Does the gradient-regulated connection improve the description of correlated metal bond properties?

Gradient-regulated connection (GRAC) is a generalized gradient approximation exchange density functional designed by combining the revPBE and PW91 exchange functionals to impose their behaviors in the slowly- and fast-varying density regions, respectively. Such a construction allows one single density functional to accurately estimate both covalent and weak interactions occurring in main-group-based molecular systems. For the first time, the assessment of the performance of the GRAC exchange functional is extended to the modeling of various metal bond energy and structure properties. This assessment shows that when GRAC is coupled with the Perdew, Burke, Ernzerhof (PBE) correlation, the resulting exchange-correlation density functional is an excellent alternative to global hybrids to model bond dissociation energy, atomic electronic excitation energy, and bond length structure properties of single-reference metal bonds. It also shows that coupling with the Tognetti, Cortona, Adamo (TCA) correlation constitutes a robust approach to tackle energy bond properties of organometallic complexes with multi-reference character.     

Diminished gradient dependence of density functionals: constraint satisfaction and self-interaction correction

The Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation for the exchange-correlation energy functional has two nonempirical constructions, based on satisfaction of universal exact constraints on the hole density or on the energy. We show here that, by identifying one possible free parameter in exchange and a second in correlation, we can continue to satisfy these constraints while diminishing the gradient dependence almost to zero (i.e., almost recovering the local spin density approximation or LSDA). This points out the important role played by the Perdew-Wang 1991 nonempirical hole construction in shaping PBE and later constructions. Only the undiminished PBE is good for atoms and molecules, for reasons we present, but a somewhat diminished PBE could be useful for solids; in particular, the surface energies of solids could be improved. Even for atoms and molecules, a strongly diminished PBE works well when combined with a scaled-down self-interaction correction (although perhaps not significantly better than LSDA). This shows that the undiminished gradient dependence of PBE and related functionals works somewhat like a scaled-down self-interaction correction to LSDA.     

Generalized gradient exchange functionals based on the gradient-regulated connection: a new member of the TCA family

A new type of generalized gradient approximation exchange functional coupled with the TCA correlation model has been proposed. Based on gradient-regulated connection, this exchange functional is able to mix performances of a modified PBE for the bulk region, to those of the PW91 for the asymptotic one, leading to a significant improvement on the modelization of weak interacting systems, while keeping a good accuracy for the atomization energies.     

Determining the role of the underlying orbital‐dependence of PBE0‐DH and PBE‐QIDH double‐hybrid density functionals

We study the orbital‐dependence of three (parameter‐free) double‐hybrid density functionals, namely the PBE0‐DH, the PBE‐QIDH models, and the SOS1‐PBE‐QIDH spin‐opposite‐scaled variant of the latter. To do it, we feed all their energy terms with different sets of orbitals obtained previously from self‐consistent density functional theory calculations using several exchange‐correlation functionals (e.g., PBE, PBE0, PBEH&H), or directly with HF‐PBE orbitals, to see their effect on selected datasets for atomization and reaction energies, the latter proned to marked self‐interaction errors. We find that the PBE‐QIDH double‐hybrid model shows a great consistency, as the best results are always obtained for the set of orbitals corresponding to its hybrid scheme, which prompts us to recommend this model without any other fitting or reparameterization. © 2017 Wiley Periodicals, Inc.     

Performance of recently developed kinetic energy density functionals for the calculation of hydrogen binding strengths and hydrogen-bonded structures

 The accuracy of predicted hydrogen binding energies and equilibrium structures for a benchmark set of molecules is compared for some recently developed density functionals, Becke's three parameter hybrid method with the Lee, Yang, and Parr (LYP) correlation functional (B3LYP), Becke's half and half functional combined with the LYP correlation functional (BHLYP), Perdew, Burke and Ernzerhof functional (PBE), Van Voorhis, Scuseria exchange correlation functional (VSXC), the hybrid Perdew, Burke and Ernzerhof functional (PBE1PBE), and meta-generalized gradient approximation (meta-GGA). Overall, the hybrid functionals which contain a portion of Hartree–Fock exchange (B3LYP, BHLYP, and PBE1PBE) yield the most accurate results. The kinetic-energy-density-dependent functionals, VSXC and meta-GGA, are significantly less accurate. Received: 10 December 1999 / Accepted: 5 March 2000 / Published online: 21 June 2000     

