Assessment of the Van Voorhis–Scuseria exchange–correlation functional for predicting excitation energies using time-dependent density functional theory

We assess the performance of the Van Voorhis–Scuseria exchange–correlation functional (VSXC), a kinetic-energy-density-dependent exchange–correlation functional recently developed in our group, for calculating vertical excitation energies using time-dependent density functional theory in a benchmark set of molecules. Overall, VSXC performs very well, with accuracy similar to that of hybrid functionals such as the hybrid Perdew–Burke–Ernzerhof functional and Becke's three parameter hybrid method with the Lee, Yang, and Parr correlation functional, which contain a portion of Hartree–Fock exchange. Received: 29 December 1999 / Accepted: 5 June 2000 / Published online: 11 September 2000     

一些密度泛函方法预测电子亲和势

选取了杂化泛函B3LYP, B3PW91, O3LYP, PBE0, 以及与之相对应的GGA泛函BLYP, BPW91, OLYP和PBE, 还选取了能更好地兼顾强相互作用和弱相互作用的X3LYP泛函和在预测NMR的化学位移有较好表现的OPBE泛函, 以及两种meta-GGA泛函VSXC和TPSS, 共12种泛函, 详细地考察了这些泛函在预测EA方面的准确性.     

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.     

Excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state of diphenylpolyenes

This paper discusses the excess polarizabilities upon excitation from the ground state to the first dipole‐allowed excited state (S₁) of diphenylpolyenes by using the time‐dependent density functional theory. Two hybrid exchange‐correlation (xc) potentials Becke‐3 Lee‐Yang‐Parr (B3LYP) and Perdew‐Burke‐Ernzerhof (PBE1PBE) were employed. Our calculations indicate that the magnitude of the excess polarizability will decrease while the molecule evolves from the unrelaxed S₁ state to the relaxed S₁ state. This decreasing trend is found to be independent of substituents, though substituents can change the value of the excess polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Predicting core level binding energies shifts: Suitability of the projector augmented wave approach as implemented in VASP

Here, we assess the accuracy of various approaches implemented in Vienna ab initio simulation package code to estimate core‐level binding energy shifts (ΔBEs) using a projector augmented wave method to treat core electrons. The performance of the Perdew–Burke–Ernzerhof (PBE) and the Tao–Perdew–Staroverov–Scuseria (TPSS) exchange‐correlation density functionals is examined on a dataset of 68 molecules containing B→F atoms in diverse chemical environments, accounting for 185 different 1s core level binding energy shifts, for which both experimental gas‐phase X‐ray photoemission (XPS) data and accurate all electron ΔBEs are available. Four procedures to calculate core‐level shifts are investigated. Janak–Slater transition state approach yields mean absolute errors of 0.37 (0.21) eV at PBE (TPSS) level, similar to highly accurate all electron ΔSCF approaches using same functionals, and close to XPS experimental accuracy of 0.1 eV. The study supports the use of these procedures to assign ΔBEs of molecular moieties on material surfaces of interest in surface science, nanotechnology, and heterogeneous catalysis. © 2017 Wiley Periodicals, Inc.     

Dimethyl ether in nanotubes: Structural variations and conformational preferences

Russian Journal of Organic Chemistry - DFT quantum chemical calculations with the Perdew–Burke–Ernzerhof (PBE) hybrid functional and triple-zeta (3ζ) basis set showed that the...     

Applicability of density functional theory in reproducing accurate vibrational spectra of surface bound species

The structural equilibrium parameters, the adsorption energies, and the vibrational frequencies of the nitrogen molecule and the hydrogen atom adsorbed on the (111) surface of rhodium have been investigated using different generalized‐gradient approximation (GGA), nonlocal correlation, meta‐GGA, and hybrid functionals, namely, Perdew, Burke, and Ernzerhof (PBE), Revised‐RPBE, vdW‐DF, Tao, Perdew, Staroverov, and Scuseria functional (TPSS), and Heyd, Scuseria, and Ernzerhof (HSE06) functional in the plane wave formalism. Among the five tested functionals, nonlocal vdW‐DF and meta‐GGA TPSS functionals are most successful in describing energetics of dinitrogen physisorption to the Rh(111) surface, while the PBE functional provides the correct chemisorption energy for the hydrogen atom. It was also found that TPSS functional produces the best vibrational spectra of the nitrogen molecule and the hydrogen atom on rhodium within the harmonic formalism with the error of ?2.62 and ?1.1% for the N? N stretching and Rh? H stretching frequency. Thus, TPSS functional was proposed as a method of choice for obtaining vibrational spectra of low weight adsorbates on metallic surfaces within the harmonic approximation. At the anharmonic level, by decoupling the Rh? H and N? N stretching modes from the bulk phonons and by solving one‐ and two‐dimensional Schrödinger equation associated with the Rh? H, Rh? N, and N? N potential energy we calculated the anharmonic correction for N? N and Rh? H stretching modes as ?31 cm^?1 and ?77 cm^?1 at PBE level. Anharmonic vibrational frequencies calculated with the use of the hybrid HSE06 function are in best agreement with available experiments. © 2014 Wiley Periodicals, Inc.     

