Evaluation of <S2> in density functional theory

The evaluation of in density functional theory (DFT) is considered. Wang et al. [J. Chem. Phys. 102, 3477 (1995)] have derived an approximate, local density expression for and in the present study their formula is evaluated using densities from unrestricted Hartree-Fock (UHF) and a range of DFT exchange-correlation functionals. The results are compared with those obtained by evaluating the conventional UHF expression using the Kohn-Sham orbitals, which is appropriate for the noninteracting system. A generalized gradient approximation for is then proposed and investigated.     

Consequences of spin contamination in unrestricted calculations on open-shell species: effect of Hartree-Fock and Møller-Plesset contributions in hybrid and double-hybrid density functional theory approaches

The extent of spin contamination in unrestricted versions of pure, hybrid and double-hybrid density functional theory (DFT) methods, and its consequences, as manifested in the difference between unrestricted and restricted energies (U - R), has been investigated for 22 homolytic bond dissociation reactions. In accordance with previous studies, increasing the amount of Hartree-Fock (HF) exchange in unrestricted hybrid DFT procedures leads to an increase in the extent of spin contamination. However, in unrestricted double-hybrid DFT procedures, which include both a proportion of HF exchange and a perturbative correlation contribution (MP2), the opposing behavior of UHF and UMP2 with respect to spin contamination leads to smaller differences between the energies predicted by unrestricted and restricted variants. For example, for the most spin-contaminated radicals, a 30-100 kJ mol(-1) |U - R| difference at the HF and MP2 levels is reduced to just 0-5 kJ mol(-1) with the double-hybrid functionals. The double-hybrid UDFT procedures can thus benefit from the inclusion of UHF and UMP2 contributions without incurring to the same extent the problems associated with spin contamination.     

Rotationally invariant ab initio evaluation of Coulomb and exchange parameters for DFT+U calculations

Conventional density functional theory (DFT) fails for strongly correlated electron systems due to large intra-atomic self-interaction errors. The DFT+U method provides a means of overcoming these errors through the use of a parametrized potential that employs an exact treatment of quantum mechanical exchange interactions. The parameters that enter into this potential correspond to the spherically averaged intra-atomic Coulomb (U) and exchange (J) interactions. Recently, we developed an ab initio approach for evaluating these parameters on the basis of unrestricted Hartree-Fock (UHF) theory, which has the advantage of being free of self-interaction errors and does not require experimental input [Mosey and Carter, Phys. Rev. B 76, 155123 (2007)]. In this work, we build on that method to develop a more robust and convenient ab initio approach for evaluating U and J. The new technique employs a relationship between U and J and the Coulomb and exchange integrals evaluated using the entire set of UHF molecular orbitals (MOs) for the system. Employing the entire set of UHF MOs renders the method rotationally invariant and eliminates the difficulty in selecting unambiguously the MOs that correspond to localized states. These aspects overcome two significant deficiencies of our earlier method. The new technique is used to evaluate U and J for Cr(2)O(3), FeO, and Fe(2)O(3). The resulting values of U-J are close to empirical estimates of this quantity for each of these materials and are also similar to results of constrained DFT calculations. DFT+U calculations using the ab initio parameters yield results that are in good agreement with experiment. As such, this method offers a means of performing accurate and fully predictive DFT+U calculations of strongly correlated electron materials.     

Stability and structure in alpha- and beta-Keggin Heteropolytungstates, [X(n)(+)W12O40)](8-n)(-), X = p-block cation

beta-[SiW(12)O(40)](4)(-) (C(3)(v) symmetry) is sufficiently higher in energy than its alpha-isomer analogue that effectively complete conversion to alpha-[SiW(12)O(40)](4)(-) (T(d)) is observed. By contrast, beta- and alpha-[AlW(12)O(40)](5)(-) (beta- and alpha-1; C(3)(v) and T(d), respectively) are sufficiently close in energy that both isomers are readily seen in (27)Al NMR spectra of equilibrated (alpha-beta) mixtures. Recently published DFT calculations ascribe the stability of beta-1 to an electronic effect of the large, electron-donating [AlO(4)](5)(-) (T(d)) moiety encapsulated within the polarizable, fixed-diameter beta-W(12)O(36) (C(3)(v)) shell. Hence, no unique structural distortion of beta-1 is needed or invoked to explain its unprecedented stability. The results of these DFT calculations are confirmed by detailed comparison of the X-ray crystal structure of beta-1 (beta-Cs(4.5)K(0.5)[Al(III)W(12)O(40)].7.5H(2)O; orthorhombic, space group Pmc2(1), a = 16.0441(10) A, b = 13.2270(8) A, c = 20.5919(13) A, Z = 4 (T = 100(2) K)) with previously reported structures of alpha-1, alpha- and beta-[SiW(12)O(40)](4)(-), and beta(1)-[SiMoW(11)O(40)](4)(-).     