The electronic spectrum of CUONg(4) (Ng = Ne, Ar, Kr, Xe): New insights in the interaction of the CUO molecule with noble gas matrices

The electronic spectrum of the CUO molecule was investigated with the IHFSCC-SD (intermediate Hamiltonian Fock-space coupled cluster with singles and doubles) method and with TD-DFT (time-dependent density functional theory) employing the PBE and PBE0 exchange-correlation functionals. The importance of both spin-orbit coupling and correlation effects on the low-lying excited-states of this molecule are analyzed and discussed. Noble gas matrix effects on the energy ordering and vibrational frequencies of the lowest electronic states of the CUO molecule were investigated with density functional theory (DFT) and TD-DFT in a supermolecular as well as a frozen density embedding (FDE) subsystem approach. This data is used to test the suitability of the FDE approach to model the influence of different matrices on the vertical electronic transitions of this molecule. The most suitable potential was chosen to perform relativistic wave function theory in density functional theory calculations to study the vertical electronic spectra of the CUO and CUONg(4) with the IHFSCC-SD method.     

Theoretical study on stabilities of multiple hydrogen bonded dimers

A series of self-constituted multiple hydrogen bonded (MHB) complexes has been investigated systematically by density functional theory (PBE1PBE /6-31G**), the Morokuma energy decomposition method (HF/6-31G**) and MP2 (6-31G** and 6-311++G**) calculation. We have discovered that (i) for doubly hydrogen bonded (DHB) complexes, both the interaction energy and stability increase with the charge transfer energy; (ii) for quadruple hydrogen bonded (QHB) complexes, cooperativity is the most important factor determining stability of the complex: stronger cooperative energy correlates well with larger interaction energy and thus more stable complex and vice versa; (iii) correlation energy plays an important role in intermolecular interactions. The correlation energy, mainly consisting of dispersive energy, also exhibits cooperativity in MHB dimers: positive for M-aadd and generally negative for other complexes.     

A new parameter-free correlation functional based on an average atomic reduced density gradient analysis

A new parameter-free correlation functional based on the local Ragot-Cortona approach [J. Chem. Phys. 121, 7671 (2004)] is presented. This functional rests on a single ansatz for the gradient correction enhancement factor: it is assumed to be given by a simple analytic expression satisfying some exact conditions and containing two coefficients. These coefficients are determined without implementing the functional and without using a fitting procedure to experimental data. Their values are determined by requiring that the functional gives a correct average reduced density gradient for atoms, which, to some extent, can be considered an intrinsic atomic property. The correlation functional is then coupled with the Perdew-Burke-Erzernhof (PBE) exchange and compared with the original PBE approach as well as with some other pure density or hybrid approaches. Standard tests for atomic and molecular systems show that our new functional significantly improves on PBE, showing very interesting properties.     

Is the uniform electron gas limit important for small Ag clusters? Assessment of different density functionals for Ag(n) (n < or = 4)

Twenty-three density functional theory (DFT) methods, including the second- and the third-generation functionals, are tested in conjunction with two basis sets (LANL2DZ and SDD) for studying the properties of neutral and ionic silver clusters. We find that DFT methods incorporating the uniform electron gas limit in the correlation functional, namely, those with Perdew's correlation functionals (PW91, PBE, P86, and TPSS), Becke's B95, and the Van Voorhis-Scuseria functional VSXC, generally perform better than the other group of functionals, e.g., those incorporating the LYP correlation functional and variations of the B97 functional. Strikingly, these two groups of functionals can produce qualitatively different results for the Ag3 and Ag4 clusters. The energetic properties and vibrational frequencies of Ag(n) are also evaluated by the different functionals. The present study shows that the choice of DFT methods for heavy metals may be critical. It is found that the exact-exchange-incorporated PBE functional (PBE1PBE) is among the best for predicting the range of properties.     

