Static Longitudinal Polarizability Research Articles

Spin-orbit coupling and the static polarizability of single-wall carbon nanotubes

We calculate the static longitudinal polarizability of single-wall carbon tubes in the long wavelength limit taking into account spin-orbit effects. We use a four-orbital orthogonal tight-binding formalism to describe the electronic states and the random phase approximation to calculate the dielectric function. We study the role of both the Rashba as well as the intrinsic spin-orbit interactions on the longitudinal dielectric response, i.e., when the probing electric field is parallel to the nanotube axis. The spin-orbit interaction modifies the nanotube electronic band dispersions, which may especially result in a small gap opening in otherwise metallic tubes. The bandgap size and state features, the result of competition between Rashba and intrinsic spin-orbit interactions, result in drastic changes in the longitudinal static polarizability of the system. We discuss results for different nanotube types and the dependence on nanotube radius and spin-orbit couplings.

Quantitative Structure−Property Relationships for Longitudinal, Transverse, and Molecular Static Polarizabilities in Polyynes

The present work reports for the first time quantitative structure-property relationships, derived at the benchmark CCSD(T)/cc-PVTZ level of theory that estimate the static longitudinal, transverse, and molecular polarizability in polyynes (C2nH2), as a function of their length (L). In the case of independent electron models, regardless of the form of the nuclei potential that the electrons experience, the polarizability increases strongly with system size, scaling as L(4). In contrast, the static longitudinal polarizability in polyynes have a considerably weaker length-dependence (L(1.64)). This is shown to predominantly arise from electron-electron repulsion rather than electron correlation by a systematic study of the polarizability length dependence in several simple quantum mechanical systems (e.g., particle-in-box, simple harmonic oscillator) and other molecular systems (e.g., H2, H2(+), polyynes). Decrease of the electron-electron repulsion term is suggested to be the key factor in enhancing nonlinear polarizability characteristics of linear oligomeric and polymeric materials.

Modeling the electric field third-order nonlinear responses of an infinite aggregate of hexatriene chains using the electrostatic interaction model

A classical electrostatic polarization scheme using the additive distribution procedure has been applied to determine the static longitudinal polarizability and second hyperpolarizability of a all-trans hexatriene molecule in an infinite stretched fiber. The parameters have been derived from ab initio coupled-perturbed Hartree-Fock calculations and the electrostatic scheme has been validated via comparison with ab initio results on small clusters. Upon packing, the polarizability of all-trans hexatriene increases by 7% whereas the second hyperpolarizability increases by as much as 61%. These increases result from the balance between the enhancement of the (hyper)polarizability due to collinear packing and the reduction associated with lateral packing.

Hartree–Fock static longitudinal polarizabilities of fluorinated polyacetylene chains

Abstract This work presents ab initio results for the static longitudinal linear polarizability, α , and second hyperpolarizability, γ , of planar and twisted fluorinated polyacetylene chains. These electric properties were calculated by the finite field (FF) method, in the framework of the Hartree–Fock approximation. Our calculations, using different basis sets (6-31G and its standard extensions) indicate that inclusion of polarization functions, through the 6-31G(d) basis set, is important in the determination of the geometric parameters, specially dihedral angles. Nevertheless for both, planar and twisted F-substituted chains, our results show that the 6-31G basis set is sufficient to provide consistent estimates for α and γ . It is observed that the twisted conformation of F-substituted compounds leads to a marked reduction on the polarizabilities, specially on the second hyperpolarizability. Using converged geometries, the polarizabilities for the polymeric polydifluoroacetylene chains were obtained by extrapolation and compared with those of polymeric polyacetylene chains.

Substitution effects on the molecular structures and the longitudinal molecular polarizabilities of all-trans polyacetylene oligomers of increasing size

AM1 calculations have been performed on all-trans polyacetylene (PA) oligomers with an increasing number of unit cells to study the effect of donor or acceptor groups capped at opposite ends of PA chains, substituents included in the monomers, substituents' number and position in the monomers, on the molecular structures, and the static longitudinal polarizabilities (αL) and second-order hyperpolarizabilities (γL). Substitution of CH3, Cl, or F group at opposite ends of an oligomer results in an increase of αL and γL, but the substitution effects on ΔαL(N) and ΔγL(N) are very small. The asymptotic limit values are unaffected by the substitution. F substituent included in the monomer of an oligomer enhances the ΔαL(N) and ΔγL(N) values, especially at large N, but including monomers with CH3 or Cl substituents substantially reduces the ΔαL(N) and ΔγL(N) values. We alter the number of F substituents included in the monomers of oligomers and find that including two F substituents in the monomer leads to the larger enhancement of ΔγL(N). The effect of F substituents' position in the monomers of oligomers on ΔαL and ΔγL is obvious. The results may be helpful for the design of new materials for applications in nonlinear optics, particularly in the area of poled polymer films. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001

Electron correlation effects upon the static (hyper)polarizabilities of push‐pull conjugated polyenes and polyynes

