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Theoretical and Computational Aspects of the Optimized Effective Potential Approach within Density Functional TheoryHeaton-Burgess, Tim January 2009 (has links)
<p>The computational success of density functional theory relies on the construction of suitable approximations to the exchange-correlation energy functional. Use of functional approximations depending explicitly upon the density alone appear unable to address all aspects of many-body interactions, such as the fundamental constraint that the ground state energy is a piecewise linear function of the total number of electrons, and the ability to model nonlocal effects. Functionals depending explicitly upon occupied and unoccupied Kohn–Sham orbitals are considered necessary to address these and other issues. This dissertation considers certain issues relevant to the successful implementation of explicitly orbital-dependent functionals through the optimized effective potential (OEP) approach, as well as extending the potential functional formalism that provides the formal basis for the OEP approach to systems in the presence of noncollinear magnetic fields.</p><p>The self-consistent implementation of orbital-dependent energy functionals is correctly done through the optimized effective potential approach—minimization of the ground state energy with respect to the Kohn–Sham potential that generates the set of orbitals employed in the energy evaluation. The focus on the potential can be problematic in finite basis set approaches as determining the exchange-correlation potential in this manner is an inverse problem which, depending upon the combination of orbital and potential basis sets employed, is often ill-posed. The ill-posed nature manifests itself as nonphysical exchange-correlation potentials and total energies. We address the problem of determining meaningful exchange-correlation potentials for arbitrary combinations of orbital and potential basis sets through an L-curve regularization approach based on biasing towards smooth potentials in the energy minimization. This approach generates physically reasonable potentials for any combination of basis sets as shown by comparisons with grid-based OEP calculations on atoms, and through direct comparison with DFT calculations employing functionals not depending on orbitals for which OEP can also be performed. This work ensures that the OEP methodology can be considered a viable many-body computational methodology.</p><p>A separate issue of our OEP implementation is that it can suffer from a lack of size-extensivity—the total energy of a system of infinitely separated monomers may not scale linearly with the total number of monomers depending upon how we construct the Kohn–Sham potential. Typically, a fixed reference potential is employed to aid in the convergence of a finite basis set expansion of the Kohn–Sham potential. This reference potential can be utilized to ensure other desirable properties of the resulting potential. In particular, it can enforce the correct asymptotic behavior. The Fermi–Amaldi potential is often used for this purpose but suffers from size-nonextensivity owing to the explicit dependence of the potential on the total number of electrons. This error is examined and shown to be rather small and rapidly approaches a limiting linear behavior. A size-extensive reference potential with the correct asymptotic behavior is suggested and examined.</p><p>We also consider a formal aspect of the potential-based approach that provides the underlying justification of the OEP methodology. The potential functional formalism of Yang, Ayers, and Wu is extended to include systems in the presence of noncollinear magnetic fields. In doing so, a solution to the nonuniqueness issue associated with mapping between potentials and wave functions in such systems is provided, and a computational implementation of the OEP in noncollinear systems is suggested.</p><p>Finally, as an example of an issue for which orbital-dependent functionals seem necessary to obtain a correct description, we consider the ground state structures of C<sub>4<italic>N</italic> + 2</sub> rings which are believed to exhibit a geometric transition from angle-alternation (<italic>N</italic> ≤ 2) to bond-alternation (<italic>N</italic> > 2). So far, no published DFT approach has been able to reproduce this behavior owing to the tendency of common density functional approximations to bias towards delocalized electron densities. Calculations are presented with the rCAM-B3LYP exchange-correlation functional that correctly predict the structural evolution of this system. This is rationalized in terms of the recently proposed delocalization error for which rCAM-B3LYP explicitly attempts to address.</p> / Dissertation
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Mechanical behaviors and Electronic Properties of Boron Nitride Nanotubes under the Axial Strain.Lien, Ting-Wei 06 September 2010 (has links)
In this study, we used the Density functional theory (DFT) to obtain the relationship between mechanical property and electronic property of Boron nitride nanotubes (BNNTs) under the uni-axial strain. Moreover, we also investigated one CO molecule adsorbed on the BNNTs under the uni-axial strain. We also use the molecular dynamics to introduce the mechanical property and dynamic behavior of (8,8)BNNT under the uni-axial strain. There were three parts in this study:
The first part:
The effect of uni-axial strain on the electronic properties of (5,5) and (8,0)boron nitride nanotubes were obtained by DFT calculation. We used the HOMO-LUMO Gap¡Bbond angle¡Bbond length and radial buckling to analyze the electronic properties and mechanical properties. The stress-strain profiles indicated that different BNNTs types displayed very similar mechanical properties, but there were variations in HOMO-LUMO gaps at different strains, indicating that the electronic properties of BNNTs not only depend on uni-axial strain, but on BNNT type. In addition, the variations in nanotube geometries, partial density of states (PDOS) and charges of boron and nitride atoms were also discussed for (8,0) and (5,5) BNNTs at different strains.
