Corrected Density Functionals Research Articles

Electronic levels and electrical response of periodic molecular structures from plane-wave orbital-dependent calculations

Plane-wave electronic-structure predictions based upon orbital-dependent density-functional theory (OD-DFT) approximations, such as hybrid density-functional methods and self-interaction density-functional corrections, are severely affected by computational inaccuracies in evaluating electron interactions in the plane-wave representation. These errors arise from divergence singularities in the plane-wave summation of electrostatic and exchange interaction contributions. Auxiliary-function corrections are reciprocal-space countercharge corrections that cancel plane-wave singularities through the addition of an auxiliary function to the point-charge electrostatic kernel that enters into the expression of interaction terms. At variance with real-space countercharge corrections that are employed in the context of density-functional theory (DFT), reciprocal-space corrections are computationally inexpensive, making them suited to more demanding OD-DFT calculations. Nevertheless, there exists much freedom in the choice of auxiliary functions and various definitions result in different levels of performance in eliminating plane-wave inaccuracies. In this work we derive exact point-charge auxiliary functions for the description of molecular structures of arbitrary translational symmetry, including the yet unaddressed one-dimensional case. In addition, we provide a critical assessment of different reciprocal-space countercharge corrections and demonstrate the improved accuracy of point-charge auxiliary functions in predicting the electronic levels and electrical response of conjugated polymers from plane-wave OD-DFT calculations.

Static NLO responses of fluorinated polyacetylene chains evaluated with long-range corrected density functionals

As an alternative to oligomeric systems with different skeleton atoms it is shown that asymmetry introduced by substitution on a symmetric π-conjugated chain can lead to molecular systems with high non-linear optical responses. First hyperpolarizability and related properties such as the bond-length alternation parameter, dipole moment and polarizability of polyfluoroacetylene (PFA) oligomers are investigated by the Hartree-Fock, DFT and MP2 approaches. Particular attention is paid to long-range corrected DFT methods (LR-DFT). Systematic behavior of the MP2/LR-DFT ratio enables to estimate Δ β L for the eicosamer to 76 × 10 3 a.u. what makes PFA oligomers attractive candidates for NLO applications.

Photoinduced charge transfer in heterofullerene–donor hybrids: A theoretical study

We investigate theoretically photoinduced charge transfer in hybrids composed of nitrogen- and boron-doped fullerenes as acceptor (A), and pyrene, tetrathiofulvane, and porphyrin molecules as donor (D), linked by a spacer chain. Our calculations have been carried out employing density functional theory using conventional, as well as long-range corrected density functionals. The near-degeneracy between A–A and D–D electronic excitations in the absorption spectrum of the N-doped heterofullerene-dyads indicates that energy and charge transfer in such compounds are strongly competing processes. In contrast, energy transfer is mostly suppressed in the B-doped heterofullerene-dyads, which are thus potentially better candidates than the N-doped hybrids for future (opto)electronic applications.

Application of the Stabilization Method to Temporary Anion States of CH3CN, CH3NC, CH3SCN, and CH3NCS in Density Functional Theory with Asymptotically Corrected Potentials

In this paper, density functional theory (DFT) with asymptotically corrected potentials is used to investigate CH(3)CN, CH(3)NC, CH(3)SCN, and CH(3)NCS molecules. For the energies of σ* and π* temporary anion states, the stabilized Koopmans' theorem (S-KT) using long-range correction functional and stabilized Koopmans-based (S-KB) approximation using local functional, are adopted. The stabilization procedure is accomplished by varying the exponents of appropriate diffuse functions. Results indicate that the calculations based on asymptotically corrected density functionals can yield better energy results of temporary anion states over conventional DFT methods.

Comprehensive evaluation of medium and long range correlated density functionals in TD-DFT investigation of DNA bases and base pairs: gas phase and water solution study

A comprehensive analysis of the performance of the TD-DFT method using different density functionals including recently developed medium and long-range correlation corrected density functionals have been carried out for lower-lying electronic singlet valence transitions of nucleic acid bases and the Watson–Crick base pairs in the gas phase and in the water solution. The standard 6-311++G(d,p) basis set was used. Ground state geometries of bases and base pairs were optimized at the M05-2X/6-311++G(d,p) level. The nature of potential energy surfaces (PES) was ascertained through the harmonic vibrational frequency analysis; all geometries were found to be minima at the respective PES. Electronic singlet vertical transition energies were also computed at the CC2/def2-TZVP level in the gas phase. The effect of state-specific water solvation on TD-DFT computed transition energies was considered using the PCM model. For the isolated bases the performance of the B3LYP functional was generally found to be superior among all functionals, but it measurably fails for charge-transfer states in the base pairs. The CC2/def2-TZVP computed transition energies were also revealed to be inferior compared with B3LYP results for the isolated bases. The performance of the ωB97XD, CAM-B3LYP and BMK functionals were found to be similar and comparable with the CC2 results for the isolated bases. However, for the Watson–Crick adenine–thymine and guanine–cytosine base pairs the performance of the ωB97XD functional was found to be the best among all the studied functionals in the present work in predicting the locally excited transitions as well as charge transfer states.