DFT performance for the hole transfer parameters in DNA π stacks

Recently, we showed that unoccupied Kohn‐Sham (KS) orbitals stemming from DFT calculations of a neutral system can be used to derive accurate estimates of the free energy and electronic couplings for excess electron transfer in DNA (Félix and Voityuk, J Phys Chem A 2008, 112, 9043). In this article, we consider the propagation of radical cation states (hole transfer) through DNA π‐stacks and compare the performance of different exchange‐correlation functionals to estimate the hole transfer (HT) parameters. Two different approaches are used: (1) calculations that use occupied KS orbitals of neutral π stacks of nucleobases, and (2) the time‐dependent DFT method which is applied to the radical cation states of these stacks. Comparison of the calculated parameters with the reference data suggests that the best results are provided by the KS scheme with hybrid functionals (B3LYP, PBE0, and BH&HLYP). The TD DFT approach gives significantly less accurate values of the HT parameters. In agreement with high‐level ab initio results, the KS scheme predicts that the hole in π stacks is confined to a single nucleobase; in contrast, the spin‐unrestricted DFT method considerably overestimates the hole delocalization in the radical cations. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Epitaxial oxide bilayer on Pt (001) nanofacets

We observed an epitaxial, air-stable, partially registered (2 × 1) oxide bilayer on Pt (001) nanofacets [V. Komanicky, A. Menzel, K.-C. Chang, and H. You, J. Phys. Chem. 109, 23543 (2005)]. The bilayer is made of two half Pt layers; the top layer has four oxygen bonds and the second layer two. The positions and oxidation states of the Pt atoms are determined by analyzing crystal truncation rods and resonance scattering data. The positions of oxygen atoms are determined by density functional theory (DFT) calculations. Partial registry on the nanofacets and the absence of such registry on the extended Pt (001) surface prepared similarly are explained in DFT calculations by strain relief that can be accommodated only by nanoscale facets.     

Time-dependent density-functional theory calculations of triplet-triplet absorption

We present density-functional theory calculations of triplet-triplet absorption by three different approaches based on time-dependent density-functional theory (DFT): unrestricted DFT linear response, open-shell restricted DFT linear response applied to the triplet state, and quadratic response with triplet excitations applied to the ground state. Comparison is also made with corresponding results obtained by Hartree-Fock and multiconfiguration self-consistent-field response theory. Two main conclusions concerning triplet-triplet transitions are drawn in this study: First, the very good agreement between unrestricted and restricted DFT results indicates that spin contamination of the triplet state is not a serious problem when computing triplet-triplet spectra of common organic molecules. Second, DFT response calculations of triplet-triplet transitions can be affected by triplet instability problems, especially for the combination of DFT quadratic response with functionals containing fractional exact Hartree-Fock exchange.     

On the variation of magnetic susceptibility of a molecular crystal with temperature: the 2,4,6-triphenylverdazyl system

Magnetic susceptibilities of spin-1/2 systems of orthorhombic and higher crystal symmetries have been numerically investigated while taking possible anisotropy in the coupling constants along different crystal axes into account. The work relies on the magnon-based theory of ferromagnetic (FM) and antiferromagnetic (AFM) crystal systems of types FFF, AFF, AAF, and AAA [J. Chem. Phys. 111, 9009 (1999)]. The AAF crystal, in particular, shows interesting changes in the temperature dependence of magnetic susceptibility when the ferromagnetic exchange coupling constant is varied. We especially show that the susceptibility anomalies of molecular crystals fit naturally within the framework of the extended magnon-theoretical formalism, and do not necessarily imply a FM --> AFM or a reverse phase transition. A real system, molecular crystal of 2,4,6-triphenylverdazyl (2,4,6-TPV), has been investigated here. It was previously interpreted as an AAF system from observed susceptibility data [Tomiyoshi et al., Phys. Rev. B 49, 16031 (1994)]. The trend of the temperature dependence of magnetic susceptibility studied in the present work also indicates that the crystal belongs to the AAF category with a less prominent FM exchange coupling constant. To reinforce our conclusions, we have adopted a two-pronged strategy. First, the geometry of the 2,4,6-TPV monomer has been optimized here by ab initio unrestricted Hartree-Fock (UHF) calculations using the STO-3G basis set. The optimized geometry is almost planar. A subsequent calculation has been carried out with the phenyl rings twisted out of the plane of the nitrogen atoms. The STO-3G optimized geometry, and the same geometry except for the twisted phenyl rings, have been used to perform ab initio coupled-cluster (UCCSD-T) calculations with the same basis, and UHF as well as density-functional (UB3LYP) calculations using the 6-31G basis set. The calculated data can easily rationalize the twists while the species remains in crystal. The magnetic category of the crystal has been unambiguously confirmed as AFA from ab initio UHF and UB3LYP calculations of the total energy in different spin states of dimers and trimers along the crystal axes. The computed energy values, however, fail to yield accurate estimates of the exchange coupling constants Ja, Jb, and Jc, because the latter are on the order of 1kBK corresponding to energy differences on the order of 10(-6) hartree between different spin states. In the second approach, the observed features of the susceptibility minimum and maximum have been used to determine the best values of the exchange coupling constants from the theoretical formulas for an anisotropic AFA crystal. The AFM (Ja and Jc) and FM (Jb) exchange coupling constants and the Neel temperature (TN) found from this analysis correspond to Ja + Jc = -1.05 kBK, Jb = 1.35 kBK, and TN = 1.75 K. The calculated J values significantly differ from those estimated from a linear Heisenberg chain model, but generate a susceptibility versus temperature graph that mimics the experimental plot.     

