Density functional finite cluster method for polarizability of large BeN three‐dimensional systems

The structures and the properties of small clusters are known to be quite different from those of the bulk material. Consequently, the focus of most studies is towards understanding the changes in electronic properties with increasing cluster size. Linear static electronic dipole polarizabilities of the Be_N (N→∞) solid are obtained at the DFT(PWB91) level by extrapolation of ab initio calculations on Be_N (N=1,…,132) clusters. For the mean polarizability, a [5s3p] basis set is shown to give accurate values if the tri‐periodic clusters are big enough. No calculation has yet been carried out on Be_N (N→∞), but it is clear that these linear properties converge relatively slowly with cluster size. For Be_N, cluster size up to N=90 atoms are sufficient to give limiting infinite solid polarizabilities with relatively small uncertainties. For N=132, the mean polarizability result is probably very accurate. These results suggest that DFT is a good method for the determination of these properties. © 2000 John Wiley & Sons, Inc. J Comput Chem 22: 230–240, 2001     

Investigation of the frequency‐dispersion effects on the Raman spectra of small polyenes

The time‐dependent Hartree–Fock scheme is applied for determining the frequency‐dependent Raman intensities of C_2nH_2n+2 molecules with n = 1–3. This analytic scheme, recently developed and implemented in the GAMESS program (Quinet, O.; Champagne, B. J Chem Phys 2001, 115, 6293), takes advantage of the 2n + 1 rule to express the polarizability derivatives in terms of first‐order derivatives. It is found that including frequency dispersion strongly modifies the intensity activy coefficients of many vibrational normal modes and therefore changes the aspect of the spectra. On the other hand, the depolarization ratio is much less frequency dependent. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

Li2 Trapped inside Tubiform [n] Boron Nitride Clusters (n=4–8): Structures and First Hyperpolarizability

The geometries and electronic properties of tubiform [n] boron nitride clusters entrapping Li₂ (Li₂@BN‐cluster(n,0); n=4–8), obtained by doping BN‐cluster(n,0) with Li₂ molecules, are investigated by means of DFT. The effects of tube diameter n on the dipole moment μ₀, static polarizability α₀, and first hyperpolarizability β₀ are elucidated. Both the dipole moment and polarizability increase with increasing tube diameter, whereas variation of the static first hyperpolarizability with tube diameter is not monotonic; β₀ follows the order 1612 (n=4)<3112 (n=5)<5534 (n=7)<8244 (n=6)<12 282 a.u. (n=8). In addition, the natural bond orbital (NBO) charges show that charge transfer takes place from the Li₂ molecule to the BN cluster, except for BN‐cluster(8,0) with larger tube diameter. Since the large‐diameter tubular BN‐cluster(8,0) can trap the excess electrons of the Li₂ molecule, Li₂@BN‐cluster(8,0) can be considered to be a novel electride compound.     

Theoretical study of silicon–sulfur clusters (SiS2)n− (n=1–6)

The possible geometrical structures and relative stability of silicon–sulfur clusters (SiS₂) (n=1–6) are explored by means of density functional theory (DFT) quantum chemical calculations. We also compare DFT with second‐order Møller–Plesset (MP2) and Hartree–Fock (HF) methods. The effects of polarization functions, diffuse functions, and electron correlation are included in MP2 and B3LYP quantum chemical calculations, and B3LYP is effective in larger cluster structure optimization, so we can conclude that the DFT approach is useful in establishing trends. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂)_n⁻ are analyzed by B3LYP. As a result, the regularity of the (SiS₂)_n⁻ cluster growing is obtained, and the calculation may predict the formation mechanism of the (SiS₂)_n⁻ cluster. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 81: 280–290, 2001     

Apparent Molar Volume and Apparent Molar Refraction of Mono-, Di-, Tri-, and Tetra(oxyethylene) Glycol in Aqueous, 1,4-Dioxane, and Benzene Solutions at 298.15?K

The density and refractive index of aqueous, 1,4-dioxane, and benzene solutions of poly (oxyethylene) glycols of the type HO–(CH₂CH₂O) _n –H (n varying from 1 to 4) were measured at 298.15K. From these experimental data the apparent molar volume and the apparent molar refraction at infinite dilution were calculated. The limiting apparent molar volume of the investigated compounds in a definite solvent depends linearly on the number of oxyethylene groups. From these data, the volume of the monomeric unit was evaluated and found to be greater in non-aqueous solvents than in water. The limiting apparent molar refraction of the solute for the investigated systems, within the experimental uncertainties, is equal to the molar refraction of the pure solute. The electronic polarizability of the solute molecule depends linearly on the number of monomeric units and the ratio of the electronic polarizability to the molecular van der Waals volume is constant and independent of the number of oxyethylene groups.     