The second part:
The DFT was used to investigate electronic properties of CO molecule adsorbed on BNNT under the uni-axial strain. The stress-strain profiles indicated that the CO molecule adsorption on BNNT leaded only to a local mechanical deformation. The strength of BNNT could not be affected when the CO molecule adsorbed on that. Moreover, we obtained that the charge of CO will slightly transfer to the adsorbed atom of BNNT when strain increased. Hence, the adsorption energy increased slightly under the uni-axial strain.
The third part:
The molecular dynamics simulations were performed to investigate deformation behaviors of (8,8)BN nanotubes under axial tensile strains at 300k. Variations with the tensile strain in the axial stress, bond lengths, bond angles, radial buckling, and slip vectors were all examined. The axial, radial, and tangential components of the slip vector were also employed to monitor, respectively, the local elongation, necking, and twisting deformation near the failure of the nanotube. The components of the slip vector grew rapidly and abruptly after the failure strain, especially for the axial component. This implies that the local elongation dominates the failure of the loaded BN nanotube and finally results in a chain-like tensile failure mode.
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Study on mechanical and electronic properties of one-dimensional zinc oxide nanostructure by Molecular Dynamics and Density Functional TheoryLee, Chia-Hung 08 September 2010 (has links)
In this study, we employed density functional theory (DFT) and molecular dynamics (MD) to investigate the mechanical and electronic properties of one-dimensional zinc oxide nanostructure. This study can be arranged into two parts:
In part I: We investigated the mechanical and electronic properties of one-dimensional zinc oxide nanostructure under axial mechanical deformations by density functional theory. In this case, we could find both the highest occupied molecular orbital and the lowest unoccupied molecular orbital gap (HOMO-LUMO gap) and value of radial buckling will decrease linearly with the increase of axial strain. The changes of bond lengths and bond angles show the variation of nanostructure dependence to the increase of axial strain. This study also used partial density of state (PDOS), bond order (BO) and deformation density to analyse the differences of the electronic properties between the zinc oxide nanotubes under axial strain.
In part II: This study, which employed molecular dynamics combines Buckingham and Core-Shell potentials, shows the different physical parameters, such as yield stress, young¡¦s modulus and slip vector to research the mechanical behavior and variation of structure of nanotube under axial strain.
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The Study of Molecular Mechanics and Density Functional Theory on Structural and Electronic Properties of Tungsten nanoparticlesLin, Ken-Huang 09 September 2010 (has links)
The structural and electronic properties of small tungsten nanoparticles Wn (n=2-16) were investigated by density functional theory (DFT) calculation. For the W10 nanoparticle, ten lowest-energy structures were first obtained by basin-hopping method (BH) and ten by big-bang method (BB) with the tight-binding many-body potential for bulk tungsten material. These fifty structures were further optimized by the DFT calculation in order to find the better parameters of tight-binding potential adquately for W nanoparticles. With these modified parameters of tight-binding potentials, several lowest-energy W nanoparticles of different sizes can be obtained by BH and BB methods and then further refined by DFT calculation. According to the values of binding energy and second-order energy difference, it reveals that the structure W12 has a relatively higher stability than those of other sizes. The vertical ionization potential (VIP), adiabatic electron affinity (AEA) and HOMO-LUMO Gap are also discussed for W nanoparticles of different sizes.
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Mechanical and Electronic Properties of the Ultra-thin Silica NanowiresLin, Kuan-Fu 29 August 2011 (has links)
In this study, we used the molecular statics, molecular dynamics, and density function theory to investigate structural, electronic, and mechanical properties of ultra-thin silica nanowires. There are two parts in this study. In the first part, we used basin-hopping method to get different diameters of silica nanowires, nemed 2MR, 2MR-2O, 3MR-3O, 4MR-4O, 5MR-5O, 4MR-3f, 4MR-4f, and 4MR-5f. The various silica nanowires were optimized by density function theory to obtain the projected density of states, Mulliken charge, and electronic density difference, and we also compared this results to £\-quartz. In the second part, the molecular dynamics simulations were performed to investigate deformation behavior of silica nanowires under axial tensile loading at 10K. The Young¡¦s modulus increases when the diameter decreases. We also
used angular correlation function to study the mechanical properties and variation of structures.
