Equation for the direct determination of the density matrix: Time-dependent density equation and perturbation theory

The density equation proposed previously for the direct determination of the density matrix, i.e. for the wave mechanics without wave, is extended to a time-dependent case. The time-dependent density equation has been shown to be equivalent to the time-dependent Schr?dinger equation so long as the density matrix, included as a self-contained variable, is N-representable. Formally, it is obtainable from the previous time-independent equation by replacing the energy E with . The perturbation theory formulas for the density equation have also been given for both the time-dependent and time-independent cases. Received: 16 June 1998 / Accepted: 2 September 1998 / Published online: 8 February 1999     

Synthesis,Crystal Structure and Density Functional Studies on 1N‐Phenyl‐3‐(2,4‐Dichlorophenyl)‐5‐(4‐Chlorophenyl)‐2‐Pyrazoline

1N‐Phenyl‐3‐(2,4‐dichlorophenyl)‐5‐(4‐chlorophenyl)‐2‐pyrazoline has been synthesized and characterized by elemental analysis, IR, UV‐Vis and X‐ray single crystal diffraction. Density functional calculations have been carried out for the title compound by using the B3LYP method with a 6‐311G** basis set. The calculated results show that the predicted geometry can reproduce well the structural parameters. The electronic absorption spectra calculated in the gas phase are better than those calculated in EtOH solvent to model the experimental electronic spectra. Natural Bond Orbital (NBO) analyses suggest that the above electronic transitions are mainly assigned to π → π* transitions. On the basis of vibrational analyses, the thermodynamic properties of the compound at different temperatures have been calculated, revealing the correlations between C⁰_{p, m}, S⁰_m, H⁰_m and temperature.     

Theoretical investigation of LaC3n+ (n = 0, 1, 2) clusters by density functional theory

LaC₃ⁿ⁺ (n=0, 1, 2) clusters have been studied using B3LYP (Becke 3-parameter–Lee-Yang-Parr) density functional method. The basis set is Dunning/Huzinaga valence double zeta for carbon and [2s2p2d] for lanthanum, denoted LANL1DZ. Four isomers are presented for each cluster; two of them are edge binding isomers with C_2v symmetry, the other two are linear chains with C_∞v symmetry. Meanwhile, two spin states for each isomer, that is, singlet and triplet for LaC₃⁺, doublet and quartet for LaC₃ and LaC₃²⁺, respectively, are also considered. Geometries, vibrational frequencies, infrared intensities, and other quantities are reported and discussed. The results indicate that at some spin states; the C_2v symmetry isomers are the dominant structures, while for the other spin states, linear isomers are energetically favored. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 66 : 301–307, 1998     

Vibrational spectra and density functional study of propylgermane

Raman and infrared spectra of propylgermane, CH₃CH₂CH₂GeH₃, and its Ge-deuterated analog, CH₃CH₂CH₂GeD₃, were investigated in their gaseous, liquid and solid states. The normal coordinate treatment was carried out by density functional theory (DFT) calculation, using B3LYP/6-31G^* and 6-311++G^** basis sets, and the corresponding fundamental vibrations were assigned. The trans (T) and gauche (G) forms around the central C–C bond coexisted in the gaseous and liquid states and only the T form existed in the solid state. From the temperature dependent measurements of the Raman spectra in the liquid state, the enthalpy difference was found to be ΔH(T−G)=−0.36±0.02 kcalmol⁻¹ with the T form being more stable. The energy differences between the isomers obtained by DFT calculations were ΔE(T−G)=−0.46 kcalmol⁻¹ and ΔE(T−G)=−0.87 kcalmol⁻¹ by the 6-31G^* basis set and 6-311++G^** basis set, respectively.     

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．     

Absolute configuration of Buagafuran:An experimental and theoretical electronic circular dichroism study

Buagafuran is a novel drug candidate derived from natural product.Its absolute configuration has been confirmed by electronic circular dichroism combined with modern quantum-chemical calculation using time-dependent density functional theory.The predicted UV absorbance peak is underestimated by several nanometers compared with the experimental data.The applicability of empirical rule for the C=C-C-O system in Buagafuran has also been discussed.Our results show that electronic circular dichroism could be a useful tool for the absolute configuration assignment of chiral drugs,especially for the oily or semisolid substances,whose crystal structures are impossible to obtain.     

