Time-dependent density functional theory for nonlinear properties of open-shell systems

This paper presents response theory based on a spin-restricted Kohn-Sham formalism for computation of time-dependent and time-independent nonlinear properties of molecules with a high spin ground state. The developed approach is capable to handle arbitrary perturbations and constitutes an efficient procedure for evaluation of electric, magnetic, and mixed properties. Apart from presenting the derivation of the proposed approach, we show results from illustrating calculations of static and dynamic hyperpolarizabilities of small Si(3n+1)H(6n+3) (n=0,1,2) clusters which mimic Si(111) surfaces with dangling bond defects. The results indicate that the first hyperpolarizability tensor components of Si(3n+1)H(6n+3) have an ordering compatible with the measurements of second harmonic generation in SiO2/Si(111) interfaces and, therefore, support the hypothesis that silicon surface defects with dangling bonds are responsible for this phenomenon. The results exhibit a strong dependence on the quality of basis set and exchange-correlation functional, showing that an appropriate set of diffuse functions is required for reliable predictions of the first hyperpolarizability of open-shell compounds.     

The trans effect in square-planar platinum(II) complexes--a density functional study

The mechanism of substitution water exchange reactions in square planar trans-Pt[(NH(3))(2)T(H(2)O)](n+) complexes is studied (T = H(2)O, NH(3), OH(-), F(-), Cl(-), Br(-), H(2)S, CH(3)S(-), SCN(-), CN(-), PH(3), CO, CH(3)(-), H(-), C(2)H(4)). The trans effect is explained in terms of sigma-donation and pi-back-donation whose relative strengths are quantified by the changes of electron occupations of 5d platinum atomic orbitals. The sigma-donation strength is linearly correlated with the Pt-H(2)O (leaving ligand) bond length (trans influence). The kinetic trans effect strength correlates proportionally with the sigma-donation ability of the trans-ligand except the ligands with strong pi-back-donation ability that stabilizes transition state structure. The sigma-donation ability of the ligand is dependent on the sigma-donation strength of the ligand in the trans position. Therefore the trans effect caused by sigma-donation can be understood as a competition between the trans-ligands for the opportunity to donate electron density to the central Pt(II) atom. The influence of the trans effect on the reaction mechanism is also shown. For ligands with a very strong sigma-donation (e.g. CH(3)(-) and H(-)), the substitution proceeds by a dissociative interchange (I(d)) mechanism. Ligands with strong pi-back donation ability (e.g. C(2)H(4)) stabilize the pentacoordinated intermediate and the substitution proceeds by a two step associative mechanism. For ligands with weak sigma-donation and pi-back-donation abilities, the highest activation barriers have to be overcome and substitutions can be described by an associative interchange (I(a)) mechanism. The results are supported by the energy decomposition and the natural orbital analysis.     

Time-dependent density functional theory study of charge transfer in collisions

We study the charge transfer between colliding ions, atoms, or molecules, within time-dependent density functional theory. Two particular cases are presented, the collision between a proton and a Helium atom, and between a gold atom and a butane molecule. In the first case, proton kinetic energies between 16?keV and 1.2?MeV are considered, with impact parameters between 0.31 and 1.9 ?. The partial transfer of charge is monitored with time. The total cross-section is obtained as a function of the proton kinetic energy. In the second case, we analyze one trajectory and discuss spin-dependent charge transfer between the different fragments.     

Time-dependent density functional theory study on optical properties of GaN doped with alkaline-earth atom

The absorption and the emission spectra of GaN and (Ga,AE)N (AE = Be, Mg, Ca) were calculated by using TDDFT method with cluster model. The calculation results show that Ga₂₆N₂₆H₅₀ cluster only has very weak absorption but has some emission bands in visible region. The band-to-band emission appears around 3.56 eV. If alkaline-earth atoms (Be, Mg and Ca) are doped into GaN, the blue emission band around 3.0 eV appears. Thereinto, Ga₂₅Ca₁N₂₆H₅₀ cluster shows a weaker yellow emission band and a stronger blue one (2.92 eV), which make (Ga,Ca)N material a promising candidate to emit blue light.     

