Pol Basis Sets Research Articles

Dynamic Polarizability and Higher-Order Electric Properties of Fluorene, Carbazole, and Dibenzofuran

Static electric properties, from the dipole moment to the second-hyperpolarizability tensor γ, of the 3-membered, isoelectronic ring molecules, fluorene (FL), carbazole (CR), and dibenzofuran (DBF), have been calculated at various levels of approximation. The electron correlation effects have been included at the coupled-cluster (CC) level, using CCSD and CC2 versions of the method. DFT calculations with the CAM-B3LYP functional have also been performed, and the results are compared to the CC values. The electric property-tailored Pol basis set and its more compact Z3Pol version have been employed in all static calculations. Differences between dipole polarizability values computed at the Pol and Z3Pol bases have been found to be almost negligible. Therefore, all components of the frequency-dependent dipole polarizability tensor α(-ω;ω) have been determined at the CAM-B3LYP/Z3Pol level. Divergence occurring at electronic resonances has been eliminated using the complex polarization propagator (CPP) formalism, explicitly introducing an imaginary iΓ parameter to account approximately for the finite lifetime of the excited state. The imaginary part of the dipole polarizability Im α(-ω;ω) has been calculated for a wide range of external radiation energies up to 10 eV, and its maxima have been compared to the calculated vertical electronic excitation energies.

Hydrides, alkalides, and halides of calcium metal chain: electronic structure and NLO property

The ground state structure and stability of linear calcium chains Ca n X 2 , XCa n Y (X,Y = H, Li, Na, K; n = 1–8), Ca 8 Y 2 , and Ca 8 XY (X = H, K; Y = F, Cl, Br) have been calculated at the B3LYP/6-311++G(d,p) level. The hyperpolarizabilities of these metal complexes are calculated by employing B2PLYP, BHHLYP, and CAM-B3LYP functionals. The electron correlation at the MP2, CCSD, and CCSD(T) levels and the effect of basis set on the second hyperpolarizability of some representative molecules are also examined. Among the chosen functionals, the CAM-B3LYP method with POL basis set shows fair agreement with the CCSD(T)/POL γ zzzz . The chosen species are found to be sufficiently stable. The dialkalide calcium chains possess larger magnitude of linear polarizability and second hyperpolarizability compared to dihydrides and dihalides. The highest value of first hyperpolarizability has been obtained for the complex Ca 8 HK. Among the investigated metal complexes, the substantially larger second hyperpolarizability is obtained for alkalides, Ca 8 LiK, Ca 8 NaK, Ca 8 K 2 in which charge transfer is significantly larger. The calculated transition energy and transition moment associated with the most crucial electronic transition play a significant role in modulating the magnitude of hyperpolarizabilities. The TD-CAMB3LYP calculated transition energy shows increasing red shift following the power law ∆E ng = bn −c with c value varying in the order Ca n H 2 >> Ca n Li 2 = Ca n Na 2 ≥ Ca n K 2 . The most interesting feature is that no saturation limit of γ can be realized on increasing the length of calcium metal chains but ∆E ng approaches to a limiting value for n → ∞.

Static second hyperpolarizability of diffuse electron compound M2X (M = Li, na; X = H, F): Ab-initio study of basis set effect and electron correlation

Present investigation reveals that diffuse electron compounds M2X predict large (106a.u.) γav value. The basis set dependence of γav showed that the quality of basis function rather than its size is more important. Sadlej’s Pol basis set which is nearly four times less in size than aug-cc-pVQZ can give reliable estimate of γav. MP2 method in conjunction with large basis sets can give comparable results of γav that could be obtained from CCSD or CCSD(T). Higher order energy correction to MP2 leads to oscillatory behavior but inclusion of triple excitations to CCSD improves the magnitude of γav.

Nonlinear optical properties of fluorobenzenes: A Time-Dependent Hartree–Fock study

Second-order electronic hyperpolarizabilities (γ) of benzene and fluorobenzenes were computed using Hartree–Fock and correlated second-order Møller–Plesset perturbation theory (MP2) with the Sadlej’s POL basis set. Dynamic γ values were determined for the nonlinear optical (NLO) Third Harmonic Generation process at the wavelength of 1910nm. The results show that, differently from the electronic polarizabilities, the average 〈γ〉 values steadily decrease with the increase of the number of fluorine atoms, following a near-additive atomic contribution law. At the MP2/POL level 〈γ〉(C6H6) is predicted to be ca. four times greater than 〈γ〉(C6F6). Fluorination produces disadvantageous contributions for third-order NLO properties of π-conjugated materials.

Dipole (hyper)polarizabilities of fluorinated benzenes: An ab initio investigation

Relative stabilities, dipole moments and response electric properties of fluorinated benzenes have been studied using Hartree–Fock (HF) and correlated second-order Møller–Plesset perturbation theory (MP2) with the Sadlej's POL basis set. At the highest MP2/POL level, on passing from benzene to hexafluorobenzene the electronic mean polarizability value increases by only 3%, whereas the difference on the polarizability anisotropy is comparatively larger (+19%). The polarizability anisotropy of fluorobenzenes depends on the fluorination, increasing progressively with the increases of the number of fluorine atoms, following a near-additive atomic contribution law. Dipole moments and first-order hyperpolarizabilities among the investigated isomers differ up to a factor of two, these properties being potentially useful to discriminate the fluorobenzene isomers. Hyperpolarizability differences between the fluorinated isomers have been elucidated using hyperpolarizability density analyses. Electron correlation effects evaluated at the MP2 level are especially important for the first-order hyperpolarizabilities, increasing the HF values by 20–30%.

