Molecular system electric response

Second, in designing new molecule-based electronic devices, one of the major goals is the precise control of the current flowing between the terminals. Electrochemical molecular junctions allow for control of the potentials of the electrodes with respect to the redox potential of incorporated redox-active molecules with well-defined, accessible, tunable energy states. These junctions represent unique systems able to predict precisely at which applied potential the current flow will take off. Even though the presence of a liquid electrolyte represents a detriment towards possible applications, they provide the concepts for designing molecular devices that mimic electronic functions and control electrical responses. 

Hair cells are the sensory cells of the auditory and vestibular systems. Hair cells are the sensory cells of the internal ear, essential for the senses of sound and balance. The hair cell s transduction apparatus, the molecular machinery that converts forces and displacements into electrical responses, can respond to mechanical stimuli of less than 1 nm in amplitude, and of tens or even hundreds of kilohertz in frequency. Indeed, our hearing is ultimately limited by Brownian motion of water molecules impinging on the transduction apparatus. 

The static dipole polarizability is the linear response of an atomic or molecular system to the application of a weak static electric field [1], It relates to a great variety of physical properties and phenomena [2-5]. Because of its importance, there have been numerous ab initio calculations of isolated atomic and molecular polarizabilities [6-14]. Particular theoretical attention has been dedicated to the polarizability of free atomic anions [15-21] because of its fragility and difficulty in obtaining direct experimental results. In recent years theoretical studies have... 

In this chapter, we therefore consider whether it is possible to eliminate spin-orbit coupling from four-component relativistic calculations. This is a situation quite different from that of more approximate relativistic methods where a considerable effort is required for the inclusion of spin-orbit coupling. We have previously shown that it is indeed possible to eliminate spin-orbit coupling from the calculation of spectroscopic constants [12,13]. In this chapter, we consider the extension of the previous result to the calculation of second-order electric and magnetic properties, i.e., linear response functions. Although the central question of this article may seem somewhat technical, it will be seen that its consideration throws considerable light on the fundamental interactions in molecular systems. We will even claim that four-component relativistic theory is the optimal framework for the understanding of such interactions since they are inherently relativistic. 

It is possible to generalize this discussion in a useful way. Spectral measurements invariably assess how a molecular system changes in energy in response to some sort of external perturbation. The example presently under discussion involves application of an external electric field. If we write the energy as a Taylor expansion in some generalized vector perturbation X, we have... 

We assume that the absorbing gas is of a uniform composition and in thermal equilibrium. The absorption coefficient, which is defined by Lambert s law, Eq. 3.1, is expressed in terms of the probabilities of transitions between the stationary states of the supermolecular system, in response to the incident radiation. Assuming the interaction of radiation and matter may be approximated by electric dipole interaction, i.e., assuming the wavelengths of the radiation are large compared with the dimensions of molecular complexes, the transition probability between the initial and... 

Calculations of time-dependent electromagnetic properties of molecules at the correlated electronic structure level are conveniently carried out by the utilization of modern response theory [43-51], The transition of modern response theory for gas phase molecular systems to solvated molecules has been established [1-6] and these methods include the use of correlated electronic wavefunctions. These methods, reviewed here, have given rise a large number of computational approaches for calculating electric and magnetic molecular properties of solvated molecules. 

It is to Piekara and his collaborators that we owe almost all the currently available significant data on non-linear electric field effects in condensed molecular systems, including at least three different forms of molecular response. See Ann. Reports (,A), 1970, 67, 87— 96. (Note by Senior Reporter.)... 

When the external electric field is time-dependent, there is no well-defined energy of the molecular system in accordance with Eq. (100), and the wave function response can thus not be retrieved from a variational condition on the energy as in the analytic derivative approach described above. Instead the response parameters have to be determined from the time-dependent Schrodinger equation, a procedure which was illustrated in Section 3 for the exact state case. In approximate state theories, however, our wave function space only partially spans the 7V-electron Hilbert space, and the response functions that correspond to an approximate state wave function will clearly be separate from those of the exact state wave function. This fact is disregarded in the sum-over-states approach, and, apart from the computational aspect of slowly converging SOS expressions, it is of little concern when highly accurate wave function models are used. But for less flexible wave function models, the correct response functions should be used in the calculation of nonlinear optical properties. 

The ab initio calculation of NLO properties has been a topic of research for about three decades. In particular, response theory has been used in combination with a number of electronic structure methods to derive so-called response functions [41 8], The latter describe the response of a molecular system for the specific perturbation operators and associated frequencies that characterize a particular experiment. For example, molecular hyperpolarizabilities can be calculated from the quadratic and cubic response functions using electric dipole operators. From the frequency-dependent response functions one can also determine expressions for various transition properties (e.g. for multi-photon absorption processes) and properties of excited states [42]. 

It has been established in a series of works that a transformation of the electric dipole interaction is valid for deriving the optical characteristics of molecular systems with a response dominated by two electronic states [68-70 73-77], This procedure relates to the employment of a fluctuation dipole operator [78,79] as given by... 

In a liquid crystal watch, the molecules contained within a thin film of the screen are reorientated each second by extremely weak electrical signals. Here is a fine example of soft matter molecular systems giving a strong response to a very weak command signal. 

We are concerned with the interaction of a molecular system with the pulsed electric field E(x, t). Within the electric dipole approximation, the response... 

Within the electric dipole approximation, the response of the molecular system to an electric field is completely described by the electric polarization P(t), which therefore represents the central quantity of interest for the calculation of spectroscopic signals. For simphcity, we want to restrict ourselves to model systems with a single dipole-allowed electronic transition (say, the g) — <1>2) transition). 

The static electric dipole polarizability of the He atom has been studied in more detail than any other response property of any other atomic or molecular system. Not only is the non-relativistic value known accurately, and the relativistic corrections computed, but - in a recent... 

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