An approximate density-functional method using the Harris-Foulkes functional

We present a method which uses the results of a molecular Kohn-Sham calculation at a reference geometry to approximate the energy at many different geometries. The Kohn-Sham electron density of the reference geometry is decomposed into atomic fragments, which move with the nuclei to approximate the density at a new geometry and the energy is evaluated with the Harris-Foulkes functional. Preliminary results for a biological quantum-mechanics/molecular-mechanics trajectory are promising: the errors of reference-geometry Harris-Foulkes (compared to full self-consistent Kohn-Sham) for the PBE exchange-correlation functional have the same magnitude as the difference between the energies of PBE and BLYP.     

Characterizing the potential energy surface of the water dimer with DFT: failures of some popular functionals for hydrogen bonding

Ten stationary points on the water dimer potential energy surface have been examined with ten density functional methods (X3LYP, B3LYP, B971, B98, MPWLYP, PBE1PBE, PBE, MPW1K, B3P86, and BHandHLYP). Geometry optimizations and vibrational frequency calculations were carried out with the TZ2P(f,d)+dif basis set. All ten of the density functionals correctly describe the relative energies of the ten stationary points. However, correctly describing the curvature of the potential energy surface is far more difficult. Only one functional (BHandHLYP) reproduces the number of imaginary frequencies from CCSD(T) calculations. The other nine density functionals fail to correctly characterize the nature of at least one of the ten (H(2)O)(2) stationary points studied here.     

A density functional theory (DFT) and time-dependent density functional theory (TDDFT) study on optical transitions in oligo(p-phenylenevinylene)-fullerene dyads and the applicability to resonant energy transfer

The optical transitions of three different size oligo(p-phenylenevinylene)-fullerene dyads (OPV(n)-MPC(60); n = 2-4) and of the corresponding separate molecules are studied using density functional theory (DFT) and time-dependent density functional theory. The DFT is used to determine the geometries and the electronic structures of the ground states. Transition energies and excited-state structures are obtained from the TDDFT calculations. Resonant energy transfer from OPV(n) to MPC(60) is also studied and the Fermi golden rule is used, along with two simple models to describe the electronic coupling to calculate the energy transfer rates. The hybrid-type PBE0 functional is used with a split-valence basis set augmented with a polarization function (SV(P)) in calculations and the calculated results are compared to the corresponding experimental results. The calculated PBE0 spectra of the OPV(n)-MPC(60) dyads correspond to the experimental spectra very well and are approximately sums of the absorption spectra of the separate OPV(n) and MPC(60) molecules. Also, the absorption energies of OPV(n) and MPC(60) and the emission energies of OPV(n) are predicted well with the PBE0 functional. The PBE0 calculated resonant energy transfer rates are in a good agreement with the experimental rates and show the existence of many possible pathways for energy transfer from the first excited singlet states of the OPV(n) molecules to the MPC(60) molecule.     

Systematic studies on the computation of nuclear magnetic resonance shielding constants and chemical shifts: the density functional models

We present a systematic density functional investigation on the prediction of the 13C, 15N, 17O, and 19F NMR properties of 23 molecules with 21 density functionals. Extensive comparisons are made for both 13C magnetic shieldings and chemical shifts with respect to the gas phase experimental data and the best CCSD(T) results. We find that the OPBE and OPW91 exchange-correlation functionals perform significantly better than some popular functionals such as B3LYP and PBE1PBE, even surpassing, in many cases, the standard wavefunction-based method MP2. Further analysis has been performed to explore the individual role played by various exchange and correlation functionals. We find that the B88 and PBE exchange functionals have a too strong tendency of deshielding, leading to too deshielded magnetic shielding constants; whereas the OPTX exchange functional performs remarkably well. We claim that the main source of error arises from the exchange functional, but correlation functional also makes important contribution. We find that the correlation functionals may be grouped into two classes. class A, such as LYP and B98, leads to deshielded NMR values, deteriorating the overall performance; whereas class B, such as PW91 and PBE, generally increases the absolute shieldings, which complements the exchange functionals, leading to improved results in the calculation of NMR data.     