Time-dependent density functional theory study of Fe2(CO)9 low-lying electronic excited states

The valence electronic excited states of Fe2(CO)9 have been studied using the time-dependent density functional theory (TDDFT). Both tribridged D3h and monobridged C2v structures have been considered, and the structure of selected low-lying singlet and triplet excited states have been optimized on the basis of the TDDFT analytical gradient. Optimized excited-state geometries are used to obtain an insight into certain aspects of the Fe2(CO)9 photochemistry. The Fe2(CO)9 (D3h) first triplet and second singlet excited states are unbound with respect to dibridged Fe2(CO)8 + CO, and the first two monobridged Fe2(CO)9 (C2v) singlet states are unbound with respect to the Fe(CO)5 + Fe(CO)4 dissociation. These results are discussed in light of the experimental data available.     

A density functional theory study of the benzene-water complex

The intermolecular interaction of the benzene-water complex is calculated using real-space pseudopotential density functional theory utilizing a van der Waals density functional. Our results for the intermolecular potential energy surface clearly show a stable configuration with the water molecule standing above or below the benzene with one or both of the H atoms pointing toward the benzene plane, as predicted by previous studies. However, when the water molecule is pulled outside the perimeter of the ring, the configuration of the complex becomes unstable, with the water molecule attaching in a saddle point configuration to the rim of the benzene with its O atom adjacent to a benzene H. We find that this structural change is connected to a change in interaction from H (water)/pi cloud (benzene) to O (water)/H (benzene). We compare our results for the ground-state structure with results from experiments and quantum-chemical calculations.     

A density functional study of S(N)2 substitution at square-planar platinum(II) complexes

The energetics and reaction path in a series of S(N)2 substitution reactions at square-planar Pt(II) complexes have been studied by the application of density functional theory (DFT). Calculated free energies show excellent correlation with their experimental counterparts, while the enthalpic and entropic contributions individually indicate the presence of weak intermolecular interactions not accounted for in the present model. The nature of the leaving ligand has been shown to be much more significant in determining the activation barrier than that of the entering ligand; it is inferred (and confirmed by analysis of individual bond energies) that the reaction is driven by the dissociation of the leaving ligand, with the entering ligand playing a more passive role. Analysis of the intrinsic reaction coordinate indicates, further, that the trans ligand plays an unexpectedly dynamic role in stabilizing the transition state due to competition between stabilization and the steric effects of the entering and leaving ligands. The cis ligands, by contrast, are shown to move only slightly through the course of the reaction.     

Synthesis,spectroscopic characterization,crystal structure,density functional theory studies and biological properties of coordination complex Ni(II) 2-fluorobenzoate with 3-hydroxypyridine

A novel Ni(II) complex containing 2-fluorobenzoate and 3-hydroxypyridine ligands was synthesized and characterized using elemental analysis, Fourier transform infrared (FT-IR) spectroscopy and single-crystal X-ray diffraction. FT-IR peaks show that the carboxylate group from 2-fluorobenzoate has a monodentate coordination mode. The coordination environment around the Ni²⁺ ion is of distorted octahedral geometry. The octahedral geometry consists of a total of four oxygen atoms from two carboxylate groups of two fluorobenzoate anions, two water molecules and two nitrogen atoms from two 3-hydroxypyridine ligands. The complex shows excellent inhibitory effects against some metabolic enzymes. K_i values for the complex were found as 108.17 ± 25.63, 124.88 ± 36.20, 28.11 ± 2.87, 20.95 ± 5.65 and 32.63 ± 9.67 μM against human carbonic anhydrase I, human carbonic anhydrase II, α-glycosidase, acetylcholinesterase and butyrylcholinesterase, respectively. In addition, geometry optimization and vibration frequencies were calculated, and single point energy was studied based on optimization. Experimental and theoretical data were compared. The B3LYP/6-31G(d,p) basis set was used for all calculations.     

