two triplet states of the molybdenum oxide molecule are reported. Equilibrium geometries and other spectroscopic constants are determined for these states and compared both with recent spectroscopic measurements and other theoretical calculations, where available. Experimental assignments of the ⁵II ground state and excited ⁵Σ⁺, ⁵Σ^?, ⁵Δ, and B^{' 5}II states are confirmed; also candidates for low-lying triplet³ Δ and ³Σ^? and septet ⁷II and ⁷Σ⁺ are presented. Theoretical calculations for ⁵Σ^?, B^{' 5}II, and ³Σ^? states are reported for the first time. The results are in many cases in better agreement with experiment than are other calculations, already at the simplest level of approximation within DFT , which confirms that this method is a useful tool for investigation of transition-metal compounds. © 1994 John Wiley & Sons, Inc.     

Efficient strategies for accurate calculations of electronic excitation and ionization energies: theory and application to the dehydro-m-xylylene anion

In the dehydro-m-xylylene (DMX) anion [Munsch; et al. J. Org. Chem. 2004, 69, 5735], three nearly degenerate orbitals host four electrons, which results in a large number of nearly-degenerate electronic states. By using this challenging example, we assess the performance of the multireference "brute force" approach and the two-step schemes based on single-reference methods for calculating accurate energy differences. Different schemes for calculating adiabatic ionization potential (IP) of DMX- are also investigated. IP calculated by single-reference based schemes is in excellent agreement with experiment.     

Ab initio quantum chemistry calculations on the electronic structure of heavier alkyne congeners: diradical character and reactivity

The electronic structure of the heavier congeners of alkynes has been studied with emphasis on characterizing their extent of diradical character. Four orbitals play a crucial role in determining the electronic structure in planar trans-bent geometries. Two are associated with an out-of-plane pi interaction, pi and pi, and two are associated with in-plane interactions and/or in-plane lone pairs, LP(n-) and LP(n+). The ordering of these orbitals can change depending upon geometry. One extreme, corresponding to the local minimum for Si-Si and Ge-Ge, is a diradicaloid multiple-bonding configuration where LP and pi are nominally occupied. Another extreme, corresponding to a local minimum for Sn-Sn, is a relatively closed-shell single-bond configuration where LP and LP are nominally occupied. This ordering leads to predicted bond shortening upon excitation from singlet to triplet state. For the heavier elements, there appears to be very little energy penalty for large geometric distortions that convert from one ordering to the other on the singlet surface. The implications of these results with respect to experimental observations are discussed.