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.     

Tautomeric equilibria of 2‐ and 4‐thiouracil in gas phase and in solvent: A density functional study

The relative stabilities of the five favored tautomers of 2‐ and 4‐thiouracil in gas phase and in water solution were determined by density functional theory employing the Becke, Lee, Yang, and Parr (B3LYP) exchange–correlation potential and the three 6‐31G(d,p), 6‐311++G(d,p), and triple‐zeta valence (TZVP) basis sets. Zero‐point vibrational corrections were also computed. Bulk solvent effects were studied in the framework of the self‐consistent reaction field approach by the polarizable continuum model. All calculations indicate that the most stable tautomer for both species, in the gas phase as well as in solution, has the oxo‐thione form, in full agreement with the previous ab initio and experimental studies. The tautomeric stability orders obtained in the aqueous solution are sensibly different from that in the gas phase. At B3LYP/6‐311++G(d,p) level in the gas phase, the following orders of stability for 2‐ and 4‐thiouracil tautomers were observed, respectively: S2U1>S2U2>S2U4>S2U5>S2U3 and S4U1>S4U2>S4U3>S4U4>S4U5. The corresponding trends in the aqueous phase are S2U1>S2U3>S2U2>S2U5>S2U4 and S4U1>S4U2>S4U3>S4U5>S4U4. On the basis of the computed energy differences we can hypothesize that only the oxo‐thione forms of 2‐ and 4‐thiouracil should exist in the gas phase and in water solution. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 44–52, 2001     

Density bifunctional theory using the mass density and the charge density

Can all the properties of a system composed of particles with masses, m _i , and charges, q _i , be determined from the charge density and the mass density? Subject to a small statistical caveat, this is true, and offers the prospect of an elegant extension of density-functional theory beyond the Born-Oppenheimer approximation.     

钼、钨四重键化合物电子光谱的含时密度泛函理论研究

运用含时密度泛函理论(TD-DFT),对具有代表性的钼、钨四重键化合物M2Cl4-8,M2Cl4(PMe3)4,M2(O2CCH3)4和M2(PhNCHNPh)4(M=Mo,W)的低占据电子激发能进行了计算,系统地考察了局域(LDA)、离域(GGA)和杂化(Hybrid)泛函对金属四重键化合物中d-d跃迁和电荷转移跃迁...     

Differentiability of Lieb functional in electronic density functional theory

A solid understanding of the Lieb functional F_L is important because of its centrality in the foundations of electronic density functional theory. A basic question is whether directional derivatives of F_L at an ensemble‐V‐representable density are given by (minus) the potential. A widely accepted purported proof that F_L is Gâteaux differentiable at EV‐representable densities would say, “yes.” But that proof is fallacious, as shown here. F_L is not Gâteaux differentiable in the normal sense, nor is it continuous. By means of a constructive approach, however, we are able to show that the derivative of F_L at an EV‐representable density ρ₀ in the direction of ρ₁ is given by the potential if ρ₀ and ρ₁ are everywhere strictly greater than zero, and they and the ground state wave function have square integrable derivatives through second order. © 2007 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Argon-matrix-isolation Raman spectra and density functional study of 1,3-butadiene conformers

