Dynamic dipole polarizability

Saue and Jensen used linear response theory within the random phase approximation (RPA) at the Dirac level to obtain static and dynamic dipole polarizabilities for Cu2, Ag2 and Au2 [167]. The isotropic static dipole polarizability shows a similar anomaly compared with atomic gold, that is, Saue and Jensen obtained (nonrelativ-istic values in parentheses) 14.2 for Cu2 (15.1 A ), 17.3 A for Ag2 (20.5 A ), and 12.1 A for Au2 (20.2 A ). They also pointed out that relativistic and nonrelativistic dispersion curves do not resemble one another for Auz [167]. We briefly mention that Au2 is metastable at 5 eV with respect to 2 Au with a barrier to dissociation of 0.3 eV [168, 169]. 

When Jens Oddershede was elected a Fellow of the American Physical Society in 1993, the citation read For contribution to the theory, computation, and understanding of molecular response properties, especially through the elucidation implementation of the Polarization Propagator formalism. Although written more than a decade ago, it is still true today. The common thread that has run through Jens work for the past score of years is development of theoretical methods for studying the response properties of molecules. His primary interest has been in the development and applications of polarization propagator methods for direct calculation of electronic spectra, radiative lifetime and linear and non-linear response properties such as dynamical dipole polarizabilities and... 

The eigenvectors Ffc determine the oscillator strengths of the excitations. This can be established using the sum-over-states representation of the standard many-electron theory for the dynamic dipole polarizability aav(co) [33]... 

We will divide the survey into three parts (3.1) static dipole polarizabilities, (3.2) static dipole hyperpolarizabilities, and (3.3) dynamic dipole polarizabilities and hyperpolarizabilities. Within each part there will be sub-sections dealing with the three isoelectronic series He, Ne, and Ar. For (3.2) and (3.3) the hydrogen atom will also be included. 

Thakkar [85] found that for 210 interactions, the combining rule produced an rms error of 0.52% with a maximum error of only 2.36%. A formal expression that can be given for Cf, coefficients [16] is that of an integral over frequency of the product of the dynamic dipole polarizabilities of the two interacting species. For like species, as in C, this would be an integral over the square of the dynamic dipole polarizability. If one takes as an approximation that the ratio of Cf,... 

Bishop, D.M., Kirtman, B. A peturbation method for calculating vibrational dynamic dipole polarizabilities and hyperpolarizabilities. J. Chem. Phys. 95, 2646-2658 (1991)... 

Spelsberg, D. and Meyer, W. ( 992i)Ab initio dynamic dipole polarizabilities for O2, J. Chem. Phys. 109, 9802-9810. 

The dynamic dipole polarizability tensor a can be expressed through eq. (1.55) when both A and B operators are the electric dipole moment... 

Calculating Vibrational Dynamic Dipole Polarizabilities and Hyperpolarizabilities. 

Kirpekar, S., Oddershede, J., 8c Jensen, H. J. Aa. (1995). Relativistic corrections to molecular dynamic dipole polarizabilities. Journal of Chemical Physics, 103, 2983. 

In linear, spherical and synnnetric tops the components of a along and perpendicular to the principal axis of synnnetry are often denoted by a and respectively. In such cases, the anisotropy is simply Aa = tty -If the applied field is oscillating at a frequency w, then the dipole polarizability is frequency dependent as well a(co). The zero frequency limit of the dynamic polarizability a(oi) is the static polarizability described above. 

Molecular dynamic studies used in the interpretation of experiments, such as collision processes, require reliable potential energy surfaces (PES) of polyatomic molecules. Ab initio calculations are often not able to provide such PES, at least not for the whole range of nuclear configurations. On the other hand, these surfaces can be constructed to sufficiently good accuracy with semi-empirical models built from carefully chosen diatomic quantities. The electric dipole polarizability tensor is one of the crucial parameters for the construction of such potential energy curves (PEC) or surfaces [23-25]. The dependence of static dipole properties on the internuclear distance in diatomic molecules can be predicted from semi-empirical models [25,26]. However, the results of ab initio calculations for selected values of the internuclear distance are still needed in order to test and justify the reliability of the models. Actually, this work was initiated by F. Pirani, who pointed out the need for ab initio curves of the static dipole polarizability of diatomic molecules for a wide range of internuclear distances. 

In contrast to the just discussed classical models [43,44], authors of works [38, 39] treated the problem of the dynamical polarizability ay(carbon cage quantum-mechanically, utilizing the 5-potential model concept, where the C60 cage is simulated by the Dirac 5-potential, V(r) = —Vo8(Rc—r). However, instead of calculating cy( >) directly, the latter was determined from experimental data on the C60 photoabsorption cross section a (o>) [60, 61] with the help of the dispersion relations for the real Re ay and imaginary Imay parts of the dipole polarizability ay ( >) ... 

The results are compared to those above for the CCI4/H2O interface. Several properties of alkane/water and CCU/water interfaces suggest that their interfacial characteristics should be similar. The measured interfacial tensions are 49.7 mN/m for hexane/water and 45 mN/m for CCU/water [73,74], with molecular dipole polarizabilities of 11.9 and 11.2 X 10 cm respectively [75]. However, IR experiments by Conrad and Strauss [76,77] show that water molecules dissolved in an alkane solvent are free to rotate while water dissolved in CCU is relatively constrained. It is the details of these molecular interactions that dominate interfacial structure and dynamics. 

Because of the expense in determining the dipoles, alternative models for the polarizability have been introduced. One, due to Sprik and Klein [65, 66], does not include dipole polarizabilities on the atoms. Instead it spreads the partial charge on an atom amongst a few sites that are very close to it. The position of the sites is fixed relative to the atom, but their charges are treated as dynamical variables that are allowed to change during an MD simulation, subject to the constraint that the total charge on the atom remains constant. 

F1F and DFT methods have been used by Smith et al.205 to calculate the dipole polarizabilities, a, of the all trans polyenes up to CigH2o, and polyacenes to CigH12 and their molecular ions. The static values and the dynamic response at 800 nm have been calculated. For the smaller molecules the results have been compared with those of correlated methods. It is found that the uncorrelated results are about 20% higher than those of the correlated methods for the neutral molecules but are very similar for the molecular ions. General conclusions about the scaling and frequency dependence of a values obtained by simpler methods are drawn. 

The situation is somewhat different for the convergence with the wavefunction model, i.e. the treatment of electron correlation. As an anisotropic and nonlinear property the first dipole hyperpolarizability is considerably more sensitive to the correlation treatment than linear dipole polarizabilities. Uncorrelated methods like HF-SCF or CCS yield for /3 results which are for small molecules at most qualitatively correct. Also CC2 is for higher-order properties not accurate enough to allow for detailed quantitative studies. Thus the CCSD model is the lowest level which provides a consistent and accurate treatment of dynamic electron correlation effects for frequency-dependent properties. With the CC3 model which also includes the effects of connected triples the electronic structure problem for j8 seems to be solved with an accuracy that surpasses that of the latest experiments (vide infra). 

A whole range of different properties can be obtained by choosing other interaction operators W t) and thus other V and A operators. Examples are given by Olsen and Jorgensen (1985) and include a diversity of properties such as derivatives of the dipole polarizability, the B term in magnetic circular dichroism, the first anharmonicity of a potential energy surface, two-photon absorption cross sections and derivatives of the dynamic hyperpolarizability. 

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