Role of charge transfer interaction and conjugation length on electrical polarizability of doped trans-polyacetylene oligomers

The effects of charge transfer and molecular chain length on the electrical polarizability of doped trans-polyacetylene oligomers have been investigated using a series of quantum chemical methods ranging from Hartree-Fock to current density functional theory. Polarizability tensors of pristine and metal-doped trans-polyacetylene oligomers have been estimated. The nature of variations of polarizability tensor components are quite different for pristine and doped oligomers. For doped samples, distinct minima in the average static polarizabilities per acetylene unit have been observed. The results suggest that the competitive role of charge-transfer interaction and oligomer chain length are responsible for the observed minima. To simulate the ab initio results on polarizability variation, we propose a mathematical model that describes the minima quite satisfactorily.     

Utilizing relativistic effective core potentials for accurate calculations of molecular polarizabilities on transition metal compounds

The requirements necessary to extend an ECP basis set for the calculation of electric and linear optical properties to the transition metals are studied. Previously an augmentation of the SBK basis set for 39 elements with s and p electron only valences (H-Rn, excluding Ga, In, and Tl) [J. Comput. Chem., 2005, 26, 1464-1471] was presented. In this work, electric dipole moments, polarizabilities, and anisotropies of selected metal hydrides, sulfides, and bromides, cisplatin, and the Fe, Ru, and Os metallocene derivatives along with many other systems are calculated and discussed. ECP calculations of molecules containing 3d and 4d metal centers among main group atoms have good agreement, often within 1-2% of the all-electron result at the time-dependent Hartree-Fock (TDHF)/Sadlej level of theory. Molecules with a 5d metal center have a large difference from and are more accurate than the all-electron results due to the inclusion of relativistic effects in the ECPs. The polarizability as calculated with and without ECPs of metallic clusters and surfaces is increasingly different as atomic number increases, again due to a lack of relativistic effects in the all-electron calculations. The augmented ECP calculations are consistent with relativistic all-electron results, while the Sadlej calculations are consistent with other nonrelativistic results. Both relativistic and basis set effects are less noticeable when the metal is in a formally positive state.     

Calculated polarizabilities for some aliphatic and aromatic hydrocarbons

Ground-state molecular polarizabilities of some aliphatic and aromatic hydrocarbons have been calculated using the method of Marchese and Jaffé. The polarizability components for the typical normal alkane n-heptane are found to be very nearly independent of conformation; those for biphenyl show a significant dependence but the average polarizability is approximately constant. The polarizabilities of the n-alkanes in general are seriously underestimated, but relatively good agreement with experiment is obtained for benzene and biphenyl.     

Theoretical investigation of the (hyper)polarizabilities of pyrrole homologues C4H4XH (X = N, P, As, Sb, Bi). A coupled-cluster and density functional theory study

Geometries, inversion barriers, static and dynamic electronic and vibrational dipole polarizability (alpha), and first (beta) and second (gamma) hyperpolarizability of the pyrrole homologues C(4)H(4)XH (X = N, P, As, Sb, Bi) have been calculated by Hartree-Fock, M?ller-Plesset second-order perturbation theory, coupled-cluster theory accounting for singles, doubles, and noniterative triple excitations methods, as well as density functional theory using B3LYP and PBE1PBE functionals and Sadlej's Pol and 6-311G basis sets. Relativistic effects on the heavier homologues stibole and bismole have been taken into account within effective core potential approximation. The results show that the electronic (hyper)polarizabilities monotonically increase with the atomic number of the heteroatom, consistent with the decrease in the molecular hardness. Ring planarization reduces the carbon-carbon bond length alternation of the cis-butadienic unit, enhancing the electronic polarizability values (alpha(e)) by 4-12% and the (hyper)polarizability values (and gamma(e)) by 30-90%. Pure vibrational and zero-point vibrational average contributions to the (hyper)polarizabilities have been determined within the clamped nucleus approach. In the static limit, the pure vibrational hyperpolarizabilities have a major contribution. Anharmonic corrections dominate the pure vibrational hyperpolarizabilities of pyrrole, while they are less important for the heavier homologues. Static and dynamic electronic response properties of the pyrrole homologues are comparable to or larger than the corresponding properties of the furan and cyclopentadiene homologue series.     