Ab initio calculations, including the electron correlation effects via the Møller–Plesset partitioning, of the static longitudinal polarizability (αL), first and second hyperpolarizabilities (βL and γL) of small push-pull molecules have been carried out with the 6-31G and 6-31G* basis sets. Two types of conjugated segment (polyacetylene and polyyne) were used as linker between the nitro and amino fragments, chosen as acceptor and donor groups. For small chains, the triply bonded structures lead to larger γL than the doubly bonded structures, although the αL and βL values order in the opposite direction. The second-order Møller–Plesset (MP2) corrections are essential to obtain correct estimates of the hyperpolarizabilities and are generally much larger than the MP3 and MP4 contributions. Geometry optimizations were carried out with both basis sets within the Hartree–Fock and MP2 schemes; the MP2 geometries lead to smaller bond length alternations and thus larger (hyper)polarizabilities. For αL a careful choice of the geometry is more crucial than the use of polarization functions during the electronic state calculations; however, for the hyperpolarizabilities, both the geometry and the basis set are of importance. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 679–688, 1997

Electron correlation effects upon the static (hyper)polarizabilities of push-pull conjugated polyenes and polyynes

Ab initio calculations, including the electron correlation effects via the Møller–Plesset partitioning, of the static longitudinal polarizability (αL), first and second hyperpolarizabilities (βL and γL) of small push-pull molecules have been carried out with the 6-31G and 6-31G* basis sets. Two types of conjugated segment (polyacetylene and polyyne) were used as linker between the nitro and amino fragments, chosen as acceptor and donor groups. For small chains, the triply bonded structures lead to larger γL than the doubly bonded structures, although the αL and βL values order in the opposite direction. The second-order Møller–Plesset (MP2) corrections are essential to obtain correct estimates of the hyperpolarizabilities and are generally much larger than the MP3 and MP4 contributions. Geometry optimizations were carried out with both basis sets within the Hartree–Fock and MP2 schemes; the MP2 geometries lead to smaller bond length alternations and thus larger (hyper)polarizabilities. For αL a careful choice of the geometry is more crucial than the use of polarization functions during the electronic state calculations; however, for the hyperpolarizabilities, both the geometry and the basis set are of importance. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65: 679–688, 1997

Hartree–Fock static longitudinal (hyper)polarizability of polyyne

The evolution in the static longitudinal polarizability and second hyperpolarizability of the C4H2 through C54H2 oligomers of polyyne is studied at the Hartree–Fock level of theory. We find that the calculated values are highly sensitive to the adopted geometry. Using improved geometries, new extrapolation procedures and careful finite field determinations we extend earlier work by others so as to provide reliable estimates for the above properties in the infinite polymer limit.

Electron-correlation effects on the static longitudinal polarizability of polymeric chains. II. Bond-length-alternation effects.

Electron-correlation effects on the static longitudinal polarizability of polymeric chains. II. Bond-length-alternation effects.

Density functional study of the static longitudinal polarizability of model polymeric chains

We present the results of calculations of the static longitudinal polarizability of model molecular hydrogen chains of increasing length using density functional methods. The study considers the performance of different functionals, different basis sets, and the influence of the degree of bond length alternation. Significant differences in the asymptotic values are obtained in comparison with recent studies which have rigorously assessed the effects of more traditional methods of taking into account electron correlation corrections on coupled Hartree–Fock results. © 1995 John Wiley & Sons, Inc.

Ab initio investigation of the static polarizability of planar and twisted infinite polythiophene chains

In this paper we investigate the electronic structure and the static longitudinal polarizability of regular finite and infinite chains of polythiophene at the ab Initio Hartree-Fock level. The effects of the inclusion of polarization functions in the basis set and the influence of introducing a torsional twist between adjacent rings are considered. © 1994 John Wiley & Sons, Inc.

Ab initio longitudinal polarizabilities and hyperpolarizabilities of polydiacetylene and polybutatriene oligomers

Ab initio SCF calculations of the static longitudinal polarizability and hyperpolarizability for polydiacetylene (PDA) and polybutatriene (PBT) oligomers through C 26 are carried out using STO-3G and 4–31G bases. The results, i.e. property versus chain length, are fairly similar to previous semi-empirical INDO results. For PBT there is no evidence of saturation as the chain length increases. Extrapolation to the infinite polymer limit for PDA involves large uncertainties, though less so than for polyacetylene. A scaled semi-empirical method is suggested to overcome the extrapolation problem and is applied to PDA.

Convergence of finite chain approximation for linear and non-linear polarizabilities of polyacetylene

Static longitudinal polarizabilities, α zz , and hyperpolarizabilities, γ zzzz , are determined at the INDO level of approximation for finite polyene chain models of polyacetylene (C 2 N H 2 N+2 ) containing up to 62 carbon atoms. Where comparison is possible the agreement with ab initio calculations is excellent. The convergence with chain length of α zz / N and, particularly, γ zzzz / N is slow. At 62 carbons the deviation from the limiting infinite N value is estimated to be 14% for the polarizability and 39% for the hyperpolarizability. In the case of the hyperpolarizability there is a factor of 4–6 difference between our values and PPP results on the smaller chains.