Determination of vibrational polarizabilities and hyperpolarizabilities using field-induced coordinates

An analytical set of field-induced coordinates is defined and is used to show that the vibrational degrees of freedom required to completely describe nuclear relaxation polarizabilities and hyperpolarizabilities is reduced from 3N-6 to a relatively small number. As this number does not depend upon the size of the molecule, the process provides computational advantages. A method is provided to separate anharmonic contributions from harmonic contributions as well as effective mechanical from electrical anharmonicity. The procedures are illustrated by Hartree-Fock calculations, indicating that anharmonicity can be very important

Field-induced coordinates for the determination of dynamic vibrational nonlinear optical properties

Three conjugated organic molecules that span a range of polarity and valence-bond/charge transfer characteristics were studied. It was found that dispersion can be insignificant, and that adequate treatment can be achieved with frequency-dependent field-induced vibrational coordinates (FD-FICs)

Nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties by means of electrical property expansions: Application to HF, CH4, CF4, and SF6

Electrical property derivative expressions are presented for the nuclear relaxation contribution to static and dynamic (infinite frequency approximation) nonlinear optical properties. For CF4 and SF6, as opposed to HF and CH4, a term that is quadratic in the vibrational anharmonicity (and not previously evaluated for any molecule) makes an important contribution to the static second vibrational hyperpolarizability of CF4 and SF6. A comparison between calculated and experimental values for the difference between the (anisotropic) Kerr effect and electric field induced second-harmonic generation shows that, at the Hartree-Fock level, the nuclear relaxation/infinite frequency approximation gives the correct trend (in the series CH4, CF4, SF6) but is of the order of 50% too small

Variational calculation of static and dynamic vibrational nonlinear optical properties

The vibrational configuration interaction method used to obtain static vibrational (hyper)polarizabilities is extended to dynamic nonlinear optical properties in the infinite optical frequency approximation. Illustrative calculations are carried out on H2 O and N H3. The former molecule is weakly anharmonic while the latter contains a strongly anharmonic umbrella mode. The effect on vibrational (hyper)polarizabilities due to various truncations of the potential energy and property surfaces involved in the calculation are examined

Calculation of Franck-Condon factors including anharmonicity: simulation of the C2 H4+ X̃2B 3u←C2 H4X̃1 Ag band in the photoelectron spectrum of ethylene

Our new simple method for calculating accurate Franck-Condon factors including nondiagonal (i.e., mode-mode) anharmonic coupling is used to simulate the C2H4+X2B 3u←C2H4X̃1 Ag band in the photoelectron spectrum. An improved vibrational basis set truncation algorithm, which permits very efficient computations, is employed. Because the torsional mode is highly anharmonic it is separated from the other modes and treated exactly. All other modes are treated through the second-order perturbation theory. The perturbation-theory corrections are significant and lead to a good agreement with experiment, although the separability assumption for torsion causes the C2 D4 results to be not as good as those for C2 H4. A variational formulation to overcome this circumstance, and deal with large anharmonicities in general, is suggested

A comparative analysis of two methods for the calculation of electric-field-induced perturbations to molecular vibration

Two common methods of accounting for electric-field-induced perturbations to molecular vibration are analyzed and compared. The first method is based on a perturbation-theoretic treatment and the second on a finite-field treatment. The relationship between the two, which is not immediately apparent, is made by developing an algebraic formalism for the latter. Some of the higher-order terms in this development are documented here for the first time. As well as considering vibrational dipole polarizabilities and hyperpolarizabilities, we also make mention of the vibrational Stark effec

The hardness profile as a tool to detect spurious stationary points in the potential energy surface

The energy and hardness profile for a series of inter and intramolecular conformational changes at several levels of calculation were computed. The hardness profiles were found to be calculated as the difference between the vertical ionization potential and electron affinity. The hardness profile shows the correct number of stationary points independently of the basis set and methodology used. It was found that the hardness profiles can be used to check the reliability of the energy profiles for those chemical system

Are the maximum hardness and minimum polarizability principles always obeyed in nontotally symmetric vibrations?

An overview is given on a study which showed that not only in chemical reactions but also in the favorable case of nontotally symmetric vibrations where the chemical and external potentials keep approximately constant, the generalized maximum hardness principle (GMHP) and generalized minimum polarizability principle (GMPP) may not be obeyed. A method that allows an accurate determination of the nontotally symmetric molecular distortions with more marked GMPP or anti-GMPP character through diagonalization of the polarizability Hessian matrix is introduced

Variational calculation of vibrational linear and nonlinear optical properties

A variational approach for reliably calculating vibrational linear and nonlinear optical properties of molecules with large electrical and/or mechanical anharmonicity is introduced. This approach utilizes a self-consistent solution of the vibrational Schrödinger equation for the complete field-dependent potential-energy surface and, then, adds higher-level vibrational correlation corrections as desired. An initial application is made to static properties for three molecules of widely varying anharmonicity using the lowest-level vibrational correlation treatment (i.e., vibrational Møller-Plesset perturbation theory). Our results indicate when the conventional Bishop-Kirtman perturbation method can be expected to break down and when high-level vibrational correlation methods are likely to be required. Future improvements and extensions are discussed

Basis set and electron correlation effects on initial convergence for vibrational nonlinear optical properties of conjugated organic molecules