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

Discrete and continuum contributions to multipole polarizabilities and shielding factors of hydrogen

Discrete and continuum contributions to the multipole polarizabilities and shielding factors of atomic hydrogen are computed. The discrete series show logarithmic convergence which can be accelerated by the u-transform. The continuum contributions increase with increasing multipole order and are already dominant in the quadrupole polarizability and shielding factor. The shielding factors have greater continuum contributions than the polarizabilities.     

Electric dipole polarizabilities and C6 dipole-dipole dispersion coefficients for sodium clusters and C60

The frequency-dependent polarizabilities of closed-shell sodium clusters containing up to 20 atoms have been calculated using the linear complex polarization propagator approach in conjunction with Hartree-Fock and Kohn-Sham density functional theories. In combination with polarizabilities for C(60) from a previous work [J. Chem. Phys. 123, 124312 (2005)], the C(6) dipole-dipole dispersion coefficients for the metal-cluster-to-cluster and cluster-to-buckminster-fullerene interactions are obtained via the Casimir-Polder relation [Phys. Rev. 73, 360 (1948)]. The B3PW91 results for the polarizability of the sodium dimer and tetramer are benchmarked against coupled cluster calculations. The error bars of the reported theoretical results for the C(6) coefficients are estimated to be 5%, and the results are well within the error bars of the experiment.     

A fast empirical method for the calculation of molecular polarizability

Summary A simple empirical method for the calculation of static molecular polarizability is described. The method is based on Slater's rules for the calculation of effective atomic nuclear shielding constants. The calculated molecular polarizabilities of a series of organic molecules correlated well (r=0.98) with experimental measurements. Accurate calculated polarizabilities can be obtained rapidly by this method and may prove useful in deriving relationships between chemical structure and properties.     

The calculation of molar polarizabilities by the CNDO/2 method: Correlation with the hydrophobic parameter,log P

Results of molecular orbital (MO) calculations by the complete neglect of differential overlap (CNDO /2) method on 50 small molecules are reported. The summation of calculated atomic polarizabilities are equated with molecular polarizabilities, and these are compared with experimentally determined values. It is found that there is very good agreement between calculated and experimental molecular polarizability. This provides a reliable method for the determination of molecular polarizabilities for compounds for which experimental values are not known. The relationship between log P and polarizability is discussed and analyzed in terms of contributions from electronic components to the partitioning energy.     

Variational calculation of dynamic polarizabilities

The finite field method of obtaining static multipole polarizabilities is extended to the calculation of dynamic polarizabilities. The first-order frequency dependent wavefunction is obtained variationally using a trial function, λ(ω)ψ₁(0). ψ₁(0) is the first-order wavefunction obtained in the static calculation. The results are applied to the approximation of the dynamic polarizability at imaginary frequencies. These are then used to calculate the coefficients for the inverse power series representation of the interatomic potential energy. The method has been applied to two simple cases, hydrogen and helium. For hydrogen the present method yields results close to the exact values for the static dipole polarizability and the dipole-dipole van der Waals coefficient; C₆. In the case of helium a simple Hartree-Fock function was perturbed but the results are still encouraging with the dipole-dipole van der Waals coefficient, C₆, calculated to within 7% of the accurate value.     

Polarizability as a local functional of the electron density

Expressions for the multipole polarizability and shielding factor for an atom are obtained using the model where the total electron energy is assumed to be a local functional of the electron density. This simple model correctly predicts the leading term in the 1/Z expansion of the polarizability. Further, the simple local density functional for the polarizability, when evaluated with ground-state Hartree-Fock densities, yields numerical values for atoms which are, in general, in reasonable agreement with those obtained from coupled Hartree-Fock theory.     