First Principles Simulations of the Structural and Dynamical Properties of Hydrated Metal Ions Me2+and Solvated Metal Carbonates (Me = Ca, Mg, and Sr)

The structural and dynamical properties of the alkaline earth metal ions Mg2+, Ca2+, and Sr2+ and their carbonate and bicarbonate complexes in aqueous solution are examined through first principles molecular dynamics simulations based on the density functional theory. Calculations were conducted in explicit heavy water molecules and at the average temperature of 400 K, conditions which are necessary to obtain a liquid-like water structure and diffusion time-scales when using gradient corrected density functionals. According to these simulations, the magnesium ion undergoes a significant contraction of its coordination sphere in the Mg(H)CO3(+) aqueous complex, whereas calcium and strontium increase their average first shell coordination number when coordinated to HCO3− or CO32−. The analysis of the water exchange processes in the hydration shells of the metals suggests the following order for metal reactivity in solution: Mg2+ < Ca2+ < Sr2+. Moreover, our simulations suggest that the structures of the mos...

On the shape dependence of cluster (hyper)polarizabilities. A combined ab initio and DFT study on large fullerene–like gallium arsenide semiconductor clusters

AbstractThe effect of the cluster shape on the magnitudes of the static dipole (hyper)polarizabilities of large gallium arsenic clusters built from 72 atoms is presented and discussed. Also, the performance of conventional and long range corrected density functionals is assessed on the prediction of the static electric dipole hyperpolarizabilities. The reported results obtained at the Hartree‐Fock, (LC‐) BLYP, (LC‐) BPW91, (CAM)‐B3LYP, and WB97XD levels of theory demonstrate that the cluster shape not only dominates the magnitude of the second hyperpolarizabilities of clusters but also affects dramatically the performance of the density functional theory functionals used. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011

ChemInform Abstract: Electronic Structure and Bonding in CuMO2 (M: Al, Ga, Y) Delafossite-Type Oxides: An ab initio Study.

The structural and electronic properties of some simple ternary oxides with the delafossite-type structure have been investigated using the periodic Hartree−Fock method and a posteriori density-functional corrections. The coexistence in the same crystal structure of different structural motifs, such as MO6 octahedra, linear O−Cu−O units, and hexagonal Cu layers with relatively short Cu−Cu distances, enables accurate calculation of the structural data for this type of material rather difficult: correlation effects seem only to be important for the description of the Cu−O bonds, while the geometry of the MO6 octahedra is best described by the Hartree−Fock method. The analysis of bonding in the Cu layers reveals the existence of weak d10−d10 interactions that are suggested to be important in the determination of the electrooptical properties of doped delafossites.

Accurate Quantum Chemical Description of Non-Covalent Interactions in Hydrogen Filled Endohedral Fullerene Complexes

The structures and binding energies of encapsulated dihydrogen in C60 and C70 have been studied by accurate quantum chemical models with large basis sets and/or extrapolation techniques. Methods based on modified perturbation theory (up to third order) as well as state-of-the-art double-hybrid density functionals have been applied. The proper inclusion of London dispersion interactions is mandatory in order to obtain accurate and consistent energies. It is found that for C60 only one H2 molecule exothermically (binding energy of −7 kcal/mol with an estimated uncertainty of ±1 kcal/mol) fits into the cage, while two H2 molecules become just unbound within the theoretical error bars. Results for the C70 cage show that complexation of two H2 can take place with a relatively large binding energy of −11 kcal/mol. Simple dispersion corrected density functionals (e.g., PBE-D) yield in general very good results (deviations <10−20% of ΔE) compared to our best reference values.

Toward spectroscopic studies of biologically relevant systems: Vibrational spectrum of adenine as a test case for performances of long-range/dispersion corrected density functionals

Several recently introduced models rooted into the density functional theory and designed for the study of weakly bound molecular systems, with particular reference to the role of dispersion interactions, have been tested for their performances in prediction of vibrational properties for adenine molecule. Results obtained by semi-empirical correction for dispersion (DFT-D), semi-local density-functionals (M05-2X, M06-2X), and long-range correction scheme (LC- ωPBE, CAM-B3LYP) have been compared to the PT2 anharmonic frequencies computed by B3LYP functional and to the experimental results. From the tested computational models only the B3LYP-D/DM scheme provided quantitative agreement with the reference data and at the same time correctly described binding of adenine dimer.