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Hydrogen storage and delivery mechanism of metal nanoclusters on a nanosheetHuang, Li-Fan 19 January 2012 (has links)
In this study, we used the Density functional theory (DFT) and Molecular dynamics (MD) to obtain the suitable hydrogen storage structure of Rh nanoclusters on the boron nitride sheet and Li atoms on the graphene. The reason of studying two type of nanoparticles is that there are two adsorption method in hydrogen storage, such as the adsorption of hydrogen molecules and hydrogen atoms. Using Rh nanoclusters on the boron nitride sheet to store hydrogen belong to the adsorption of hydrogen atoms. Using Li atoms on the graphene to store hydrogen belong to the adsorption of hydrogen molecules. We use these two models to simulate the hydrogen storage in this study. There were four parts in this study:
The first part:
The Density functional theory is utilized to obtain the configuration and corresponding energy of Rh nanoclusters, boron nitride sheet, Rh nanoclusters adsorbed on the boron nitride sheet, Li atoms adsorbed on the graphene, hydrogen adsorbed on the graphene and hydrogen adsorbed on the Li atoms. Then, we use the Force-matching method (FMM) to modify the parameters of potential function by the reference data which are obtained by Density functional theory. Finally, we use the modified parameters of potential function to perform Molecular dynamics in this study.
The second part:
In this part, the dynamical behavior of Rh nanoclusters with different sizes on the boron nitride sheet are investigated in temperature-rise period. The migration trajectory, square displacement and mean square displacement of the mass center of the Rh nanoclusters are used to analyze the dynamics behavior of Rh nanoclusters on the boron nitride sheet.
The third part:
In this part, the pristine graphene and graphen with Li atoms are investigated the efficiency of hydrogen storage at different temperature and pressure. In order to obtain the temperature (77K and 300K) and pressure effect of hydrogen storage, the densimetric distribution and gravimetric capacity (wt%) are analyzed.
The fourth part:
The Molecular dynamics is utilized to study the hydrogen storage and delivery when the distance between two graphene is different. Then, the temperature effect (77K and 300K) of hydrogen storage, the gravimetric capacity (wt%) are analyzed. In addition, the gravimetric capacity (wt%) of hydrogen delivery are also analyzed in the larger system space at 300K.
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Adsorption, dissociation and diffusion behaviors of hydrogen molecule on ultrathin Pd nanowires : the density functional theory studyHuang, Wen-Cheng 21 July 2012 (has links)
In this study, the structures of two ultrathin Pd nanowires were predicted by the simulated annealing basin-hopping method (SABH) with the tight-binding potential. The thermal stability of the Pd wires and adsorption, dissociation and diffusion behaviors were further examined by the density functional theory (DFT) calculation and DFT molecular dynamics (DFT-MD) simulation. In terms of thermal stability, these two Pd nanowires are still very stable at temperatures as high as 400 K. The configurations and adsorption energy have been calculated for H atom and H2 molecular adsorption on Pd nanowires. The minimum energy pathways and transition states of H2 molecular dissociation and H atom diffusion process on Pd nanowires were studied by the nudged elastic band (NEB) method. For the dissociation of hydrogen molecules, results show the dissociation is almost barrierless so the dissociation is easy to occur at very low temperatures, and their catalytic reactivity is very similar to the Pd bulk material. The thermal stability of the H atom within these Pd nanowires were also investigated by DFT-MD, with results showing that the H atom can only stay within Pd nanowires at temperatures much lower than room temperature (298 K). This phenomenon is very different from that of H atoms within Pd bulk material or other reported nanomaterials, leading to hydrogen embrittlement. Our results reveal that these two ultrathin Pd nanowires not only possess the same excellent catalytic activity for hydrogen molecules as the bulk Pd materials or other Pd nanomaterials do, but also avoid the hydrogen embrittlement occur.
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Understanding mechanisms for C-H bond activationVastine, Benjamin Alan 15 May 2009 (has links)
The results from density functional theory (DFT) studies into C–H bond
activation, hydrogen transfer, and alkyne–to–vinylidene isomerization are presented in
this work.
The reaction mechanism for the reductive elimination (RE) of methane from [ κ3-
TpPtIV(CH3)2H (1)] (Tp = hydridotris(pyrazolyl)borate) by oxidative addition (OA) of
benzene to form [ κ3-TpPtIV(Ph)2H] (19) was investigated through DFT calculations.
For 31 density functionals, the calculated values for the barriers to methane formation
(Ba1) and release (Ba2) from 1 were benchmarked against the experimentally reported
values of 26 (Ba1) and 35 (Ba2) kcal•mol-1, respectively. The values for Ba1 and Ba2,
calculated at the B3LYP/DZP level of theory, are 24.6 and 34.3 kcal•mol-1, respectively.
The best performing functional was BPW91 where the m.a.e. for the calculated values
of the two barriers is 0.68 kcal•mol-1.