Dual‐parameter correlations on rate of an aromatic nucleophilic substitution reaction in aqueous solutions of methanol,ethanol, and propan‐2‐ol

Reaction kinetics of 1‐chloro‐2,4‐dinitrobenzene with piperidine was studied spectrophotometrically in aqueous solutions of methanol, ethanol, and propan‐2‐ol at 25°C. The reaction in these solutions is not catalyzed by piperidine. The plots of second‐order rate constants of the reaction vs. mole fraction of water show maxima in the all‐aqueous solutions. Single‐parameter correlations of log k₂ vs. π* (dipolarity/polarizability), α (hydrogen‐bond donor acidity), and E_T^N (normalized polarity parameter) are very poor in the all solutions (for example, in aqueous solutions of ethanol, regression coefficients are 0.814, 0.113, and 0.486, respectively). Dual‐parameter correlations of log k₂ vs. π* and α in all cases represent significant improvement with regard to the single‐parameter models (in aqueous solutions of ethanol: n = 11, r = 0.980, and s = 0.034). Dipolarity/polarizability and hydrogen‐bond donor acidity (HBD) of media have opposite effects on the reaction rate. The activated complex leading to the zwitterionic intermediate is expected to be favored by increasing the solvent dipolarity/polarizability parameter. Increasing the hydrogen‐bond donor acidity of solvent stabilizes piperidine and hence the reaction rate decreases. A dual‐parameter equation of log k₂ vs. π* and α was obtained in the all‐aqueous solutions (n = 31, r = 0.956, s = 0.055) in which π* and α have approximately equal and opposite effects on the reaction rate. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 118–123, 2001     

Dipole polarizabilities of germanium clusters

Dipole polarizabilities of Ge_n clusters with 2–25 atoms are calculated using finite field (FF) method within density functional theory. The dipole moments and polarizabilities of clusters are sensitively dependent on the cluster geometries and electronic structures. The clusters with low symmetry and large HOMO–LUMO gap prefer to large dipole moments. The polarizabilities of the Ge_n clusters increase rapidly in the size range of 2–5 atoms and then fluctuate around the bulk value. The larger HOMO–LUMO gap may lead to smaller polarizability. As compared with the compact structure and diamond structure, the prolate cluster structure corresponds to a larger polarizability.     

Static and frequency dependent polarizabilities and hyperpolarizabilities of H2Sn

The structure–polarization relationship was investigated in a series of polysulfanes, H₂S_n. The reported results demonstrate that the forms of change of the polarizability components, α_ii, and the second hyperpolarizability components, γ_iiii, as well as the average values α and γ, respectively, of H₂S_n with n are similar. This shows that polarizability components can be easily used to determine corresponding hyperpolarizability data. A remarkable change of the hyperpolarizabilities with the molecular geometry of H₂S_n was found. This result can be used for the design of nonlinear optical materials with optimum properties. The present study uses the flexible σ bonded H₂S_n and is complementary to the works that considered the effect of conformational changes of π-conjugated systems on their hyperpolarizabities. The present computations were performed using the semiempirical approaches MNDO and MNDO/d, as well as ab initio methods with STO-3G, extended with polarization and diffuse functions, and [3s2p/7s5p2d] sets for H₂S_n. At the ab initio level, the electronic and the vibrational contributions to polarizabilities and hyperpolarizabilities were both computed for several members of H₂S_n. The frequency dependence of the above contributions and the static limit were discussed. Electron correlation was taken into account for several test cases using MP2 theory. The selected methods and the variety of the approximations on which they rely allow the systematic consideration of the effect of changes of the geometry of H₂S_n on their polarizabilities and second hyperpolarizabilities. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1698–1715, 1998     

Theoretical study of endohedral metallofullerenes: Sc3−nLanN@C80 (n=0–3)

To provide theoretical insight into the structures and properties of Sc₃N@C₈₀, which has been isolated in high yield and purity as a new stable endohedral metallofullerene, density functional calculations are carried out for the Sc_3?nLa_nN@C₈₀ (n=0–3) series. Because of electron transfer from Sc₃N to C₈₀, the electronic structure of Sc₃N@C₈₀ is formally described as (Sc₃N)⁶⁺C$_{80}^{6-}$. The encapsulated Sc₃N cluster takes a planar structure with long Sc–Sc distances and is highly stabilized inside the I_h cage of C₈₀, which rotates rapidly. As the number of La atoms increases, the Sc_3?nLa_nN cluster is forced to maintain a pyramidal structure in Sc_3?nLa_nN@C₈₀. In addition, the C₈₀ cage takes an open‐shell electronic structure due to an increase in the number of electrons transferring from Sc_3?nLa_nN. These make the endohedral structure less stable and more reactive. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1353–1358, 2001     