Hartree-Fock-Roothaan calculations of dipolar polarizabilities for closed-shell atoms

Methods are suggested for optimization of Slater type atomic orbitals in polarizability calculations of closed-shell atoms using “bound” perturbation theory (algebraic version of the Hartree-Fock method). The size and composition of the basis set of atomic orbitals providing the Hartree-Fock limit for perturbation parameters are considered. Dipolar polarizabilities are calculated for He, Be, Ne, and Mg atoms and their isoelectronic series. Translated fromZhurnal Strukturnoi Khimii, Vol. 41, No. 3, pp. 439-448, May–June, 2000.     

Electron-correlated calculations of the nuclear-shielding polarizability and magnetizability polarizability of H2, N2, HF, and CO

The effects of a uniform static electric field on the NMR shielding and magnetizability of H₂, N₂, HF, and CO are reported. The appropriate defining quantities are the shielding and magnetizability polarizabilities and these are calculated in a mixed numeric-analytic scheme with allowance for electron correlation via third-order Møller-Plesset (MP3) theory or linearized coupled cluster double excitation (L-CCD) theory. This is the first time that these theories have been applied to these properties. Our primary conclusion for the shielding polarizabilities is that, with the exception of H₂, the use of coupled cluster theory is necessary to establish the definitive values for these properties because of their extreme sensitivity to electron correlation. For the magnetizability polarizabilities we find the MP3 values to be in better agreement with the L-CCD results than the MP2 values are.     

Feasibility of density functional methods to predict dielectric properties of polymers

Feasibility of density functional theory (DFT) to predict dielectric properties such as polarizability of saturated polymers is investigated. Small saturated molecules, methane and propane, which is a monomer of polypropylene chain, are used in testing the methods. Results for polarizabilities based on several density functionals together with different basis sets are compared and contrasted with each other, with results by Hartree-Fock and second-order Moller-Plesset perturbation theory, as well as experimental data. The generalized gradient approximation PW91 method together with the 6-311++G(**) basis set is found to be the most suitable method, in terms of sufficient accuracy and computational efficiency, to calculate polarizabilities for large oligomers of polypropylene. The dielectric constant is then determined using the calculated polarizabilities and the Clausius-Mossotti equation. The molecular DFT methods at the PW916-311++G(**) level together with the Clausius-Mossotti equation give dielectric constants for saturated polymers such as polypropylene in good accordance with the experimental values.     

Polarizabilities of the alkali anions: Li- to Fr-

Static dipole polarizabilities are calculated for the ground states of the alkali anions from Li- to Fr-. The polarizabilities include scalar relativistic effects at the second-order Douglas-Kroll level and were computed using the finite-field, coupled-cluster CCSD(T) method with large, carefully optimized basis sets. The relativistic polarizabilities increase with Z, reach a maximum at Cs-, and then decrease again unlike their nonrelativistic counterparts which increase monotonically with Z.     

A comparative study of the dipole polarizability of some Zn clusters

We have employed a hierarchy of basis sets and computational techniques in order to approach the polarizability (alpha) of Zn(m), m = 2-20, in a systematic way. This procedure allows the proper approximate results to be selected and validated. More specifically, we have developed in a systematic way a series of basis sets that have been employed for the computation of the polarizability of the Zn atom. Comparison of the computed with the experimental and the best theoretical results allows us to comment on the quality of the basis sets, and to select some of the more successful ones in order to compute the polarizabilities of Zn(m), m = 2-20. We have employed a series of methods to take into account the correlation contribution. These include the following techniques: MP2, CC2, CCSD, CCSD(T), and DFT(B3LYP). We have used two effective core potentials, one small (3s2 3p6 3d10 4s2) and one large (4s2) core. The relativistic contribution to the properties is found to be significant. Thus we have studied in detail the relativistic effects on the polarizability of some small zinc clusters, by employing the Douglas-Kroll approximation in connection with the polarized basis sets developed by Kell? and Sadlej and the methods HF, CC2, and CCSD. Most of the polarizability values are static, but some frequency-dependent properties have also been computed in order to find out the difference between the dynamic and static ones. It is considered that the sharp changes of alpha(Zn(m))/m vs m may be correlated with the change of bonding, from van der Waals to covalent and finally to metallic bonding, in Zn(m). The present comprehensive study of the polarizabilities of Zn(m) includes a limited number of results for the first and second hyperpolarizability of some of the considered zinc clusters.     