Optimal operators for Hartree–Fock exchange from long-range corrected hybrid density functionals

The long-range operators for Hartree–Fock exchange from two recently proposed long-range corrected hybrid functionals, ωB97 and ωB97X [J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 128 (2008) 084106], are discussed. A conserved property is found in the middle-range region of the operator from ωB97X. We argue that the fine details of the Hartree–Fock exchange mixing in this region are responsible for the accuracy of the long-range corrected hybrid functionals in thermochemistry and barrier heights.

TREATMENTS OF THE EXCHANGE ENERGY IN DENSITY-FUNCTIONAL THEORY

Following a recent work [Gál, Phys. Rev. A64, 062503 (2001)], a simple derivation of the density-functional correction of the Hartree–Fock equations, the Hartree–Fock–Kohn–Sham equations, is presented, completing an integrated view of quantum mechanical theories, in which the Kohn–Sham equations, the Hartree–Fock–Kohn–Sham equations and the ground-state Schrödinger equation formally stem from a common ground: density-functional theory, through its Euler equation for the ground-state density. Along similar lines, the Kohn–Sham formulation of the Hartree–Fock approach is also considered. Further, it is pointed out that the exchange energy of density-functional theory built from the Kohn–Sham orbitals can be given by degree-two homogeneous N-particle density functionals (N = 1, 2, …), forming a sequence of degree-two homogeneous exchange-energy density functionals, the first element of which is minus the classical Coulomb-repulsion energy functional.

Adiabatic Corrections to Density Functional Theory Energies and Wave Functions

The adiabatic finite-nuclear-mass-correction (FNMC) to the electronic energies and wave functions of atoms and molecules is formulated for density-functional theory and implemented in the deMon code. The approach is tested for a series of local and gradient corrected density functionals, using MP2 results and diagonal-Born-Oppenheimer corrections from the literature for comparison. In the evaluation of absolute energy corrections of nonorganic molecules the LDA PZ81 functional works surprisingly better than the others. For organic molecules the GGA BLYP functional has the best performance. FNMC with GGA functionals, mainly BLYP, show a good performance in the evaluation of relative corrections, except for nonorganic molecules containing H atoms. The PW86 functional stands out with the best evaluation of the barrier of linearity of H2O and the isotopic dipole moment of HDO. In general, DFT functionals display an accuracy superior than the common belief and because the corrections are based on a change of the electronic kinetic energy they are here ranked in a new appropriate way. The approach is applied to obtain the adiabatic correction for full atomization of alcanes C(n)H(2n+2), n = 4-10. The barrier of 1 mHartree is approached for adiabatic corrections, justifying its insertion into DFT.

Systematic optimization of long-range corrected hybrid density functionals

A general scheme for systematically modeling long-range corrected (LC) hybrid density functionals is proposed. Our resulting two LC hybrid functionals are shown to be accurate in thermochemistry, kinetics, and noncovalent interactions, when compared with common hybrid density functionals. The qualitative failures of the commonly used hybrid density functionals in some "difficult problems," such as dissociation of symmetric radical cations and long-range charge-transfer excitations, are significantly reduced by the present LC hybrid density functionals.

Evaluation of range-separated hybrid density functionals for the prediction of vibrational frequencies, infrared intensities, and Raman activities.

We present an assessment of different density functionals, with emphasis on range-separated hybrids, for the prediction of fundamental and harmonic vibrational frequencies, infrared intensities, and Raman activities. Additionally, we discuss the basis set convergence of vibrational properties of H2O with long-range corrected hybrids. Our results show that B3LYP is the best functional for predicting vibrational frequencies (both fundamental and harmonic); the screened-PBE hybrid (HSE) density functional works best for infrared intensities, and the long-range corrected PBE (LC-omegaPBE), M06-HF, and M06-L density functionals are almost as good as MP2 for predicting Raman activities. We show the predicted Raman spectrum of adenine as an example of a medium-size molecule where a DFT/Sadlej pVTZ calculation is affordable and compare our results against the experimental spectrum.