s-trans, s-cis and gauche conformers of 1,3-butadiene have been studied using density functional theory and the coupled-cluster method using double substitutions (CCD). Matrix isolation Raman and IR data for the minor conformer were obtained and are used in combination with the theoretical results to resolve earlier ambiguities in vibrational assignments. Based on high-quality Hessians, new harmonic stretching force constants are reported for the carbon backbone of s-trans-1,3-butadiene. For the minor conformer the best unscaled root mean square error of the calculated frequencies for the s-cis and gauche geometries are 17.5 cm⁻¹ and 7.4 cm⁻¹, respectively, primarily due to a better agreement of the gauche results for the vibrations at 983 cm⁻¹, 596 cm⁻¹ and 470 cm⁻¹ which depend strongly on the torsional angle. Although this points towards the gauche form rather than the s-cis form, the calculated transition dipole moment directions at the CCD/6-311G(d,p) level confirm the earlier conclusion that the minor conformer has C _{2 v} symmetry in the matrix. It is concluded that either the better agreement between the frequencies calculated for the gauche form and the observed values is coincidental, or that the molecule is indeed nonplanar in the matrix and tunnels very rapidly between the two mirror-image forms (or its lowest vibrational level lies above the barrier). Received: 1 July 1998 / Accepted: 26 October 1998 / Published online: 15 February 1999     

The active catalytic species and its isomerisation in the catalytic carbonylation of methanol — a density functional study

The Monsanto acetic acid process is one of the most effective ways to produce acetic acid industrially. This process has been studied experimentally but theoretical investigations are so far sparse. In the current work the active catalytic species [Rh(CO)₂I₂]⁻ (1) and its isomerisation has been studied theoretically using the hybrid B3LYP exchange and correlation functional. Similar calculations has been performed for the iridium complex [Ir(CO)₂I₂]⁻ (2) that also is catalytically active in the methanol carbonylation. Experimental work has confirmed the existence of the cis forms of the active catalytic species, but they do not rule out the possibility of the trans isomers. Our gas phase results show that cis-1 has 4.95 kcal/mol lower free energy than trans-1, and cis-2 has 10.39 kcal/mol lower free energy than trans-2. In the case of rhodium, trans-1 can take part to the catalytic cycle but in case of iridium this is not very likely. We have also investigated the possible mechanisms of the cis to trans conversions. The ligand association mechanism gave free energy barrier of 13.7 kcal/mol for the rhodium complex and 19.8 kcal/mol for iridium. Thus the conversion for the rhodium complex is feasible whereas for iridium it is unlikely.     

Comment on “density and physical current density functional theory” by Xiao‐Yin Pan and Viraht Sahni

A recent paper by Xiao‐Yin Pan and Viraht Sahni [Int. J. Quant. Chem. 110, 2833 (2010)] claims that current density functional theory should be based on the physical current density rather than the paramagnetic current density, as in the standard Vignale‐Rasolt formulation. In this comment we show that the claims in the paper by Pan and Sahni are erroneous. © 2012 Wiley Periodicals, Inc.     

Theoretical studies of ground and excited electronic states in a series of heteroleptic iridium complexes using density functional theory

A series of new heteroleptic iridium(III) complexes [Ir(C^?N)₂(N^?N)]PF₆ ( 1 ‐ 6 ) (each with two cyclometalating C^?N ligands and one neutral N^?N ancillary ligand, where C^?N = 2‐phenylpyridine (ppy), 5‐methyl‐2‐(4‐fluoro)phenylpyridine (F‐mppy), and N^?N = 2,2′‐dipyridyl (bpy), 1,10‐phenanthroline (phen), 4,4′‐diphenyl‐2,2′‐dipyridy (dphphen) were found to have rich photophysical properties. Theoretical calculations are employed for studying the photophysical and electrochemical properties. All complexes are investigated using density functional theory. Excited singlet and triplet states are examined using time‐dependent density functional theory. The low‐lying excited‐state geometries are optimized at the ab initio configuration interaction singles level. Then, the excited‐state properties are investigated in detail, including absorption and emission properties, photoactivation processes. The excited state of complexes is complicated and contains triplet metal‐to‐ligand charge transfer, triplet ligand‐to‐ligand charge transfer simultaneously. Importantly, the absorption spectra and emission maxima can be tuned significantly by changing the N^?N ligands and C^?N ligands. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Structural and electronic properties of stable Aun (n = 2–13) clusters: A density functional study