The level of ab initio theory which is necessary to compute reliable values for the static and dynamic (hyper)polarizabilities of three medium size π-conjugated organic nonlinear optical (NLO) molecules is investigated. With the employment of field-induced coordinates in combination with a finite field procedure, the calculations were made possible. It is stated that to obtain reasonable values for the various individual contributions to the (hyper)polarizability, it is necessary to include electron correlation. Based on the results, the convergence of the usual perturbation treatment for vibrational anharmonicity was examined

Initial convergence of the perturbation series expansion for vibrational nonlinear optical properties

Initial convergence of the perturbation series expansion for vibrational nonlinear optical (NLO) properties was analyzed. The zero-point vibrational average (ZPVA) was obtained through first-order in mechanical plus electrical anharmonicity. Results indicated that higher-order terms in electrical and mechanical anharmonicity can make substantial contributions to the pure vibrational polarizibility of typical NLO molecules

Electronic and vibrational contributions to first hyperpolarizability of donor-acceptor-substituted azobenzene

In this study we report on the electronic and vibrational (hyper)polarizabilities of donor–acceptorsubstituted azobenzene. It is observed that both electronic and vibrational contributions to the electricdipole first hyperpolarizability of investigated photoactive molecule substantially depend on the conformation. The contributions to the nuclear relaxation first hyperpolarizability are found to be quite important in the case of two considered isomers (cis and trans). Although the double-harmonic term is found to be the largest in terms of magnitude, it is shown that the total value of the nuclear relaxation contribution to vibrational first hyperpolarizability is a result of subtle interplay of higher-order contributions. As a part of the study, we also assess the performance of long-range-corrected densityfunctional theory in determining vibrational contributions to electric dipole (hyper)polarizabilities. In most cases, the applied long-range-corrected exchange correlation potentials amend the drawbacks of their conventional counterparts

Acoustic transport of charge and spins in GaAs-based heterostructures

Report for the scientific sojourn carried out at the Paul Drude Institut für Festkörperelektronik of the Stanford University, USA, from 2010 to 2012. The objective of this project is the transport and control of electronic charge and spin along GaAs-based semiconductor heterostructures. The electronic transport has been achieved by taking advantage of the piezolectric field induced by surface acoustic waves in non-centrosymmetric materials like GaAs. This piezolectric field separates photogenerated electrons and holes at different positions along the acoustic wave, where they acummulate and are transported at the same velocity as the wave. Two different kinds of structures have been studied: quantum wells grown along the (110) direction, both intrinsic and n-doped, as well as GaAs nanowires. The analysis of the charge acoustic transport was performed by micro-photoluminescence, whereas the detection of the spin transport was done either by analyzing the polarization state of the emitted photoluminescence or by Kerr reflectometry. Our results in GaAs quantum wells show that charge and spin transport is clearly observed at the non-doped structures,obtaining spin lifetimes of the order of several nanoseconds, whereas no acoutically induced spin transport was detected for the n-doped quantum wells. In the GaAs nanowires, we were able of transporting successfully both electrons and holes along the nanowire axis, but no conservation of the spin polarization has been observed until now. The photoluminescence emitted by these structures after acoustic transport, however, shows anti-bunching characteristics, making this system a very good candidate for its use as single photon emitters.

A new technique to measure micromotion distribution around a cementless femoral stem.

The interfacial micromotion is closely associated to the long-term success of cementless hip prostheses. Various techniques have been proposed to measure them, but only a few number of points over the stem surface can be measured simultaneously. In this paper, we propose a new technique based on micro-Computer Tomography (μCT) to measure locally the relative interfacial micromotions between the metallic stem and the surrounding femoral bone. Tantalum beads were stuck at the stem surface and spread at the endosteal surface. Relative micromotions between the stem and the endosteal bone surfaces were measured at different loading amplitudes. The estimated error was 10μm and the maximal micromotion was 60μm, in the loading direction, at 1400N. This pilot study provided a local measurement of the micromotions in the 3 direction and at 8 locations on the stem surface simultaneously. This technique could be easily extended to higher loads and a much larger number of points, covering the entire stem surface and providing a quasi-continuous distribution of the 3D interfacial micromotions around the stem. The new measurement method would be very useful to compare the induced micromotions of different stem designs and to optimize the primary stability of cementless total hip arthroplasty.

Electoral Platforms, Implemented Policies, and Abstention

Recent studies of American politics evidence that political polarization of both the electorate and the political elite have moved 'almost in tandem for the past half century' (McCarty et al., 2003, p.2), and that party polarization has steadily increased since the 1970s. On the other hand, the empirical literature on party platforms and implemented policies has consistently found an imperfect but nonnegligible correlation between electoral platforms and governmental policies: while platforms tend to be polarized, policies are moderate or centrist. However, existing theoretical models of political competition are not manifestly compatible with these observations. In this paper, we distinguish between electoral platforms and implemented policies by incorporating a non-trivial policy-setting process. It follows that voters may care not only about the implemented policy but also about the platform they support with their vote. We find that while parties tend to polarize their positions, the risk of alienating their constituency prevents them from radicalizing. The analysis evidences that the distribution of the electorate, and not only the (expected) location of a pivotal voter, matters in determining policies. Our results are consistent with the observation of polarized platforms and moderate policies, and the alienation and indifference components of abstention.