Effective molecular polarizabilities and crystal refractive indices estimated from x-ray diffraction data

Although it was proposed some time ago that (hyper)polarizabilities might be estimated from the results of x-ray charge density refinements, early results were unconvincing. In this work we show that the one particle density obtained from the usual multipole refinement model does not contain sufficient information to determine these response properties and instead pursue the "constrained wave function" approach of fitting to x-ray structure factors. Simplified sum-over-states expressions are derived for determining the dipole polarizability from these wave functions, and these clearly show that the earlier work ignored important two-electron expectation values for the dipole polarizability, and two- and three-electron terms for Beta, etc. Correction factors for the simplified sum-over-states polarizability tensors from the constrained wave function are obtained by calibration against coupled Hartree-Fock ab initio results to yield in-crystal effective polarizability tensors. Results obtained for benzene, urea, and 2-methyl-4-nitroaniline demonstrate that the effective molecular polarizabilities clearly include the effects of intermolecular interactions and electron correlation, especially for urea where the effects on the polarizability are known to be quite large. We also carefully consider the way in which the linear bulk susceptibility, chi((1)), and refractive indices are determined from the x-ray fitted polarizabilities, employing three models based on a rigorous treatment of the local field. Incorrect results are obtained for the sort of molecules that are of interest in nonlinear optical applications if the molecules are approximated by single point dipoles. In contrast, the use of Lorentz-factor tensors averaged over several sites yields excellent results, with refractive indices obtained using this model in remarkably good agreement with optical measurements extrapolated to zero frequency.     

Cun、Agn和Aun(n≤9)团簇的静电极化率

The static polarizabilities and polarizability anisotropies of Cun,Agn and Aun (n≤9)clusters have been calculated by the B3LYP density functional method,which is a three parameter mixture of density functional and"exact" Hartree Fock exchange. The calculated results are compared with experimental polarizabilities of sodium clusters. It is shown that the size dependency of the static polarizabilities per atom of Cun,and Agn clusters possesses the same trend as that observed in sodium clusters exception of the Aunclusters while the polarizability of Au atom is much smaller than these of Cu and Ag.The(α-)of Au atom is the smallest and the(α-)per atom of Au approach to the values of Cu from the dimmer to the hexamer. It indicates that in Au clusters the electrons are more strongly attracted by the nuclei because of the more electrons. However,the absolute polarizabilities of the noble mental clusters are considerably smaller than those of the sodium clusters and the electronic structures of the noblemental are much more compact.     

Polarizabilities of heteroaromatic molecules: Azines revisited

Ab initio electron-correlated calculations of the equilibrium geometries, dipole moments, and static dipole polarizabilities are reported for benzene and 12 heteroaromatic six-membered rings obtained from it by aza-substitution. Our geometries and dipole moments agree well with available experimental microwave determinations. The polarizabilities are in reasonable agreement with the fragmentary experimental data available. Uncoupled Hartree-Fock calculations indicate that as much as half the polarizability comes from the σ-electrons. Simple empirical formulas based on atom- and bond-additive models correlate the calculated polarizabilities of 33 five- and six-membered heteroaromatic rings (10 azoles, 10 oxazoles, 13 azines) quite well. The correlation improves significantly if systematic data of uniform quality are used. © 1996 John Wiley & Sons, Inc.