Structural and electronic properties of polyyne and cumulene chains with phenylene as central aromatic group: a density functional theory study

Structural Chemistry - The present work studies effects of the introduction of phenylene group as the central aromatic group on the structural and electronic properties of polyyne (Pol-[HCN]2Ph)...     

On the electronic structures and spectroscopic properties of polyyne and its derivatives

We present a theoretical study on the electronic structure and spectroscopic properties of polyyne and its derivatives using periodic density functional theory study and semiempirical ZINDO/s methods. The electronic density of states were calculated, which indicates that polyyne behaves like a semiconductor and the insertion of aromatic groups into the polymer chain gives rise to significant metallic characters in the materials. The vibrational and UV–vis spectra of polyyne and its derivatives were simulated using a monomer or oligomer model. The effects of aromatic insertion into polyyne chain on their electronic and spectroscopic properties were discussed. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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.     

Calculation of electronic g-tensors for transition metal complexes using hybrid density functionals and atomic meanfield spin-orbit operators

We report the first implementation of the calculation of electronic g-tensors by density functional methods with hybrid functionals. Spin-orbit coupling is treated by the atomic meanfield approximation. g-Tensors for a set of small main group radicals and for a series of ten 3d and two 4d transition metal complexes have been compared using the local density approximation (VWN functional), the generalized gradient approximation (BP86 functional), as well as B3-type (B3PW91) and BH-type (BHPW91) hybrid functionals. For main group radicals, the effect of exact-exchange mixing is small. In contrast, significant differences between the various functionals arise for transition metal complexes. As has been shown previously, local and in particular gradient-corrected functionals tend to underestimate the "paramagnetic" contributions to the g-tensors in these cases and thereby recover only about 40-50% of the range of experimental g-tensor components. This is improved to ca. 60% by the B3PW91 functional, which also gives slightly reduced standard deviations. The range increases to almost 100% using the half-and-half functional BHPW91. However, the quality of the correlation with experimental data worsens due to a significant overestimate of some intermediate g-tensor values. The worse performance of the BHPW91 functional in these cases is accompanied by spin contamination. Although none of the functionals tested thus appears to be ideal for the treatment of electronic g-tensors in transition metal complexes, the B3PW91 hybrid functional exhibited the overall most satisfactory performance. Apart from the validation of hybrid functionals, some aspects in the treatment of spin-orbit contributions to the g-tensor are discussed.     

Local hybrid functionals based on density matrix products

We present a novel similarity metric comparing exact and semilocal density functional theory (DFT) exchange holes in real space. This metric is obtained from the product of the one-particle density matrix and the uniform electron gas model density matrix. The metric is bound between 0 and 1, 1 in the uniform electron gas, 0 in regions asymptotically far from finite systems, and can detect delocalization of the exact exchange hole and effective fractional occupations. We also present a parameter-free local hybrid functional that uses this similarity metric to locally mix exact and semilocal DFT exchange energy densities. The resulting functional gives better thermochemistry and reaction barrier heights than our original local hybrids [Jaramillo et al., J. Chem. Phys. 118, 1068 (2003)], while retaining moderate accuracy for symmetric radical cation dimers.     

Ab initio molecular dynamics using hybrid density functionals

Ab initio molecular dynamics simulations with hybrid density functionals have so far found little application due to their computational cost. In this work, an implementation of the Hartree-Fock exchange is presented that is specifically targeted at ab initio molecular dynamics simulations of medium sized systems. We demonstrate that our implementation, which is available as part of the CP2K/Quickstep program, is robust and efficient. Several prescreening techniques lead to a linear scaling cost for integral evaluation and storage. Integral compression techniques allow for in-core calculations on systems containing several thousand basis functions. The massively parallel implementation respects integral symmetry and scales up to hundreds of CPUs using a dynamic load balancing scheme. A time-reversible multiple time step scheme, exploiting the difference in computational efficiency between hybrid and local functionals, brings further time savings. With extensive simulations of liquid water, we demonstrate the ability to perform, for several tens of picoseconds, ab initio molecular dynamics based on hybrid functionals of systems in the condensed phase containing a few thousand Gaussian basis functions.     

