Polarizability, static dipole, clusters

TOO Schwerdtfeger, P. (2006) Atomic Static Dipole Polarizabilities, in Computational Aspects of Electric Polarizability Calculations Atoms, Molecules and Clusters (ed. G. Maroulis), Imperial College Press, London, pp. 1-32. 

Density functional static dipole polarizability and first-hyperpolarizability calculations of Na (w = 2,4,6,8) clusters using an approximate CPKS method and its comparison with MP2 calculations ... 

Thakkar and Lupinetti5 have used the coupled-cluster method in conjunction with the Douglas-Kroll relativistic Hamiltonian to obtain a very accurate value for the static dipole polarizability of the sodium atom. Their revised value for a(Na) = 162.88 0.6 au resolves a previous discrepancy between theory and experiment and when combined with an essentially exact value for lithium, establishes the ratio a(Li)/a(Na) = 1.0071 0.0037, so that, because of the... 

Table 8. The static dipole polarizability for the ground state and the first excited singlet state of pyrimidine in a.u. Coupled cluster values from [121]. The polarizability anisotropy parameter is defined as y = + a )/2 — Reproduced from [58]...

Haskopoulos and MarouUs [10] studied the interaction electric properties of H20 Rg (Rg = He, Ne, Ar, Kr, Xe). Correlation effects have been taken into account by employing M0Uer-Plesset (MP2, MP4) and coupled-cluster theories (CCSD, CCSD(T)) in connection with flexible, carefully designed basis sets. Bara-nowska et al. [11] computed the interaction-induced axial static dipole moments, polarizabilities and first hyperpolarizabilities of HCHO (HF)n (n= 1,2). They employed a series of methods (e.g. MP2, CCSD(T)) in connection with various basis sets. 

Hohm et al. have calculated the static dipole polarizability of P4 clusters using ab initio finite-field MP and coupled-cluster methods. The results have been compared with frequency-dependent measurements obtained fi-om the gas phase refi active index. 

Rayane D, AUouche AR, Benichou E et al (1999) Static electric dipole polarizabilities of alkali clusters. Eur Phys 19 243-248... 

Antoine R, Rayane D, AUouche AR et al (1999) Static dipole polarizability of small mixed sodium-lithium clusters. J Chem Phys 110 5568-5577... 

Figure 2-11. Comparison of experimental static dipole polarizabilities of Na clusters with theoretical SCF-CI values for Li clusters as a function of the cluster size. Reproduced with permission from [25]. Copyright 1991 American Chemical Society.

The static dipole polarizabilities for the Pq ground state of the neutral group-14 elements C, Si, Ge, Sn, Pb, and element Z = 114 have been determined from all-electron relativistic coupled cluster theory. It is shown that the isotropic and anisotropic components of the polarizability increase monotonically with the nuclear charge, except for the spin-orbit coupled /=0 states, which start to decrease from Sn to Pb and even further to element 114. So, spin-orbit coupling leads to a significant reduction of the polarizability of element 114, i.e., from 47.9 a.u. at the scalar-relativistic Douglas-Kroll level to 31.5 a.u. at the Dirac-Coulomb level of theory, which is below the value of Si. The calculations further demonstrate that relativistic and electron correlation effects are nonadditive. The measured dipole polarizabilities of Sn (42.4 11 a.u.) and Pb (47.1 7) are in reasonable agreement with the theoretical values, 52.9 a.u. and 47.3 a.u., respectively. 

The static polarizability of Sn clusters ( = 6-20) has been calculated using DFT and the B3P86 XC functional Agreement with experiment is good, provided the dipole moment of the cluster is taken into account. Indeed, in electric deflection experiment, the apparent polarizability of a rigid spherical rotor is the sum of the pure electronic contribution and of one due to the permanent dipole moment, 2/9 p /kBTrot, with Trot, the rotational temperature, which has been set to 3.5K in Ref. 101. 