Small clusters of aluminum and tin: highly correlated calculations and validation of density functional procedures

We present results of molecular electronic structure treatments of multireference configuration interaction (MRCI) type for clusters Al(n) and Sn(n) in the range up to n = 4, and of coupled cluster singles and doubles with perturbative triples corrections (CCSD(T)) type in the range up to n = 10. Basis sets of quadruple zeta size are employed, computed energy differences, such as cohesive energies, E(coh), or dissociation energies for the removal of a single atom, D(e), differ from the complete basis set limit by only a few 0.01 eV. MRCI and CCSD(T) results are then compared to those obtained from density functional theory (DFT) treatments, which show that all computational procedures agree with the general features of D(e) and E(coh). The best agreement of DFT with CCSD(T) is found for the meta-GGA (generalized gradient approximation) TPSS (Tao, Perdew, Staroverov, Scuseria) for which D(e) differs from CCSD(T) by at most 0.15 eV for Al(n) and 0.21 eV for Sn(n). The GGA PBE (Perdew, Burke, Ernzerhof) is slightly poorer with maximum deviations of 0.23 and 0.24 eV, whereas hybrid functionals are not competitive with GGA and meta-GGA functionals. A general conclusion is that errors of D(e) and/or energy differences of isomers computed with DFT procedures may easily reach 0.2 eV and errors for cohesive energies E(coh) 0.1 eV.     

Benchmarking dispersion and geometrical counterpoise corrections for cost‐effective large‐scale DFT calculations of water adsorption on graphene

The physisorption of water on graphene is investigated with the hybrid density functional theory (DFT)‐functional B3LYP combined with empirical corrections, using moderate‐sized basis sets such as 6‐31G(d). This setup allows to model the interaction of water with graphene going beyond the quality of classical or semiclassical simulations, while still keeping the computational costs under control. Good agreement with respect to Coupled Cluster with singles and doubles excitations and perturbative triples (CCSD(T)) results is achieved for the adsorption of a single water molecule in a benchmark with two DFT‐functionals (Perdew/Burke/Ernzerhof (PBE), B3LYP) and Grimme's empirical dispersion and counterpoise corrections. We apply the same setting to graphene supported by epitaxial hexagonal boron nitride (h‐BN), leading to an increased interaction energy. To further demonstrate the achievement of the empirical corrections, we model, entirely from first principles, the electronic properties of graphene and graphene supported by h‐BN covered with different amounts of water (one, 10 water molecules per cell and full coverage). The effect of h‐BN on these properties turns out to be negligibly small, making it a good candidate for a substrate to grow graphene on. © 2014 Wiley Periodicals, Inc.     

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.     

Optical rotation calculated with time-dependent density functional theory: the OR45 benchmark

Time-dependent density functional theory (TDDFT) computations are performed for 42 organic molecules and three transition metal complexes, with experimental molar optical rotations ranging from 2 to 2 × 10(4) deg cm(2) dmol(-1). The performances of the global hybrid functionals B3LYP, PBE0, and BHLYP, and of the range-separated functionals CAM-B3LYP and LC-PBE0 (the latter being fully long-range corrected), are investigated. The performance of different basis sets is studied. When compared to liquid-phase experimental data, the range-separated functionals do, on average, not perform better than B3LYP and PBE0. Median relative deviations between calculations and experiment range from 25 to 29%. A basis set recently proposed for optical rotation calculations (LPol-ds) on average does not give improved results compared to aug-cc-pVDZ in TDDFT calculations with B3LYP. Individual cases are discussed in some detail, among them norbornenone for which the LC-PBE0 functional produced an optical rotation that is close to available data from coupled-cluster calculations, but significantly smaller in magnitude than the liquid-phase experimental value. Range-separated functionals and BHLYP perform well for helicenes and helicene derivatives. Metal complexes pose a challenge to first-principles calculations of optical rotation.     