Constrained active space unrestricted mean-field methods for controlling spin-contamination

We have recently proposed a novel approach for obtaining high-spin restricted open-shell Hartree-Fock wave functions by imposing constraints on the unrestricted Hartree-Fock (UHF) method [T. Tsuchimochi and G. E. Scuseria, J. Chem. Phys. 133, 141102 (2010)]. We here extend these ideas to the case where the constraints are released in an active space but imposed elsewhere. If the active space is properly chosen, our constrained UHF (CUHF) method greatly benefits from a controlled broken-symmetry effect while avoiding the massive spin contamination of traditional UHF. We also revisit and apply Lo?wdin's projection operator to CUHF and obtain multireference wave functions with moderate computational cost. We report singlet-triplet energy splittings showing that our constrained scheme outperforms fully unrestricted methods. This constrained approach can be readily used in spin density functional theory with similar favorable effects.     

Cage and tube structures of medium-sized zinc oxide clusters (ZnO)n (n=24, 28, 36, and 48)

Following our recent work which revealed that the lowest-energy structures of (ZnO)n (n=9-18) follow cage and tube structural growth patterns with stacks of small subunits of (ZnO)2 and (ZnO)3 [Wang et al., J. Phys. Chem. C 111, 4956 (2007)], we have extended the search for the most stable structures to some larger clusters, i.e., (ZnO)n (n=24, 28, 36, and 48) by using gradient-corrected density-functional theory (DFT). A number of starting configurations belonging to different structural motifs were generated from handmade constructions with chemical intuition and then optimized via DFT calculations. Within the size range studied, cage and tube structures were found to be the most preferred structural motifs for the (ZnO)n clusters.     

Benchmark database of barrier heights for heavy atom transfer, nucleophilic substitution, association, and unimolecular reactions and its use to test theoretical methods

A benchmark database of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions has been developed by using Weizmann 1 calculations, and 29 DFT methods and 6 ab initio wave-function theory (WFT) methods have been tested against the new database as well as against an older database for hydrogen atom transfer reactions. Among the tested hybrid DFT methods without kinetic energy density, MPW1K is the most accurate model for calculations of barrier heights. Among the tested hybrid meta DFT methods, BB1K and MPWB1K are the two most accurate models for the calculations of barrier heights. Overall, the results show that BB1K and MPWB1K are the two best DFT methods for calculating barrier heights, followed in order by MPW1K, MPWKCIS1K, B1B95, MPW1B95, BH and HLYP, B97-2, mPW1PW91, and B98. The popular B3LYP method has a mean unsigned error four times larger than that of BB1K. Of the methods tested, QCISD(T) is the best ab initio WFT method for barrier height calculations, and QCISD is second best, but QCISD is outperformed by the BB1K, MPWB1K, MPWKCIS1K, and MPW1K methods.     

Comparing ab initio density-functional and wave function theories: the impact of correlation on the electronic density and the role of the correlation potential

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order M?ller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.     

A dual-level state-specific time-dependent density-functional theory

A highly efficient new algorithm for time-dependent density-functional theory (TDDFT) calculations is presented. In this algorithm, a dual-level approach to speed up DFT calculations (Nakajima and Hirao, J Chem Phys 2006, 124, 184108) is combined with a state-specific (SS) algorithm for TDDFT (Chiba et al., Chem Phys Lett 2006, 420, 391). The dual-level SS-TDDFT algorithm was applied to excitation energy calculations of typical small molecules, the Q bands of the chlorophyll A molecule, the charge-transfer energy of the zincbacteriochlorin-bacteriochlorin model system, and the lowest-lying excitation of the circumcoronene molecule. As a result, it was found that the dual-level SS-TDDFT gave correct excitation energies with errors of 0.2-0.3 eV from the standard TDDFT approach, with much lower CPU times for various types of excitation energies of large-scale molecules.     