GGA versus van der Waals density functional results for mixed gold/mercury molecules and pure Au and Hg cluster properties

Dispersion forces, which originate the van der Waals interaction, are indispensable to describe numerous systems and processes, including metallic clusters and surfaces. In this work is used an efficient numerical implementation in the context of density functional theory of a non-local correlation van der Waals density functional (vdW-DF) to self-consistently solve the structure and electronic properties of small molecules (ArAu, AuF, ArAuF, ArCuF, Au(2)Hg, Au(2)Hg(2)), as well as Au(2-15) and Hg(2-6) clusters. Three different flavours of that vdW-DF exchange-correlation (xc) functional are tested. The results for small molecules are compared with those from the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE) against experiments or highly accurate quantum chemical calculations. It is found that, on average, vdw-DF improves PBE binding energies and overestimates bond distances. Our vdW-DF calculations lead to planar structures as lowest energy isomers of Au(14) and Au(15) clusters. The calculated polarizability of Au(2-15) isomers dramatically decreases in passing from two-dimensional (2D) to three-dimensional (3D) equilibrium geometries. A combination of the density of states of two vdw-DF planar isomers of the Au(12)(-) anion is proposed to explain the photoelectron spectroscopy experiments. Contrary to PBE results, the vdW-DF calculations predict that the O(h) isomer of Hg(6) is more stable than the C(2v) one.     

General formulation of spin-flip time-dependent density functional theory using non-collinear kernels: theory, implementation, and benchmarks

We report an implementation of the spin-flip (SF) variant of time-dependent density functional theory (TD-DFT) within the Tamm-Dancoff approximation and non-collinear (NC) formalism for local, generalized gradient approximation, hybrid, and range-separated functionals. The performance of different functionals is evaluated by extensive benchmark calculations of energy gaps in a variety of diradicals and open-shell atoms. The benchmark set consists of 41 energy gaps. A consistently good performance is observed for the Perdew-Burke-Ernzerhof (PBE) family, in particular PBE0 and PBE50, which yield mean average deviations of 0.126 and 0.090 eV, respectively. In most cases, the performance of original (collinear) SF-TDDFT with 50-50 functional is also satisfactory (as compared to non-collinear variants), except for the same-center diradicals where both collinear and non-collinear SF variants that use LYP or B97 exhibit large errors. The accuracy of NC-SF-TDDFT and collinear SF-TDDFT with 50-50 and BHHLYP is very similar. Using PBE50 within collinear formalism does not improve the accuracy.     

Electronic structures of 4d transition metal monoxides by density functional theory

Bond distances, dissociation energies, ionization potentials and electron affinities of 4d transition metal monoxides from YO to CdO and their positive and negative ions were studied by use of density functional methods B3LYP, BLYP, B3PW91, BPW91, B3P86, BP86, SVWN, MPW1PW91 and PBE1PBE. It was found that calculated properties are highly dependent on the functionals employed, especially for dissociation energy. For most neutral species, pure density functionals BLYP, BPW91 and BP86 have good performance in predicting dissociation energy than hybrid density functionals B3LYP, B3PW91 and B3P86. In addition, BLYP gives the largest bond distance compared with other density functional methods, while SVWN gives shortest bond distance, largest dissociation energy and electron affinity. For the ground state, the spin multiplicity of the charged species can be obtained by ± 1 of their corresponding neutral species.     

Single wall carbon nanotubes density of states: comparison of experiment and theory

We study the electronic structure of a variety of single wall carbon nanotubes and report density of states obtained with the Perdew–Burke–Ernzerhof (PBE) generalized gradient approximation and hybrid PBE0 approximation of density functional theory using Gaussian orbitals and periodic boundary conditions. PBE gives very good results for metallic tubes but the addition of a portion of exact exchange in the hybrid PBE0 functional worsens the agreement between experiment and theory. On the other hand, the PBE0 hybrid significantly improves the theoretical predictions (compared to PBE) for semiconducting tubes.     

Density functional study of AuXq (X = O, S, Se, Te, q = +1, 0, -1) molecules

Bond distances, vibrational frequencies, electron affinity, ionization potential, and dissociation energies of the title molecules were studied by use of density functional methods B3LYP, B3P86, B3PW91, BHLYP, BLYP, BP86, mPW1PW91, and PBE1PBE. It was found that the ground electronic state is doublet for neutral species, singlet for the anion, and triplet for the cation, in agreement with experiments and previous theoretical studies. The calculated properties are highly dependent on the functionals employed, in particular for the dissociation energy. The predicted bond distances and vibrational frequencies are in agreement with experiments and previous theoretical results. BP86 and BLYP have relatively good performance in reproducing the experimental results, while BHLYP is the worst functional method compared with the other density functional methods used for the title molecules.