Ionic quantum effects

By increasing pressure and/or decreasing temperature, ionic quantum effects can become relevant. Those effects are important for hydrogen at high pressure [7, 48]. Static properties of quantum systems at finite temperature can be obtained with the Path Integral Monte Carlo method (PIMC) [19]. We need to consider the ionic thermal density matrix rather than the classical Boltzmann distribution ... 

The Car-Parrinello method is similar in spirit to the extended system methods [37] for constant temperature [38, 39] or constant pressure dynamics [40], Extensions of the original scheme to the canonical NVT-ensemble, the NPT-ensemble, or to variable cell constant-pressure dynamics [41] are hence in principle straightforward [42, 43]. The treatment of quantum effects on the ionic motion is also easily included in the framework of a path-integral formalism [44-47]. 

A common alternative is to synthesize approximate state functions by linear combination of algebraic forms that resemble hydrogenic wave functions. Another strategy is to solve one-particle problems on assuming model potentials parametrically related to molecular size. This approach, known as free-electron simulation, is widely used in solid-state and semiconductor physics. It is the quantum-mechanical extension of the classic (1900) Drude model that pictures a metal as a regular array of cations, immersed in a sea of electrons. Another way to deal with problems of chemical interaction is to describe them as quantum effects, presumably too subtle for the ininitiated to ponder. Two prime examples are, the so-called dispersion interaction that explains van der Waals attraction, and Born repulsion, assumed to occur in ionic crystals. Most chemists are in fact sufficiently intimidated by such claims to consider the problem solved, although not understood. 

Properties that can be exploited to provide novel and unique properties to materials include surface and quantum effects, for example, van der Waals forces elec-trostaticinteraction ionic,covalent andhydrogenbonding andquantumconfinement. Additionally nonconventional means of molecular assembly and atomic manipulation can lead to novel material properties. Control and exploitation of these effects can lead to new and useful changes to the thermal, magnetic, electrical, optical and mechanical, and biological and physicochemical properties of materials. 

This illustrates that we are far from the point where we can develop robust and transferable semiempirical potentials for the general M/C interface. This task is fundamentally difficult because the bonding changes character at the interface, from metallic to ionic, and because of the structural complexity present. This probably requires explicit inclusion of quantum effects, at least at a low level. 

M. Benoit, D. Marx, and M. Parrinello (1999) The role of quantum effects and ionic defects in high-density ice. Solid State Ionics 125, p. 23... 

This relation was proved by Nyquist (10) to be a consequence of basic thermodynamics laws and, except for quantum corrections, was never really challenged. Studies performed with glass microelectrodes (II) and heterogeneous ionic systems (12) showed that for zero ionic gradients and zero applied currents, the measured levels of noise were in agreement with noise levels calculated from the impedance according to eq 1. Hence, a study of electrical noise of a system under equilibrium conditions can be initiated for only two reasons. First, if there is some a priori information that the system is in equilibrium, then measurements of the system impedance or temperature can be performed without external perturbations (quantum effects are not considered here). Second, if impedance and temperature are measured independently by some other techniques, noise measurements can verify that the system under study is in an equilibrium state. 

Studies of small chloride ion water clusters indicate that the intermolecular nuclear quantum effects stabilize the ionic hydrogen bonds in the single-shell structures, while they are destabilized through the competition with intramolecular nuclear quantum effects in the multishell structures [231]. Nuclear quantum effects on the hydrogen-bonded structure of base pairs were recently studied in Ref. [232] and in the out-of-plane ring deformation of hydrogen maleate anion in Ref. [233]. 

To describe the simple phenomena mentioned above, we would hke to have only transparent approximations as in the Poisson-Boltzmann theory for ionic systems or in the van der Waals theory for non-coulombic systems [14]. Certainly there are many ways to reach this goal. Here we show that a field-theoretic approach is well suited for that. Its advantage is to focus on some aspects of charged interfaces traditionally paid little attention for instance, the role of symmetry in the effective interaction between ions and the analysis of the profiles in terms of a transformation group, as is done in quantum field theory. 

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