Yb、YbO电子激发态的相对论含时密度泛函理论研究

本文用基于精确二分量哈密顿（exact two—component Hamiltonian）的相对论含时密度泛函理论（time-dependent relativistic density functional theory）计算了Yb和YbO的电子激发态,并利用对称性、自然原子轨道对激发态性质和归属进行了详细分析,所得结果支持实验对YbO基态与激发态的指认．     

Time-dependent four-component relativistic density functional theory for excitation energies

Time-dependent four-component relativistic density functional theory within the linear response regime is developed for calculating excitation energies of heavy element containing systems. Since spin is no longer a good quantum number in this context, we resort to time-reversal adapted Kramers basis when deriving the coupled Dirac-Kohn-Sham equation. The particular implementation of the formalism into the Beijing density functional program package utilizes the multipolar expansion of the induced density to facilitate the construction of the induced Coulomb potential. As the first application, pilot calculations on the valence excitation energies and fine structures of the rare gas (Ne to Rn) and Group 12 (Zn to Hg) atoms are reported. To the best of our knowledge, it is the first time to be able to account for spin-orbit coupling within time-dependent density functional theory for excitation energies.     

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 based Ehrenfest dynamics

Time-dependent density functional theory based Ehrenfest dynamics with atom-centered basis functions is developed in present work. The equation of motion for electrons is formulated in terms of first-order reduced density matrix and an additional term arises due to the time-dependence of basis functions through their dependence on nuclear coordinates. This time-dependence of basis functions together with the imaginary part of density matrix leads to an additional term for nuclear force. The effects of the two additional terms are examined by studying the dynamics of H(2) and C(2)H(4), and it is concluded that the inclusion of these two terms is essential for correct electronic and nuclear dynamics.     

Time-dependent density functional theory study on intramolecular charge transfer and solvent effect of dimethylaminobenzophenone

The lower singlet excited states for dimethylaminobenzophenone have been investigated as a function of the twisting motion with inclusion of solvent effects. Theoretical calculations have been performed using time-dependent density functional theory. The B3LYP and MPW1PW91 functionals with a 6-311+G(2d,p) basis set have been used to compute transition energies. The solvent effects have been described within the polarizable continuum model. Ground-state geometries are optimized using density functional theory with both B3LYP and MPW1PW91 functionals combined with 6-31G(d) basis sets. Vertical absorption energy calculations characterize the lower singlet excited states both in vacuum and in different kinds of solvents. A large redshift of the absorption maximum in the polar solvent suggests an intramolecular charge transfer character of the excited state. We have constructed the potential energy curves of two possible twisting motions of the excited states both in vacuum and in the polar solvent of acetonitrile: the twisting of only the dimethylamino group and the twisting of the dimethylaminophenyl group with respect to the benzoyl group. Both twisting processes predict the formation of the twisted intramolecular charge transfer state associated with the crossing of a low barrier. The presence of the polar solvent significantly changes the shape of the energy curves. Calculated emission energies for both the isolated and the solvated systems show a large Stokes shift between the absorption and fluorescence maxima. Two possible twisting motions produce similar fluorescence spectroscopic consequences. Our results including solvent effects explain the weak "dual-fluorescence" feature of dimethylaminobenzophenone, and imply that the two possible twisting motions may occur in the excited-state relaxation dynamics, but the twisting of the dimethylamino group seems to take place easier.     

Time-dependent density functional theoretical study of low lying excited states of F2

The utility of time-dependent density functional theory (TDDFT) in predicting excitation energies is tested for the low lying excited states of F₂, a system that has posed severe challenges to ab initio quantum theory. It is shown that TDDFT using B3LYP functional predicts the excitation energies in good agreement with experiment. In some cases, the agreement is better than that for the post-Hartree–Fock methods like CASSCF and MRCI.     

Two hydrogen ligands on tetrairidium clusters: a relativistic density functional study

Structural and energetic properties of Ir(4)H(2) have been determined by applying a relativistic density functional method. As previously obtained for Ir(4)H, terminal coordination of H ligands is preferred, in contrast to some other transition metals. Square-planar Ir(4) isomers with an H binding energy of up to 318 kJ mol(-1) per atom were determined as the most stable structures of Ir(4)H(2). Isomers with a tetrahedral or butterfly structure of the metal framework exhibit average H atom binding energies of up to approximately 300 kJ mol(-1). For all three types of isomers, a surprisingly large number of stable minima was identified. Unexpectedly, structural as well as energetic properties of Ir(4)H(2) complexes are very similar to Ir(4)H. Thus binding of an H atom to Ir(4) is only slightly affected by the presence of a second H ligand. In all cases examined, the reaction H(2)+ Ir(4)--> H(2)Ir(4) was found to be exothermic with reaction energies of up to 170 kJ mol(-1).     