All-electron scalar relativistic calculations have been performed to investigate the electronic structures of neutral gold clusters (Au_n, n = 2–13) in the gas phase using density functional theory with the generalized gradient approximation. Full geometry optimizations of topologically different clusters and clusters belonging to different symmetry groups have been carried out. Binding energies, ionization potentials, electron affinities, and chemical hardness values are calculated and they are found to be comparable with the available experimental and theoretical results. The most stable structure of each of the cluster has a two-dimensional planar configuration. A three dimensional distorted Y shaped structure (4b) for Au₄, a tri-capped triangle (6b), a chair (6f), and a see-saw structure (6j) for Au₆, an eclipsed sandwich structure (7g) for Au₇, a condensed trigonal bipyramid (9e) and a boat shaped structure (9f) for Au₉, a staggered sandwich (11c) and an eclipsed sandwich structure (11d) for Au₁₁, a ladderane structure (12d) for Au₁₂, and a staggered (13d) and a distorted sandwich structure (13e) for Au₁₃ are characterized for the first time in this work.     

Structure and Bonding in Stannadiphospholes and their Dianions SnC2P2R2m (R=H,tBu m=0, −2): A Comparative Study with C5H5+ and C5H5− Analogues

The potential energy surfaces of both neutral and dianionic SnC₂P₂R₂ (R=H, tBu) ring systems have been explored at the B3PW91/LANL2DZ (Sn) and 6‐311+G* (other atoms) level. In the neutral isomers the global minimum is a nido structure in which a 1,2‐diphosphocyclobutadiene ring (1,2‐DPCB) is capped by the Sn. Interestingly, the structure established by X‐ray diffraction analysis, for R=tBu, is a 1,3‐DPCB ring capped by Sn and it is 2.4 kcal mol^?1 higher in energy than the 1,2‐DPCB ring isomer. This is possibly related to the kinetic stability of the 1,3‐DPCB ring, which might originate from the synthetic precursor ZrCp₂tBu₂C₂P₂. In the case of the dianionic isomers we observe only a 6π‐electron aromatic structure as the global minimum, similarly to the cases of our previously reported results with other types of heterodiphospholes. 1 , 4 , 19 The existence of large numbers of cluster‐type isomers in neutral and 6π‐planar structures in the dianions SnC₂P₂R₂^2? (R=H, tBu) is due to 3D aromaticity in neutral clusters and to 2D π aromaticity of the dianionic rings. Relative energies of positional isomers mainly depend on: 1) the valency and coordination number of the Sn centre, 2) individual bond strengths, and 3) the steric effect of tBu groups. A comparison of neutral stannadiphospholes with other structurally related C₅H₅⁺ analogues indicates that Sn might be a better isolobal analogue to P⁺ than to BH or CH⁺. The variation in global minima in these C₅H₅⁺ analogues is due to characteristic features such as 1) the different valencies of C, B, P and Sn, 2) the electron deficiency of B, 3) weaker pπ–pπ bonding by P and Sn atoms, and 4) the tendency of electropositive elements to donate electrons to nido clusters. Unlike the C₅H₅⁺ systems, all C₅H₅^? analogues have 6π‐planar aromatic structures as global minima. The differences in the relative ordering of the positional isomers and ligating properties are significant and depend on 1) the nature of the π orbitals involved, and 2) effective overlap of orbitals.     

Study of oxygen adsorption on β-Si3N4(0 0 0 1) by the density functional theory

The density functional theory (DFT) B3LYP method is used to theoretically investigate the interaction of O₂ with the β-Si₃N₄ surface (0 0 0 1) at 1200 °C. All the calculations have been performed at the 6-31G^∗ basis set level using H-saturated cluster. From the total energy minimization, the chemisorption on the center of the molecule lying above an Si site and the molecular axis paralleling to the surface is the most stable. After adsorption, the O–O bond is easier to dissociate compared to the free O₂. The electron transferred from the substrate to the O₂ molecule occupies the O₂ anti-bonding orbital, thus leading to a weakening off the bond strength, which is reflected by the elongated O₂ bond length. The changing trend of the O–O population and vibrational frequency is consistent with the change of the O–O bond length. The significant chemisorption energy and the short adsorption bond length indicate that the oxidation occurs on the β-Si₃N₄(0 0 0 1) surface at 1200 °C more easily.