Frequency-dependent response properties and excitation energies from one-electron density matrix functionals

The recent formulation of the time-dependent density matrix functional theory (TD-DMFT) has opened an avenue to calculations of frequency-dependent response properties and excitation energies of atoms and molecules. In practice, the accuracy of the computed data is limited by both the errors inherent to the adiabatic approximation or its modifications and the quality of the energy functionals. The relative importance of these two factors is carefully assessed with test calculations on diatomic molecules with few electrons. The test results clearly demonstrate the superiority of an ad hoc approach that corrects the improper behavior of the adiabatic approximation at the low-frequency limit. Even more importantly, TD-DMFT convincingly removes the ambiguity in the choice of the two-electron integrals that is present in the stationary-state case. On the other hand, paralleling the previously reached conclusions pertinent to ionization potentials, the presently available BBC-type functionals are found to be insufficiently accurate to provide reliable quantitative predictions of excitation energies.     

Performance of conventional and range-separated hybrid density functionals in calculations of electronic circular dichroism spectra of transition metal complexes

A number of density functionals, including 'pure' (nonhybrid) functionals, global hybrids, and range-separated hybrids, were used to calculate the electronic circular dichroism (CD) spectra of 10 tris-bidentate transition metal complexes. The results are compared to one another and to experimental CD spectra, in an effort to illustrate the shortcomings of particular approximations in time-dependent density functional theory (TDDFT). The use of an origin invariant formalism to calculate magnetic transition dipole moments with the help of gauge-including atomic orbitals (GIAOs) is also investigated. With valence basis sets of moderate flexibility, good agreement between GIAO results and rotatory strengths calculated from the dipole-velocity representation is obtained for selected test cases. Empirically broadened vertical CD spectra calculated with the global hybrid functionals B3LYP and PBE0 are found to agree overall the best with experimental CD spectra.     

Some formal properties of ensemble density functionals

Formal properties of ensemble density functionals are examined. Expressions for the difference between energy functionals where the particle number differs by one are constructed in terms of their first functional derivatives for the universal energy functional, the electron–electron repulsion energy functional, and the interacting kinetic energy functional. Equations that must be satisfied by second and higher order functional derivatives are derived. It is also shown that the shape of ${\delta V_{ee}[\rho]\over\delta\rho({\bf r})}$ and ${\delta K[\rho]\over\delta\rho({\bf r})}$ , the functional derivatives of the mutual electron–electron repulsion, and kinetic energy, respectively, are separately particle number independent for particle numbers between successive integers. © 2013 Wiley Periodicals, Inc.     

The importance of middle-range Hartree-Fock-type exchange for hybrid density functionals

Hybrid functionals are responsible for much of the utility of modern Kohn-Sham density functional theory. When rigorously applied to solid-state metallic and small band gap systems, however, the slow decay of their nonlocal Hartree-Fock-type exchange makes hybrids computationally challenging and introduces unphysical effects. This can be remedied by using a range-separated hybrid which only keeps short-range nonlocal exchange, as in the functional of Heyd et al. [J. Chem. Phys. 118, 8207 (2003)]. On the other hand, many molecular properties require full long-range nonlocal exchange, which can also be included by means of a range-separated hybrid such as the recently introduced LC-omegaPBE functional [O. A. Vydrov and G. E. Scuseria, J. Chem. Phys. 125, 234109 (2006)]. In this paper, we show that a three-range hybrid which mainly includes middle-range Hartree-Fock-type exchange and neglects long- and short-range Hartree-Fock-type exchange yields excellent accuracy for thermochemistry, barrier heights, and band gaps, emphasizing that the middle-range part of the 1/r potential seems crucial to accurately model these properties.     

Molecular dynamics simulation of liquid water: hybrid density functionals

The structure, dynamical, and electronic properties of liquid water utilizing different hybrid density functionals were tested within the plane wave framework of first-principles molecular dynamics simulations. The computational approach, which employs modified functionals with short-ranged Hartree-Fock exchange, was first tested in calculations of the structural and bonding properties of the water dimer and cyclic water trimer. Liquid water simulations were performed at the state point of 350 K at the experimental density. Simulations included three different hybrid functionals, a meta-functional, four gradient-corrected functionals, and the local density and Hartree-Fock approximations. It is found that hybrid functionals are superior in reproducing the experimental structure and dynamical properties as measured by the radial distribution function and self-diffusion constant when compared to the pure density functionals. The local density and Hartree-Fock approximations show strongly over- and understructured liquids, respectively. Hydrogen bond analysis shows that the hybrid functionals give slightly smaller average numbers of hydrogen bonds than pure density functionals but similar hydrogen bond populations. The average molecular dipole moments in the liquid from the three hybrid functionals are lower than those of the corresponding pure density functionals.     