Application of density functional theory for studies of excited states and phosphorescence of platinum(II) acetylides

The electronic states of different conformations of platinum acetylides Pt(PH3)2(C[triple bond]C-Ph)2 and Pt(PH3)2(C[triple bond]C-PhC[triple bond]C-Ph)2 (PE1 and PE2) were calculated with density functional theory (DFT) using effective core potential basis sets. Time dependent DFT calculations of UV absorption spectra showed strong dependence of the intense absorption band maxima on mutual orientation of the phenyl rings with respect to the P-Pt-P axis. Geometry optimization of the first excited triplet state (T1) indicates broken symmetry structure with the excitation being localized in one ligand. This splits the two substitution ligands into a nondistorted aromatic ring with the C[triple bond]C-Ph bonds for one side and into a quinoid structure with a cumulenic C=C=C link on the other side. Quadratic response (QR) calculations of spin-orbit coupling and phosphorescence radiative lifetime (tauR) indicated a good agreement with experimental tauR values reported for solid PE1 and PE2 and PE2 capped with dendrimers in tetrahydrofuran solutions. The QR calculations reproduced an increase of tauR upon prolongation of pi chain of ligands and concommittant redshift of the phosphorescence. Moreover, it is shown how the phosphorescence borrows intensity from sigma-->pi* transitions localized at the C[triple bond]C-Pt-P fragments and that there is no intensity borrowing from delocalized pi-->pi* transitions.     

Time-dependent density functional theory scheme for efficient calculations of dynamic (hyper)polarizabilities

The authors present an efficient perturbative method to obtain both static and dynamic polarizabilities and hyperpolarizabilities of complex electronic systems. This approach is based on the solution of a frequency-dependent Sternheimer equation, within the formalism of time-dependent density functional theory, and allows the calculation of the response both in resonance and out of resonance. Furthermore, the excellent scaling with the number of atoms opens the way to the investigation of response properties of very large molecular systems. To demonstrate the capabilities of this method, they implemented it in a real-space (basis-set-free) code and applied it to benchmark molecules, namely, CO, H2O, and para-nitroaniline. Their results are in agreement with experimental and previous theoretical studies and fully validate their approach.     

Time-dependent density functional theory study on electronic and spectroscopic properties for Ph<Subscript>2</Subscript>Bq and its complexes

The molecular structures of the ground state and the first singlet excited state for diphenylboron analogs of Alq₃ [Ph₂Bq where q is 8-hydroxyquinoline (QH)] and its three derivatives were optimized with the Density Functional Theory and ab initio “configuration interaction with single excitations” method, respectively. The frontier molecular orbital characteristics of Ph₂Bq were analyzed systematically in order to study the electronic transition mechanism. Electronic and spectroscopic properties of complexes have been investigated with Time-Dependent Density Functional Theory, which indicates that the emissions of Ph₂Bq and its derivatives originate from the electronic π → π* transitions within the QH ligands. That means that one might tune the emission wavelengths and improve charge transfer properties through the effect of substituent on the 8-hydroxyquinoline ligand. Similar calculations were carried out for isolated QH and its three derivatives for comparison. We found that the highest occupied molecular orbital and the lowest unoccupied molecular orbital of Ph₂Bq are similar to those of QH and their spectroscopic properties change similarly when they are substituted by the same group, which suggests that one can search possibility of a red or blue emission from Ph₂Bq derivatives by analyzing QH and its derivatives.     