Effects of pressure and temperature on the carrier transports in organic crystal: a first-principles study

By employing density-functional theory coupled with Holstein-Peierls model, we investigate the pressure and temperature dependence of the hole and electron mobilities in naphthalene single crystal from atmospheric pressure up to 2.1 GPa (at room temperature) and from 5 to 296 K (at ambient pressure). It is found that the pressure reduces the electron-phonon coupling strength and enhances the mobilities. Importantly, we point out that only when temperature-dependent structure modifications are taken into account can one better describe the temperature-dependent transport behavior. Especially, the band to hopping crossover transition temperature for the electron transport in the c'-axis is calculated to be around 153 K, which is close to the experimental result of between 100 and 150 K. If this temperature-dependent structure modifications were neglected, the transition temperature would be only about 23 K, as previously obtained [L. J. Wang et al., J. Chem. Phys. 127, 044506 (2007)].     

A global 12-dimensional ab initio potential energy surface and dynamical studies for the SiH4+H-->SiH3+H2 reaction

A global 12-dimensional ab initio interpolated potential energy surface (PES) for the SiH(4)+H-->SiH(3)+H(2) reaction is presented. The ab initio calculations are based on the unrestricted quadratic configuration interaction treatment with all single and double excitations together with the cc-pVTZ basis set, and the modified Shepard interpolation method of Collins and co-workers [K. C. Thompson et al., J. Chem. Phys. 108, 8302 (1998); M. A. Collins, Theor. Chem. Acc. 108, 313 (2002); R. P. A. Bettens and M. A. Collins, J. Chem. Phys. 111, 816 (1999)] is applied. Using this PES, classical trajectory and variational transition state theory calculations have been carried out, and the computed rate constants are in good agreement with the available experimental data.     

A dodecanuclear Zn cluster sandwiched by polyoxometalate ligands

A dodecazinc silicotungstate K(20)Na(2)[Zn(6)(OH)(7)(H(2)O)(Si(2)W(18)O(66))](2)·34H(2)O (1) has been synthesized and characterized by X-ray crystallography, elemental analysis, infrared, UV-vis spectroscopy, cyclic voltammetry, acid-base titration, and DFT calculations. The twelve zinc atoms between the two [Si(2)W(18)O(66)](16-) frameworks make this complex more stable hydrolytically than the heteropolytungstate ligands, [Si(2)W(18)O(66)](16-), themselves. The structurally unique central Zn(12) core is formed by the fusion of two [Zn(6)(OH)(7)(H(2)O)](5+) units through two edge-sharing Zn6 atoms. DFT B3LYP calculations give HOMO-LUMO and (HOMO - 1)-LUMO energy gaps of ～3.65 and 3.91 eV, respectively, as compared to the band gap in ZnO of 3.35 eV.     

Formulation of unrestricted and restricted Hartree–Fock–Bogoliubov equations

The Hartree–Fock–Bogoliubov (HFB) method, dealing with Bogoliubov orbitals, which consist of particle and hole part, can provide states with pair correlations associated with Cooper pairs. The dimension of HFB Fock matrices can be reduced by restrictions of spin states of Bogoliubov orbitals similarly to ordinary Hartree–Fock (HF) equations such as restricted HF (RHF), unrestricted HF (UHF), and generalized HF (GHF). However, there are few studies of moderate restricted HFB equations such as UHF‐based HFB equations. In this article, formulation and calculations of restricted HFB equations are described. The solutions of general and restricted HFB equations are compared. Pair correlations taking account of restricted and general HFB equations are discussed. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2004     

Effect of self-interaction error in the evaluation of the bond length alternation in trans-polyacetylene using density-functional theory

The calculation of the bond-length alternation (BLA) in trans-polyacetylene has been chosen as benchmark to emphasize the effect of the self-interaction error within density-functional theory (DFT). In particular, the BLA of increasingly long acetylene oligomers has been computed using the M?ller-Plesset wave-function method truncated at the second order and several DFT models. While local-density approximation (LDA) or generalized gradient corrected (GGA) functionals strongly underestimate the BLA, approaches including self-interaction corrections (SIC) provide significant improvements. Indeed, the simple averaged-density SIC scheme (ADSIC), recently proposed by Legrand et al. [J. Phys. B 35, 1115 (2002)], provides better results for the structure of large oligomers than the more complex approach of Krieger et al. [Phys. Rev. A 45, 101 (1992)]. The ADSIC method is particularly promising since both the exchange-correlation energy and potential are improved with respect to standard LDA/GGA using a physically appealing correction, through a different route than the more popular approach through the Hartree-Fock exchange inclusion within the hybrid functionals.