Many-electron self-interaction and spin polarization errors in local hybrid density functionals

Errors for systems with noninteger occupation have been connected to common failures of density functionals. Previously, global hybrids and pure density functionals have been investigated for systems with noninteger charge and noninteger spin state. Local hybrids have not been investigated for either of those systems to the best of our knowledge. This study intends to close this gap. We investigate systems with noninteger charge to assess the many-electron self-interaction error and systems with noninteger spin state to assess the spin polarization error of recently proposed local hybrids and their range-separated variants. We find that long-range correction is very important to correct for many-electron self-interaction error in cations, whereas most full-range local hybrids seem to be sufficient for anions, where long-range-corrected density functionals tend to overcorrect. On the other hand, while all hitherto proposed long-range-corrected density functionals show large spin polarization errors, the Perdew-Staroverov-Tao-Scuseria (PSTS) functional performs best of all local hybrids in this case and shows an outstanding behavior for the dependence of the energy on the spin polarization.     

Long-range corrected hybrid density functionals with damped atom-atom dispersion corrections

We report re-optimization of a recently proposed long-range corrected (LC) hybrid density functional [J.-D. Chai and M. Head-Gordon, J. Chem. Phys., 2008, 128, 084106] to include empirical atom-atom dispersion corrections. The resulting functional, omegaB97X-D yields satisfactory accuracy for thermochemistry, kinetics, and non-covalent interactions. Tests show that for non-covalent systems, omegaB97X-D shows slight improvement over other empirical dispersion-corrected density functionals, while for covalent systems and kinetics it performs noticeably better. Relative to our previous functionals, such as omegaB97X, the new functional is significantly superior for non-bonded interactions, and very similar in performance for bonded interactions.     

Ab initio calculation of the electronic absorption of functionalized octahedral silsesquioxanes via time-dependent density functional theory with range-separated hybrid functionals

Recent advances in the ability to functionalize octahedral silsesquioxanes with different photoactive ligands, and thereby tune their optical properties, suggest that these molecules may serve as potential building blocks of light-harvesting, photovoltaic, and photonic devices. In this paper we report extensive ab initio calculations of the excitation energies underlying the absorption spectra of these systems. The calculations are based on density functional theory for the ground electronic state and time-dependent density functional theory for the excited electronic states. The ability of the commonly used B3LYP functional to reproduce the experimentally observed absorption excitation energies is compared to that of recently developed range-separated hybrid functionals. The importance of pairing the range-separated hybrid functionals with basis sets that include diffuse and polarization basis functions is demonstrated in the case of vinyl-functionalized silsesquioxanes. Absorptive excitation energies are then calculated and compared with experiment for octahedral silsesquioxanes functionalized with larger ligands. The tunability of optical properties is demonstrated by considering the effect on the excitation energies of functionalizing the ligands with electron-donating or -withdrawing groups.     

硫化聚乙炔结构对其电子性能的影响

本文用硫原子和共轭多烯的复合物模拟硫化聚乙炔结构, 并采用一维紧束缚的LCAO-SCF-MO法, 探讨了硫化聚乙炔结构对其电子性能的影响, 揭示出影响的原因, 确定了最佳结构, 为实验合成提供了理论依据。     

Efficient time-dependent density functional theory approximations for hybrid density functionals: analytical gradients and parallelization

In this paper, we present the implementation of efficient approximations to time-dependent density functional theory (TDDFT) within the Tamm-Dancoff approximation (TDA) for hybrid density functionals. For the calculation of the TDDFT/TDA excitation energies and analytical gradients, we combine the resolution of identity (RI-J) algorithm for the computation of the Coulomb terms and the recently introduced "chain of spheres exchange" (COSX) algorithm for the calculation of the exchange terms. It is shown that for extended basis sets, the RIJCOSX approximation leads to speedups of up to 2 orders of magnitude compared to traditional methods, as demonstrated for hydrocarbon chains. The accuracy of the adiabatic transition energies, excited state structures, and vibrational frequencies is assessed on a set of 27 excited states for 25 molecules with the configuration interaction singles and hybrid TDDFT/TDA methods using various basis sets. Compared to the canonical values, the typical error in transition energies is of the order of 0.01 eV. Similar to the ground-state results, excited state equilibrium geometries differ by less than 0.3 pm in the bond distances and 0.5° in the bond angles from the canonical values. The typical error in the calculated excited state normal coordinate displacements is of the order of 0.01, and relative error in the calculated excited state vibrational frequencies is less than 1%. The errors introduced by the RIJCOSX approximation are, thus, insignificant compared to the errors related to the approximate nature of the TDDFT methods and basis set truncation. For TDDFT/TDA energy and gradient calculations on Ag-TB2-helicate (156 atoms, 2732 basis functions), it is demonstrated that the COSX algorithm parallelizes almost perfectly (speedup ~26-29 for 30 processors). The exchange-correlation terms also parallelize well (speedup ~27-29 for 30 processors). The solution of the Z-vector equations shows a speedup of ~24 on 30 processors. The parallelization efficiency for the Coulomb terms can be somewhat smaller (speedup ~15-25 for 30 processors), but their contribution to the total calculation time is small. Thus, the parallel program completes a Becke3-Lee-Yang-Parr energy and gradient calculation on the Ag-TB2-helicate in less than 4 h on 30 processors. We also present the necessary extension of the Lagrangian formalism, which enables the calculation of the TDDFT excited state properties in the frozen-core approximation. The algorithms described in this work are implemented into the ORCA electronic structure system.     