Excited states of phosphorescent platinum(II) complexes containing N wedge C wedge N-coordinating tridentate ligands: spectroscopic investigations and time-dependent density functional theory calculations

The absorption and emission spectra of the Pt(II) complexes containing N wedge C wedge N-coordinating tridentate ligands, platinum(II) 1,3-di(2-pyridyl)benzene chloride [Pt(dpb)Cl] and platinum(II) 3,5-di(2-pyridyl)toluene chloride [Pt(dpt)Cl], together with their corresponding free ligands, 1,3-di(2-pyridyl)benzene (dpbH) and 3,5-di(2-pyridyl)toluene (dptH), have been analyzed by density functional theory (DFT) for the ground state and time-dependent DFT (TDDFT) for the excited states. T(1)(A(1)) and S(1)(B(2)) of the complexes (in C(2)(v) symmetry) were assigned on the basis of the calculated excitation energies as well as comparison of the experimental spectroscopic properties and the calculated states' characteristics. The calculated excitation energies for T(1) and S(1) of the complexes as well as those for T(1) of the free ligands were in good agreement with their observed values within 600 cm(-1). The d-pi* characters of the excited states were evaluated from the change in electron densities between the ground and excited states by Mulliken population analysis; values of 25% for T(1) and 32% for S(1) were obtained for both complexes. The calculated values of d-pi* character were found to be consistent with the reported emission lifetimes as well as the observed emission energy shifts from the corresponding free ligands. Most spectroscopic properties of the complexes and the free ligands, which include solvatochromic shift, Stokes shifts, methyl substitution shifts, and emission spectra profiles, were well explained from the calculation results.     

A time-dependent density functional theory investigation of the spectroscopic properties of the beta-subunit in C-phycocyanin

By using time-dependent density functional theory combined with the polarizable continuum model, a satisfactory assignment of the absorption and circular dichroism spectra and energy transfer flow of the beta-subunit in C-phycocyanin (C-PC) was achieved when the protonation of beta-84 and beta-155 phycocyanobilin (PCB) and their interaction with the protein moiety in C-PC have been taken into account. We attribute the main peak for both beta-84 and beta-155 as arising from the pi electron excitation of the pyrrole rings and the shoulder peak as arising from the charge transfer from the asparate residue to PCBH(+). The satisfactory agreement between theory and experiment suggests that F?rster resonance theory prevails such that energy transfer occurs from beta(s) (beta-155) to beta(f) (beta-84).     

Structures and spectroscopic properties of bis(phthalocyaninato) yttrium and lanthanum complexes: theoretical study based on density functional theory calculations

Density functional theory (DFT) calculations were carried out to describe the molecular structures, molecular orbitals, atomic charges, UV-vis absorption spectra, IR, and Raman spectra of bis(phthalocyaninato) rare earth(III) complexes M(Pc)(2) (M = Y, La) as well as their reduced products [M(Pc)(2)](-) (M = Y, La). Good consistency was found between the calculated results and experimental data. Reduction of the neutral M(Pc)(2) to [M(Pc)(2)]- induces the reorganization of their orbitals and charge distribution and decreases the inter-ring interaction. With the increase of ionic size from Y to La, the inter-ring distance of both the neutral and reduced double-decker complexes M(Pc)(2) and [M(Pc)(2)](-) (M = Y, La) increases, the inter-ring interaction and splitting of the Q bands decrease, and corresponding bands in the IR and Raman spectra show a red shift. The orbital energy level and orbital nature of the frontier orbitals are also described and explained in terms of atomic character. The present work, representing the first systemic DFT study on the bis(phthalocyaninato) yttrium and lanthanum complexes sheds further light on clearly understanding structure and spectroscopic properties of bis(phthalocyaninato) rare earth complexes.     

Time-dependent density functional theory gradients in the Amsterdam density functional package: geometry optimizations of spin-flip excitations

An implementation of time-dependent density functional theory (TDDFT) energy gradients into the Amsterdam density functional theory program package (ADF) is described. The special challenges presented by Slater-type orbitals in quantum chemical calculation are outlined with particular emphasis on details that are important for TDDFT gradients. Equations for the gradients of spin-flip TDDFT excitation energies are derived. Example calculations utilizing the new implementation are presented. The results of standard calculations agree well with previous results. It is shown that starting from a triplet reference, spin-flip TDDFT can successfully optimize the geometry of the four lowest singlet states of CH₂ and three other isovalent species. Spin-flip TDDFT is used to calculate the potential energy curve of the breaking of the C?CC bond of ethane. The curve obtained is superior to that from a restricted density functional theory calculation, while at the same time the problems with spin contamination exhibited by unrestricted density functional theory calculations are avoided.     