Lim, I.S., Pernpointer, M., Laerdahl, J.K., Schwerdtfeger, P., Neogrady, P., Urban, M. Relativistic coupled-cluster static dipole polarizabilities of the alkali metals from Li to element 119. Phys. Rev. A. 60, 2822-2828 (1999)... 

Chandrakumar, K. R. S., Ghanty, T. K., Ghosh, S. K. (2004). Static dipole polarizability and binding energy of sodium clusters Na ( = 1 - 10) A critical assessment of all-electron based post-Hartree-Fock and density functional methods. Journal of Chemical Physics, 120, 6487. 

Rayane, D., Allouche, A. R.> Benichou, E., Antoine, R., Aubert-Frecon, M.> Dugourd, P, Broyer, M., Ristori, C.> Chandezon, F.> Hubert, B. A., 8c Guet, C. (1999). Static electric dipole polarizabilities of alkali clusters. The European Physical Journal D, 9, 243. 

Bazterra, V. E., Caputo, M. C., Ferraro, M. B., Fuentealba, P. (2002). On the theoretical determination of the static dipole polarizability of intermediate size silicon clusters. Journal of Chemical Physics, 227(24), 11158-11165. 

Karamanis, R, Maroulis, G., 8c Pouchan, C. (2006a). Basis set and electron correlation effects in all-electron ab initio calculations of the static dipole polarizability of small cadmium selenide clusters, (CdSe) , n = 1,2,3,4. Chemical Physics, 331(1), 19-25. 

Other Work on Water-Related Systems. Sonoda et al.61 have simulated a time-resolved optical Kerr effect experiment. In this model, which uses molecular dynamics to represent the behaviour of the extended medium, the principle intermolecular effects are generated by the dipole-induced-dipole (DID) mechanism, but the effect of the second order molecular response is also include through terms involving the static molecular / tensor, calculated by an MP2 method. Weber et al.6S have applied ab initio linear scaling response theory to water clusters. Skaf and Vechi69 have used MP2/6-311 ++ G(d,p) calculation of the a and y tensors of water and dimethylsulfoxide (DMSO) to carry out a molecular dynamics simulation of DMSO/Water mixtures. Frediani et al.70 have used a new development of the polarizable continuum model to study the polarizability of halides at the water/air interface. 

Exact static optical susceptibilities are conveniently calculated as successive derivatives on an applied electric field of the gs polarization, defined, in linear aggregates, as the dipole moment per unit length. The linear polarizability (a), the first and second hyperpolarizabilities (jS and y, respectively) obtained for 16-sites clusters are shown as full lines in Fig. 5. Left, middle and right panels refer to A, B and C clusters, respectively, for the parameters that, in Fig. 4 drive the system through the neutral-zwitterionic interface. Susceptibilities show a strong and non-trivial dependence on the intermolecular distance, and, to understand the physical origin of this complex and interesting behavior we shall discuss several approximated results. 

Linear and non-linear susceptibilities calculated within the mf approach, but relaxing the OGM approximation, lead to much better results, as shown by the dashed lines in Fig. 5. These results are calculated from the field derivatives of the total mf polarization, i.e. from the field derivatives of the sum of molecular dipole moments, rather than summing up derivatives of the molecular dipole moments as done in mf-OGM. Apart from very narrow regions around the neutral-zwitterionic interface in attractive lattices where the mf approximation itself is rather poor (cf results for p in Fig. 4, and the discussion in the next Section), the mf approximation to linear and non-linear susceptibilities is fairly good, suggesting that cooperativity dominates the gs properties of the material. ITiis observation gives confidence on the reliability of mf approaches to static optical responses, as that proposed by Tsiper and Soos [25, 62, 63, 64] for the calculation of the linear polarizability of clusters of non-polar molecules, and suggests its extension to clusters of polar molecules, and to the calculation of non-linear susceptibilities. 

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