Pseudopotentials for H to Kr optimized for gradient-corrected exchange-correlation functionals

Pseudopotential parameter sets for the elements from H to Kr using the relativistic, norm-conserving, separable, dual-space Gaussian-type pseudopotentials of Goedecker, Teter, and Hutter (GTH) are presented as optimized for the gradient-corrected exchange-correlation functionals of Becke, Lee, Yang, and Parr (BLYP), Becke and Perdew (BP), and Perdew, Burke, and Ernzerhof (PBE). The accuracy and reliability of the GTH pseudopotentials is shown by calculations for a series of small molecules. Contribution to Karl Jug Honorary Issue     

First‐principles calculations on the four phases of BaTiO3

The calculations based on linear combination of atomic orbitals basis functions as implemented in CRYSTAL09 computer code have been performed for cubic, tetragonal, orthorhombic, and rhombohedral modifications of BaTiO₃ crystal. Structural and electronic properties as well as phonon frequencies were obtained using local density approximation, generalized gradient approximation, and hybrid exchange‐correlation density functional theory (DFT) functionals for four stable phases of BaTiO₃. A comparison was made between the results of different DFT techniques. It is concluded that the hybrid PBE0 [J. P. Perdew, K. Burke, M. Ernzerhof, J. Chem. Phys. 1996, 105, 9982.] functional is able to predict correctly the structural stability and phonon properties both for cubic and ferroelectric phases of BaTiO₃. The comparative phonon symmetry analysis in BaTiO₃ four phases has been made basing on the site symmetry and irreducible representation indexes for the first time. © 2012 Wiley Periodicals, Inc.     

Comparative study of unscreened and screened molecular static linear polarizability in the Hartree–Fock,hybrid‐density functional,and density functional models

The sum‐over‐states (SOS) polarizabilities are calculated within approximate mean‐field electron theories such as the Hartree–Fock approximation and density functional models using the eigenvalues and orbitals obtained from the self‐consistent solution of the single‐particle equations. The SOS polarizabilities are then compared with those calculated using the finite‐field (FF) method. Three widely used mean‐field models are as follows: (1) the Hartree–Fock (HF) method, (2) the three parameter hybrid generalized gradient approximation (GGA) (B3LYP), and (3) the parameter‐free generalized gradient approximation due to Perdew–Burke–Ernzerhof (PBE). The comparison is carried out for polarizabilities of 142 molecules calculated using the 6‐311++G(d,p) basis set at the geometries optimized at the B3LYP/6‐311G** level. The results show that the SOS method almost always overestimates the FF polarizabilities in the PBE and B3LYP models. This trend is reversed in the HF method. A few exceptions to these trends are found. The mean absolute errors (MAE) in the screened (FF) and unscreened (SOS) polarizability are 0.78, 1.87, and 3.44 ų for the HF, B3LYP, and PBE‐GGA methods, respectively. Finally, a simple scheme is devised to obtain FF quality polarizability from the SOS polarizability. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

Harmonic frequency scaling factors for Hartree-Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2 with the Sadlej pVTZ electric property basis set

Scaling factors for obtaining fundamental vibrational frequencies from harmonic frequencies calculated at six of the most commonly used levels of theory have been determined from regression analysis for the polarized-valence triple-zeta (pVTZ) Sadlej electric property basis set. The Sadlej harmonic frequency scaling factors for first- and second-row molecules were derived from a comparison of a total of 900 individual vibrations for 111 molecules with available experimental frequencies. Overall, the best performers were the hybrid density functional theory (DFT) methods, Becke's three-parameter exchange functional with the Lee–Yang–Parr fit for the correlation functional (B3-LYP) and Becke's three-parameter exchange functional with Perdew and Wang's gradient-corrected correlation functional (B3-PW91). The uniform scaling factors for use with the Sadlej pVTZ basis set are 0.9066, 0.9946, 1.0047, 0.9726, 0.9674 and 0.9649 for Hartree–Fock, the Slater–Dirac exchange functional with the Vosko–Wilk–Nusair fit for the correlation functional (S-VWN), Becke's gradient-corrected exchange functional with the Lee–Yang–Parr fit for the correlation functional (B-LYP), B3-LYP, B3-PW91 and second-order M?ller–Plesset theory with frozen core (MP2(fc)), respectively. In addition to uniform frequency scaling factors, dual scaling factors were determined to improve the agreement between computed and observed frequencies. The scaling factors for the wavenumber regions below 1800 cm⁻¹ and above 1800 cm⁻¹ are 0.8981 and 0.9097, 1.0216 and 0.9857, 1.0352 and 0.9948, 0.9927 and 0.9659, 0.9873 and 0.9607, 0.9844 and 0.9584 for Hartree–Fock, S-VWN, B-LYP, B3-LYP, B3-PW91 and MP2(fc), respectively. Hybrid DFT methods along with the Sadlej pVTZ basis set provides reliable theoretical vibrational spectra in a cost-effective manner. Received: 22 May 2000 / Accepted: 30 August 2000 / Published online: 28 February 2001