Apparent Molar Volume and Apparent Molar Refraction of Mono-, Di-, Tri-, and Tetra(oxyethylene) Glycol in Aqueous, 1,4-Dioxane,and Benzene Solutions at 298.15 K

Summary. The density and refractive index of aqueous, 1,4-dioxane, and benzene solutions of poly (oxyethylene) glycols of the type HO–(CH₂CH₂O) _n –H (n varying from 1 to 4) were measured at 298.15K. From these experimental data the apparent molar volume and the apparent molar refraction at infinite dilution were calculated. The limiting apparent molar volume of the investigated compounds in a definite solvent depends linearly on the number of oxyethylene groups. From these data, the volume of the monomeric unit was evaluated and found to be greater in non-aqueous solvents than in water. The limiting apparent molar refraction of the solute for the investigated systems, within the experimental uncertainties, is equal to the molar refraction of the pure solute. The electronic polarizability of the solute molecule depends linearly on the number of monomeric units and the ratio of the electronic polarizability to the molecular van der Waals volume is constant and independent of the number of oxyethylene groups.Received February 24, 2003; accepted (revised) April 10, 2003 Published online August 18, 2003     

Density functional studies of AnF6 (An=U,Np, and Pu) and UF6−nCln (n=1–6) using hybrid functionals: geometries and vibrational frequencies

We have compared the performance of widely used hybrid functionals for calculating the bond lengths and harmonic vibrational frequencies of AnF₆ (An=U, Np, and Pu) and UF_6?nCl_n (n=1–6) molecules using “small‐core” relativistic effective core potentials and extended basis sets. The calculated spectroscopic constants compare favorably with experimental data for the bond lengths (average error ≤ 0.01 Å) and vibrational frequencies (average error ≤ 7 cm^?1) of the AnF₆ molecules. The experimental vibrational frequencies of the stretching modes were available for most of the UF_6?nCl_n (n=1–6) molecules. The calculated vibrational frequencies are in good agreement with the experimental data to within 4.6 cm^?1 and 7.6 cm^?1 for selected Becke1 and Lee, Yang, Parr (B1LYP), and Becke3 and Perdew, Wang (B3PW91) functionals, respectively. We conclude that one can predict reliable geometries and vibrational frequencies for the unknown related systems using hybrid density functional calculations with the RECPs. The geometries and vibrational frequencies of the UF_6?nCl_n (n=1–6) molecules that have not been determined experimentally are also presented and discussed. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 2010–2017, 2001     

A proposed modification of CBS-4M model chemistry for application to molecules of increasing molecular size

 In order to calculate more accurately the enthalpies of formation, ΔH _f°(298 K), for large molecules using the CBS-4M method, a new formulation of the empirical higher-level correction to the energy is proposed: ΔE=a|S|² _{i i} I _{i i} +b(n _α+n _β)+cΔ<S ²>+Σn _i d _{i .} The new methodology (CBS-4MB) applied to a set of 114 molecules of different size significantly decreases the mean absolute deviation from 3.78 to 2.06 kcal/mol. Received: 7 February 2001 / Accepted: 5 April 2001 / Published online: 13 June 2001     

DFT studies on TinC2n (n=1–6) clusters

The geometric configurations and electronic structures of the Ti_nC_2n (n=1–6) clusters were studied by using the quantum chemical ab initio density functional theory (DFT) method. Our studies showed that these Ti_nC_2n (n=1–6) could grow gradually to form cyclic clusters through the subunits TiC₂ bonding to each other by C C or Ti C bond. The result could explain the existing experimental fact. The studies might also be helpful to the knowledge of the formation mechanism of the Met‐Cars. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 71: 313–318, 1999     

Theoretical study of silicon–sulfur clusters (SiS2)n (n = 1–6)

 The possible geometrical structures and relative stability of (SiS₂) _n (n=1–6) silicon–sulfur clusters are explored by means of density functional theory quantum chemical calculations. The effects of polarization functions and electron correlation are included in these calculations. The electronic structures and vibrational spectra of the most stable geometrical structures of (SiS₂) _n are analyzed by the same method. As a result, the regularity of the (SiS₂) _n cluster growth is obtained, and the calculation may used for predicting the formation mechanism of the (SiS₂) _n cluster. Received: 17 November 1999 / Accepted: 3 November 2000 / Published online: 3 May 2001     

Efficient calculation of Franck–Condon factors and vibronic couplings in polyatomics

We present a technique for the calculation of Franck–Condon factors and other integrals between vibronic wave functions belonging to different electronic states. The technique is well suited for the determination of the nonadiabatic or spin‐orbit couplings related to radiationless decays in polyatomics. Rigorous or approximate partitions of the internal coordinate space are exploited to achieve better efficiency and/or to go beyond the harmonic approximation. The technique is tested by computing the Internal Conversion and InterSystem Crossing rates of (CH₃)₃CNO in its ¹(n→π*) state. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 968–975, 2001     