Structural and electronic properties of heptachlor

In this work, the molecular geometry of heptachlor is investigated using ab initio HF, DFT, LDA, and GGA methods. The natural bond orbital (NBO) analysis is performed at the B3LYP/6-311++G(d,p) level of theory. The first order hyperpolarizability β_total, the mean polarizability Δα, the anisotropy of the polarizability Δα, and the dipole moment μ, are calculated by B3LYP/6-311++G(d,p) and HF/6- 311++G(d,p) methods. The first order hyperpolarizability (β_total) is calculated based on the finite field approach. UV spectral parameters along with HOMO, LUMO energies for heptachlor are determined in vacuum and the solvent phase using HF, DFT, and TD-DFT/B3LYP methods implemented with the 6-311++G(d,p) basis set. Atomic charges and electron density of heptachlor in vacuum and ethanol are calculated using DFT/B3LYP and TD-DFT/B3LYP methods and the 6-311++G(d,p) basis set. In addition, after the frontier molecular orbitals (FMOs), the molecular electrostatic potential (MEP), the electrostatic potential (ESP), the electron density (ED), and the solvent accessible surface of heptachlor are visualized as a results of the B3LYP/6-311++G(d,p) calculation. Densities of states (DOS), the external electric field (EF) effect on the HOMO-LUMO gap, and the dipole moment are investigated by LDA and GGA methods.     

The performance of semilocal and hybrid density functionals in 3d transition-metal chemistry

We investigate the performance of contemporary semilocal and hybrid density functionals for bond energetics, structures, dipole moments, and harmonic frequencies of 3d transition-metal (TM) compounds by comparison with gas-phase experiments. Special attention is given to the nonempirical metageneralized gradient approximation (meta-GGA) of Tao, Perdew, Staroverov, and Scuseria (TPSS) [Phys. Rev. Lett. 91, 146401 (2003)], which has been implemented in TURBOMOLE for the present work. Trends and error patterns for classes of homologous compounds are analyzed, including dimers, monohydrides, mononitrides, monoxides, monofluorides, polyatomic oxides and halogenides, carbonyls, and complexes with organic pi ligands such as benzene and cyclopentadienyl. Weakly bound systems such as Ca(2), Mn(2), and Zn(2) are discussed. We propose a reference set of reaction energies for benchmark purposes. Our all-electron results with quadruple zeta valence basis sets validate semilocal density-functional theory as the workhorse of computational TM chemistry. Typical errors in bond energies are substantially larger than in (organic) main group chemistry, however. The Becke-Perdew'86 [Phys. Rev. A 38, 3098 (1988); Phys. Rev. B 33, 8822 (1986)] GGA and the TPSS meta-GGA have the best price/performance ratio, while the TPSS hybrid functional achieves a slightly lower mean absolute error in bond energies. The popular Becke three-parameter hybrid B3LYP underbinds significantly and tends to overestimate bond distances; we give a possible explanation for this. We further show that hybrid mixing does not reduce the width of the error distribution on our reference set. The error of a functional for the s-d transfer energy of a TM atom does not predict its error for TM bond energies and bond lengths. For semilocal functionals, self-interaction error in one- and three-electron bonds appears to be a major source of error in TM reaction energies. Nevertheless, TPSS predicts the correct ground-state symmetry in the vast majority of cases and rarely fails qualitatively. This further confirms TPSS as a general purpose functional that works throughout the periodic table. We also give workstation timing comparisons for the 645-atom protein crambin.