Time-dependent density functional theoretical study of the absorption properties of BN-substituted C60 fullerenes

Time-dependent density functional theoretical calculations using the B3LYP functional and 6-31G* basis set for a series of BN-substituted C60 fullerenes reveal that, unlike C60, these molecules would absorb in the visible region and that the optical and electronic properties of fullerenes can be fine-tuned with proper BN substitution.     

The stability of small helical gold nanorods: a relativistic density functional study

Multistrand 7-1 helical Au(24), Au(32), and Au(40) structures with three, four, and five gold atoms in the central strand and 21, 28, and 35 gold atoms in the coaxial tube are investigated using relativistic density functional theory. We demonstrate that these helical gold nanorods are stable structures with a rather large HOMO-LUMO gap, a large binding energy per atom, a very large vertical dissociation energy, and an extremely large electron affinity. On the basis of the atomic charges and the nature of the frontier orbitals, they are also expected to have strong selective reactivity toward electrophiles and nucleophiles. Furthermore, we show that these helical Au(n) structures and, in particular, the helical Au(40) structure are competitive energetically and chemically with respect to alternate cage and compact Au(n) structures. We consider two fragmentations of the helical Au(40) structure and perform a density of states analysis to examine both charge transfer and electronic polarization.     

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.     

Uranyl complexation by monodentate nitrogen donor ligands. A relativistic density functional study

To examine the interaction of uranyl with nitrogen containing groups of humic substances, the model complexes [UO₂(H₂O)₄L_N]²⁺, L_N = NH₂CH₃, N(CH₃)₃, and NC₅H₅ in aqueous solution were studied computationally with an all‐electron relativistic density functional method. Results are compared with the corresponding penta‐aqua complex of uranyl. Although pyridine coordinates with about the same strength as L = H₂O, methylamine binds ～10 kJ mol^?1 stronger and trimethylamine ～40 kJ mol^?1 weaker than a fifth aqua ligand. Yet, each of these ligands L_N donates about the same amount of charge to uranyl as L = H₂O. U? N bonds are ～10 pm longer than the U? O bonds of the aqua ligands. From the present model results, one does not expect that, when compared with carboxyl groups, monodentate N‐containing functional groups contribute significantly to uranyl complexation by humic substances. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

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.     

Adsorption of small molecules on helical gold nanorods: A relativistic density functional study

We study the adsorption of a variety of small molecules on helical gold nanorods using relativistic density functional theory. We focus on Au₄₀ which consists of a central linear strand of five gold atoms with seven helical strands of five gold atoms on a coaxial tube. All molecules preferentially adsorb at a single low‐coordinated gold atom on the coaxial tube at an end of Au₄₀. In most cases, there is significant charge transfer (CT) between Au₄₀ and the adsorbate, for CO and NO₂, there is CT from the Au₄₀ to adsorbate while for all other molecules there is CT from the adsorbate to Au₄₀. Thus, Au₄₀‐adsorbate can be described as a donor–accepter complex and we use charge decomposition analysis to better understand the adsorption process. We determine the adsorption energy order to be C₅H₅N >NO₂ > CO > NH₃ > CH₂?CH₂ > CH₂?CH? CHO > NO > HC?CH > H₂S > SO₂ > HCN > CH₃OH > H₂C?O > O₂ > H₂O > CH₄ > N₂. We find that the Au? C, Au? N, Au? S, and Au? O bonds are surprisingly strong, with clear implications for reactivity enhancement of the adsorbate. The Au? H bond is relatively weak but, for interactions via an H atom that is bonded to a carbon atom (e.g., CH₄), we find that there is large charge polarization of the Au? H? C moiety and partial activation of the inert C? H bond. Although the Au? S and Au? O bonds are generally weaker than the Au? C and Au? N bonds, we find that adsorption of H₂S or H₂O causes greater distortion of Au₄₀ in the binding region. However, the degree of distortion is small and the helical structure is retained, demonstrating the stability of the helical Au₄₀ nanorod under perturbations. © 2014 Wiley Periodicals, Inc.     