Time-dependent density functional theory calculations of the photoabsorption of fluorinated alkanes

Time-dependent density functional theory (TD-DFT) calculations of the transition energies and oscillator strengths of fluorinated alkanes have been performed. The TD-DFT method with the non-local B3LYP potential yields transition energies for the methanes, which are smaller by about 10% as compared to the experimental values. An empirical linear correlation was found between the calculated and experimental transition energies both at the B3LYP/DZ+Ryd(C, F) and B3LYP/cc-pVTZ+Ryd(C, F, H) levels for a total of 19 transitions of the fluorinated methanes with linear correlation coefficients of 0.987 for the former and 0.988 for the latter. This empirical correlation for fluorinated methane molecules is found to agree well with the previously obtained empirical correlations between calculated and experimental values for non-fluorinated molecules. The results show that a single empirical-correlation relationship can be used for both non-fluorinated and fluorinated molecules to predict transition energies. This linear relationship is then used to predict the photoabsorption spectra of ethane, propane, butane, and partially and fully fluorinated derivatives. A key result of these calculations is the dominance of Rydberg transitions in the spectral region of interest.     

Dinuclear Zn(II) complex catalyzed phosphodiester cleavage proceeds via a concerted mechanism: a density functional theory study

Density functional theory (DFT) calculations were used to study the mechanism for the cleavage reaction of the RNA analogue HpPNP (HpPNP = 2-hydroxypropyl-4-nitrophenyl phosphate) catalyzed by the dinuclear Zn(II) complex of 1,3-bis(1,4,7-triazacyclonon-1-yl)-2-hydroxypropane (Zn(2)(L(2)O)). We present a binding mode in which each terminal phosphoryl oxygen atom binds to one zinc center, respectively, and the nucleophilic 2-hydroxypropyl group coordinates to one of the zinc ions, while the hydroxide from deprotonation of a water molecule coordinates to the other zinc ion. Our calculations found a concerted mechanism for the HpPNP cleavage with a 16.5 kcal/mol reaction barrier. An alternative proposed stepwise mechanism through a pentavalent oxyphosphorane dianion reaction intermediate for the HpPNP cleavage was found to be less feasible with a significantly higher energy barrier. In this stepwise mechanism, the deprotonation of the nucleophilic 2-hydroxypropyl group is accompanied with nucleophilic attack in the rate-determining step. Calculations of the nucleophile (18)O kinetic isotope effect (KIE) and leaving (18)O KIE for the concerted mechanism are in reasonably good agreement with the experimental values. Our results indicate a specific-base catalysis mechanism takes place in which the deprotonation of the nucleophilic 2-hydroxypropyl group occurs in a pre-equilibrium step followed by a nucleophilic attack on the phosphorus center. Detailed comparison of the geometric and electronic structure for the HpPNP cleavage reaction mechanisms in the presence/absence of catalyst revealed that the catalyst significantly altered the determining-step transition state to become far more associative or tight, that is, bond formation to the nucleophile was remarkably more advanced than leaving group bond fission in the catalyzed mechanism. Our results are consistent with and provide a reliable interpretation for the experimental observations that suggest the reaction occurs by a concerted mechanism (see Humphry, T.; Iyer, S.; Iranzo, O.; Morrow, J. R.; Richard, J. P.; Paneth, P.; Hengge, A. C. J. Am. Chem. Soc. 2008, 130, 17858-17866) and has a specific-base catalysis character (see Yang, M.-Y.; Iranzo, O.; Richard, J. P.; Morrow, J. R. J. Am. Chem. Soc. 2005, 127, 1064-1065).