Self-consistentGWcalculations for semiconductors and insulators

We present $GW$ calculations for small and large gap systems comprising typical semiconductors (Si, SiC, GaAs, GaN, ZnO, ZnS, CdS, and AlP), small gap semiconductors (PbS, PbSe, and PbTe), insulators (C, BN, MgO, and LiF), and noble gas solids (Ar and Ne). It is shown that the ${G}_{0}{W}_{0}$ approximation always yields too small band gaps. To improve agreement with experiment, the eigenvalues in the Green's function $G$ $(G{W}_{0})$ and in the Green's function and the dielectric matrix $(GW)$ are updated until self-consistency is reached. The first approximation leads to excellent agreement with experiment, whereas an update of the eigenvalues in $G$ and $W$ gives too large band gaps for virtually all materials. From a pragmatic point of view, the $G{W}_{0}$ approximation thus seems to be an accurate and still reasonably fast method for predicting quasiparticle energies in simple $sp$-bonded systems. We furthermore observe that the band gaps in materials with shallow $d$ states (GaAs, GaN, and ZnO) are systematically underestimated. We propose that an inaccurate description of the static dielectric properties of these materials is responsible for the underestimation of the band gaps in $G{W}_{0}$, which is itself a result of the incomplete cancellation of the Hartree self-energy within the $d$ shell by local or gradient corrected density functionals.

Non-Hamiltonian molecular dynamics implementation of the Gibbs ensemble method. I. Algorithm

In this paper (paper I) and the following paper (paper II) [C. Bratschi, H. Huber, and D. J. Searles, J. Chem. Phys. 126, 164105 (2007)], a new molecular dynamics algorithm implementing the Gibbs ensemble will be presented and then on applied to the liquid-vapor coexistence curve for two ab initio CO2 potentials. In paper I, the Gibbs ensemble molecular dynamics algorithm using non-Hamiltonian molecular dynamics techniques is introduced. It is shown that states of the correct probability density function are sampled and the correct exchange probability is generated. The extended system Nose-Hoover formalism is used to generate a constant temperature ensemble with equal pressures in the subsystems, combined with single particle transfers between the subsystems, over several time steps, to get equal chemical potentials.

The performance of nonhybrid density functionals for calculating the structures and spin states of Fe(II) and Fe(III) complexes.

The local density approximation and a range of nonhybrid gradient corrected density functionals (PW91, BLYP, PBE, revPBE, RPBE) have been assessed with respect to the prediction of geometries and spin-state energy preferences for a range of homoleptic Fe(II)L6 and Fe(III)L6 complexes, where L = Cl-, CN-, NH3, pyridine, imidazole, H2O, O=CH2 and tetrahydrofuran. While the qualitative spin-state energies from in vacuo structure optimizations are reasonable the geometries are relatively poorly treated, especially for [FeCl6]3-/4-. Structural results for all the complexes are significantly improved by including environmental effects. The best compromise between structural and spin-state predictive accuracy was obtained for the RPBE functional in combination with the COSMO solvation approach. This approach systematically overestimates the energetic preference for a low spin state, which is partly due to the well-known effect of the lack of exact exchange in nonhybrid functionals and partly due to the larger solvation stabilization of low-spin complexes that have shorter bond lengths and thus smaller molecular volumes than their high-spin partners. Calculations on low spin [Fe(bipy)3]2+ and [Fe(phen)3]2+ and their ortho methyl substituted analogs, which are high spin at room temperature but cross over to low spin at low temperature, suggest the RPBE/COSMO combination generates low spin states which are too stable by approximately 13 kcal mol(-1).

On the prediction of band gaps from hybrid functional theory

Details of the band gap and band widths within materials are of fundamental importance to a wide range of applications. A hybrid scheme is used to predict the band gaps of a variety of materials. The electronic structure of silicon is examined in some detail and comparisons with alternative theories are made. Agreement with experimentally derived band gaps is at least as good as that obtained with sophisticated correlated calculations or perturbation theories. The functional is straightforward to implement, computationally efficient and produces ground state energy surfaces which are significantly more accurate than those computed using the best gradient corrected density functionals currently in use.

Structure function and spectral density of fractal profiles

Spectral density and structure function for fractal profile are analyzed. It is found that the fractal dimension obtained from spectral density is not exactly the same as that obtained from structure function. The fractal dimension of structure function is larger than that of spectral density for small fractal dimension, and is smaller than that of spectral density for larger fractal dimension. The fractal dimension of structure function strongly depends on the spectral density at low and high wave numbers. The spectral density at low wave number affects the structure function at long distance, especially for small fractal dimension. The spectral density at high wave number affects the structure function at short distance, especially for large fractal dimension. This problem is more serious for bifractal profiles. Therefore, in order to obtain a correct fractal dimension, both spectral density and structure function should be checked.