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: past, present, and future

Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope, and yields predictions for many more properties. We discuss some of the challenges involved in making accurate predictions for these properties.     

Scalar relativistic all-electron density functional calculations on periodic systems

Scalar relativistic effects are included in periodic boundary conditions calculations with Gaussian orbitals. This approach is based on the third-order Douglas-Kroll-Hess approximation, allowing the treatment of all electrons on an equal footing. With this methodology, we are able to perform relativistic all-electron density functional calculations using the traditional local spin-density and generalized gradient approximations (GGA), as well as meta-GGA and hybrid density functionals. We present benchmark results for the bulk metals Pd, Ag, Pt, and Au, and the large band gap semiconductors AgF and AgCl.     

Time-dependent density functional study of the electronic potential energy curves and excitation spectrum of the oxygen molecule

Orbital energies, ionization potentials, molecular constants, potential energy curves, and the excitation spectrum of O(2) are calculated using time-dependent density functional theory (TDDFT) with Tamm-Dancoff approximation (TDA). The calculated negative highest occupied molecular orbital energy (-epsilon(HOMO)) is compared with the energy difference ionization potential for five exchange correlation functionals consisting of the local density approximation (LDAxc), gradient corrected Becke exchange plus Perdew correlation (B(88X)+P(86C)), gradient regulated asymptotic correction (GRAC), statistical average of orbital potentials (SAOP), and van Leeuwen and Baerends asymptotically correct potential (LB94). The potential energy curves calculated using TDDFT with the TDA at internuclear distances from 1.0 to 1.8 A are divided into three groups according to the electron configurations. The 1pi(u) (4)1pi(g) (2) electron configuration gives rise to the X (3)Sigma(g) (-), a (1)Delta(g), and b (1)Sigma(g) (+) states; the 1pi(u) (3)1pi(g) (3) electron configuration gives rise to the c (1)Sigma(u) (-), C (3)Delta(u), and A (3)Sigma(u) (+) states; and the B (3)Sigma(u) (-), A (1)Delta(u), and f (1)Sigma(u) (+) states are determined by the mixing of two or more electron configurations. The excitation spectrum of the oxygen molecule, calculated with the aforementioned exchange correlation functionals, shows that the results are quite sensitive to the choice of functional. The LDAxc and the B(88X)+P(86C) functionals produce similar spectroscopic patterns with a single strongly absorbing band positioned at 19.82 and 19.72 eV, respectively, while the asymptotically corrected exchange correlation functionals of the SAOP and the LB94 varieties yield similar excitation spectra where the computed strongly absorbing band is located at 16.09 and 16.42 eV, respectively. However, all of the exchange correlation functionals yield only one strongly absorbing band (oscillator strength greater than 0.1) in the energy interval of 0-20 eV, which is assigned to a X (3)Sigma(g) (-) to (3)Sigma(u) (-) transition. Furthermore, the oxygen molecule has a rich spectrum in the energy range of 14-20 eV and no spin allowed absorption bands are predicted to be observed in the range of 0-6 eV.     

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.     

Reaction mechanism of platinum dimer cation with ammonia based on the relativistic density functional study

The gas‐phase reactions between Pt and NH₃ have been investigated using the relativistic density functional approach (ZORA‐PW91/TZ2P). The quartet and doublet potential energy surfaces of Pt + NH₃ have been explored. The minimum energy reaction path proceeds through the following steps: Pt(⁴Σ_u) + NH₃ → q‐1 → d‐2 → d‐3 → d‐4 → d‐Pt₂NH⁺ + H₂. In the whole reaction pathway, the step of d‐2 → d‐3 is the rate‐determining step with a energy barrier of 36.1 kcal/mol, and exoergicity of the whole reaction is 12.0 kcal/mol. When Pt₂NH⁺ reacts with NH₃ again, there are two rival reaction paths in the doublet state. One is degradation of NH and another is loss of H₂. In the case of degradation of NH, the activation energy is only 3.4 kcal/mol, and the overall reaction is exothermic by 8.9 kcal/mol. Thus, this reaction is favored both thermodynamically and kinetically. However, in the case of loss of H₂, the rate‐determining step's energy barrier is 64.3 kcal/mol and the overall reaction is endothermic by 8.5 kcal/mol, so it is difficult to take place. Predicted relative energies and barriers along the suggested reaction paths are in reasonable agreement with experimental observations. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007