Theoretical Studies on the Electronic and Optical Properties of a New Class of Aromatic Oligomers and Polymers

The purpose of this work is to provide an in‐depth interpretation of the optical and electronic properties of a series of aromatic oligomers and polymers, including [N‐(4‐(5‐(3‐(1,3,4‐oxadiazol‐2,5‐ylene)phenyl)‐1,3,4‐oxadiazol‐2‐ylene)phenyl)‐N‐(1,4‐phenylene)amine]_n (NPPP)_n and [N‐(4‐(5‐(3‐(1,3,4‐oxadiazol‐2,5‐ylene)phenyl)‐1,3,4‐oxa‐diazol‐2‐ylene)phenyl)‐N‐(1,4‐phenylene)naphthalene‐1‐amine]_n (NPPN)_n (n=1–4). These polymers and oligomers show great potential for application to organic light‐emitting diodes (OLEDs) as efficient blue emitters due to the tuning of the optical and electronic properties. The geometric and electronic structures of the oligomers in the ground state were investigated using density functional theory (DFT) and the ab initio HF, whereas the lowest singlet excited state of NPPP₁ was optimized with ab initio configuration interaction singles (CIS). To assign the absorption and emission peaks observed in the experiment, the absorption and emission spectra of the ground and lowest singlet excited states were calculated with time‐dependent DFT (TD‐DFT) and Zerner's independent neglect of differential overlap (ZINDO). All DFT calculations were performed using the B3LYP functional and the 6‐31G basis set. The results show that the HOMO, LUMO, energy gaps, ionization potentials, and electron affinities for these polymers are affected by increasing the conjugated chain, which favors the hole and electron injection into OLED. The trend of the variation of Δ_H‐L and the lowest excitation energies with 1/n, and the electronic structure and optical properties of these polymers were extrapolated and analyzed. The absorption spectra exhibit red shifts to some extent [the absorption spectra: 359.47 (NPPP₁)<370.84 (NPPP₂)<373.84 (NPPP₃)<375.33 nm (NPPP₄); 361.14 (NPPN₁)<370.34 (NPPN₂)<373.39 (NPPN₃)<374.62 nm (NPPN₄)]. Our calculated spectra agree well with the experimental findings where available, showing small but systematic deviations.     

Calculated properties of neutral and charged Al<Subscript><Emphasis Type="Italic">n</Emphasis></Subscript>Co<Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> clusters by density functional theory

Density functional calculations are performed to study the structures and electronic properties of Al _n Co _m clusters with n = 1–7 and m = 1–2. Frequency analysis is also performed after structural optimization to make sure that the calculated ground states are real minima. The corresponding total and binding energies, adiabatic electron affinities and ionization potentials are presented and discussed to aid the identification of our calculations. The BSSE correction is also considered in our calculation. Among Al _n Co _m , Al _n Co _m ⁻, and Al _n Co _m ⁼ clusters (n = 1–7 and m = 1–2), Al₄Co⁻, Al₆Co⁻, Al₂Co₂, and Al₆Co₂ are predicted to be more stable. Our results are consistent with the available experimental data.     

Simulation of phase‐separated structures of liquid‐crystalline polymer/flexible polymer blends

The phase‐separation kinetics of liquid‐crystalline polymer/flexible polymer blends was studied by the coupled time‐dependent Ginzberg–Landau equations for compositional order parameter ? and orientational order parameter S_ij. The computer simulations of phase‐separated structures of the blends were performed by means of the cell dynamical system in two dimensions. The compositional ordering processes of phase separation are demonstrated by the time evolution of ?. The influence of orientational ordering on compositional ordering is discussed. The small‐angle light scattering patterns are numerically reproduced by means of the optical Fourier transformation of spatial variation of the polarizability tensor α_ij, and the azimuthal dependence of the scattering intensity distribution is interpreted. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2915–2921, 2001     

Static and dynamic density functional investigation of hydrated beryllium dications

Using density functional theory with Becke's gradient correction for the exchange part and Vanderbilt's ultrasoft pseudopotentials, we investigated [Be(H₂O)_n]²⁺ clusters for n = 1 and 3. A new scheme implemented with the Car-Parrinello method is used, upon which no periodic boundary conditions are imposed so that isolated and possibly charged molecules can also be treated dynamically in a plane-wave basis. Harmonic vibrational frequencies are obtained via a fit of the molecular dynamics trajectory in terms of harmonic oscillators, for which we use a fragmentation scheme to analyze complex spectra. Based on this combination of techniques, we find good agreement with data from SCF calculations and correlated methods. © 1996 John Wiley & Sons, Inc.