Classic and newly proposed mechanisms for metal-mediated hydrogen transfer
(HT) were analyzed with density functional theory (DFT) and Bader's "Atoms In
Molecules" (AIM) analysis. Seven sets of bonding patterns that characterize theconnectivity in metal-mediate HT were found from the analysis of representative
models for σ-bond metathesis ( σBM), oxidative addition / reductive elimination
(OA/RE), and alternative mechanisms.
The mechanism for the formation of the alkynyl, vinylidene complex,
[(PiPr3)2Rh(CCPh)(CC(H)(Ph))] (2), by the addition of two equivalents of
phenylacetylene (PA) to [( η3-C3H5)Rh(PiPr3)2] (1) was studied through DFT
calculations. Two experimentally observed intermediates on the reaction coordinate are
the η2-PA, alkynyl complex, [(PiPr3)2Rh( η2-HCCPh)(CCPh)] (Ia) and the fivecoordinate,
pseudo square-pyramidal, RhIII–H complex, [(PiPr3)2Rh(H)(CCPh)2] (Ib),
and were found to be in equilibrium. The relative energies of Ia, Ib, and 2 (relative to 1
+ 2PA) depend on the phosphine that was used in the calculation; the predicted product
is 2 with PiPr3 and PEt3 but Ia with PMe3, PMe2Ph, PMePh2, PPh3, and PH3. The
equilibrium between Ia and Ib was calculated with PEt3 and one conformation of PiPr3.
We investigated the mechanism for the formation of 2 from Ia, and a lower energy
pathway where the π-bound PA of Ia slips to bind through the σ-C–H bond prior to the
formation of 2 through hydrogen migration was found.
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Intramolecular electronic communication between dimetal units with multiple metal??al bondsLi, Zhong 15 May 2009 (has links)
No description available.
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Theoretical Studies of Structures and Mechanisms in Organometallic and Bioinorganic Chemistry: Heck Reaction with Palladium Phosphines, Active Sites of Superoxide Reductase and Cytochrome P450 Monooxygenase, and Tetrairon Hexathiolate Hydrogenase ModelSurawatanawong, Panida 2009 May 1900 (has links)
The electronic structures and reaction mechanisms of transition-metal complexes
can be calculated accurately by density functional theory (DFT) in cooperation with the
continuum solvation model. The palladium catalyzed Heck reaction, iron-model
complexes for cytochrome P450 and superoxide reductase (SOR), and tetrairon
hexathiolate hydrogenase model were investigated.
The DFT calculations on the catalytic Heck reaction (between phenyl-bromide
and ethylene to form the styrene product), catalyzed by palladium diphosphine indicate a
four-step mechanism: oxidative addition of C6H5Br, migratory insertion of C6H5 to
C2H4, b-hydride transfer/olefin elimination of styrene product, and catalyst regeneration
by removal of HBr. For the oxidative addition, the rate-determining step, the reaction
through monophosphinopalladium complex is more favorable than that through either
the diphosphinopalladium or ethylene-bound monophosphinopalladium. In further
study, for a steric phosphine, PtBu3, the oxidative-addition barrier is lower on monopalladium monophosphine than dipalladium diphosphine whereas for a small
phosphine, PMe3, the oxidative addition proceeds more easily via dipalladium
diphosphine. Of the phosphine-free palladium complexes examined: free-Pd, PdBr-, and
Pd(h2-C2H4), the olefin-coordinated intermediate has the lowest barrier for the oxidativeaddition.
P450 and SOR have the same first-coordination-sphere, Fe[N4S], at their active
sites but proceed through different reaction paths. The different ground spin states of the
intermediate FeIII(OOH)(SCH3)(L) model {L = porphyrin for P450 and four imidazoles
for SOR} produce geometric and electronic structures that assist i) the protonation on
distal oxygen for P450, which leads to O-O bond cleavage and formation of
(FeIV=O)(SCH3)(L) H2O, and ii) the protonation on proximal oxygen for SOR, which
leads to (FeIII-HOOH)(SCH3)(L) formation before the Fe-O bond cleavage and H2O2
production. The hydrogen bonding from explicit waters also stabilizes FeIII-HOOH over
FeIV=O H2O products in SOR.
The electrochemical hydrogen production by Fe4[MeC(CH2S)3]2(CO)8 (1) with
2,6-dimethylpyridinium (LutH ) were studied by the DFT calculations of proton-transfer
free energies relative to LutH and reduction potentials (vs. Fc/Fc ) of possible
intermediates. In hydrogen production by 1, the second, more highly reductive, applied
potential (-1.58 V) has the advantage over the first applied potential (-1.22 V) in that the
more highly reduced intermediates can more easily add protons to produce H2.
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