Basis set and electron correlation effects on static electric properties of 1,3-thiazoles and 1,3-benzothiazoles as potential fragments in push–pull NLO chromophores

Dipole moments μ, static averaged polarizabilities ⟨αrang;, and hyperpolarizabilities βvec of thiazole, benzothiazole, and their dipolar substituted derivatives have been computed by means of B3LYP and MP2 theories with the Pol basis set. Basis set effects have been considered for thiazole, benzothiazole, and doubly substituted thiazole and benzothiazole derivatives at the B3LYP level of theory and in the case of thiazole also at the HF and MP2 levels. Attention has been paid to thiazole geometry effects on the electric properties. The effectiveness of thiazole and benzothiazole as a conjugative pathway between electron donor NH2 and electron acceptor NO2 substituents has been compared with benzene. With one exception, differences in geometry appear to influence only modestly the calculated electric properties. The dipole moment- and polarizability-oriented Sadlej Pol basis set and also its reduced form ZPol basis sets are able to reproduce the aug-cc-pVTZ generated μ, ⟨αrang;, and also βvec at all levels of theory (HF, B3LYP, and MP2) very satisfactorily. All approaches yield almost identical basis set trends. A very good agreement in ⟨αrang; values between the B3LYP and MP2 approach has been found. While the doubly substituted thiazole derivatives possess smaller βvec calculated at the B3LYP level than at the MP2 level, for doubly substituted benzothiazole derivatives the B3LYP estimates of βvec exceed the MP2 estimates. The trends established by the B3LYP functional parallel the trends obtained with the MP2 method. The 2-nitrobenzothiazole-6-amine and 6-nitrobenzothiazole-2-amine exhibit the largest electric properties from the investigated set of molecules. Thiazole (benzothiazole) as a bridging unit between NH2 and NO2 shows slightly reduced (enhanced) NLO characteristic than pNA. Thiazole behaves as a dipolar bridge rather than just an electron acceptor substituent in singly substituted derivatives. Concerning the charge transfer process, NO2 group interacts better with thiazole than NH2, which can result from the tendency to pyramidization of the NH2 group.

Theoretical investigation of the dipole polarisability and second hyperpolarisability of cyclopentadiene homologues C4H4XH2 (X=C, Si, Ge, Sn)

Abstract Static and frequency-dependent electronic dipole polarisability, α, and second hyperpolarisability, γ, of the cyclopentadiene homologues C4H4XH2 (X=C, Si, Ge, Sn) were calculated by ab initio HF, MP2 and DFT-B3LYP methods using Sadlej POL basis sets, including vibrational and relativistic effects. The latter calculations were extended also to the furan homologues for comparison. The results show that both α and γ values increase monotonically as the heteroatom size increases. The energy values of the electronic transitions to the two lowest singlet 1 1 B 2 and 2 1 A 1 excited states decrease not uniformly as the heteroatom becomes heavier and the two-state model approximation is not adequate to explain the evolution of the (hyper)polarisability along the series, which indeed is essentially determined by the heteroatom property. Frequency dispersion correction on α increases down the group, by contrast γ dispersion is highest in cyclopentadiene and almost constant, at a lower value, in the heavier homologues. Electron correlation correction on the calculated properties is positive and rather large on γ. HF relativistic effects on 〈α〉 and 〈γ〉 are of little importance for both stannole and tellurophene and cannot account for the observed large discrepancy between the experimental and theoretical 〈γe〉(−ω;ω,ω,−ω) value in the latter compound. Vibrational contributions are calculated for the optically-heterodyned optical Kerr process (OHD-OKE). They are non negligible and show a clear heavy atom dependence. In the cyclopentadiene series they amount to 4–10% of 〈αe〉 and to 8–16% of 〈γe〉(−ω;ω,ω,−ω), while they are somewhat lower in the furan series. The transversal γxxxx value is higher in the cyclopentadiene than in the furan series by ca. 30–40%, suggesting that α-α′-linked cyclopentadiene homologues can be considered as valid alternatives to the corresponding furan homologues in projecting π-conjugated oligomers and polymers for NLO applications.

Nonlinear electric properties of alkali metal halides

The first and second hyperpolarizabilities as well as the dipole moments and dipole polarizabilities are studied for a series of the alkali metal halides (MeX, Me = Li, Na, K, X = F, Cl, Br). The static results have been calculated at various levels of including the electron correlation contribution. The frequency-dependent data for different nonlinear optical processes correspond to TDHF calculations and can be approximately scaled for the electron correlation contribution. The present study also gives a systematic comparison of the performance of the so-called Pol basis sets and the recently developed basis sets (HyPol) designed for calculations of electric hyperpolarizabilities. Several regularities in the calculated data are observed and discussed in terms of ionic models supplemented by the electron density confinement effect. For some of the studied systems the first and second hyperpolarizabilities are found to have interestingly high values, comparable to those for molecules used in nonlinear optical materials.