Generalized interatomic pair-potential function
Graphical abstract
Meta-stable diatomic dication : comparison of potential energies between five-parameter potential (this Letter), full CI calculation (AH 1992), multi-reference double excitation CI calculation (MNB 1987), James-Coolidge-method based calculation (YSW 1977), and accurate data.
Introduction
The nature of interatomic potentials [1], [2], [3], [4], [5], [6] determines the static and dynamical properties of matter in solid, liquid and gas phases, such as equilibrium geometry [2], threshold displacement energy [5], chemical-reaction mechanism [4], heat conductivity [2], transport coefficients [3], stability of biologic compounds DNA and RNA [2], and high-density energy storage materials [6]. Further, in many areas today, computer simulations [2], [3], [4] are becoming an integral part of many research investigations and provide help in understanding various problems at atomistic levels, for example, exploring macroscopic properties of gases under extreme conditions (e.g., hyper-high pressures, high temperature) [2] inaccessible for experimental measurement. But they require the potential functions for a wide range of interatomic separations [2]. Thus, interatomic potential plays an important role in solving a wide class of problems in physics, chemistry, and biology.
Theoretically, interatomic potentials can be directly predicted using advanced quantum-chemical approaches, more refined mathematical methods, and high-speed computers [2]. In principle, very accurate potentials can be obtained for a wide range of internuclear distances if sufficient electronic configurations are included in electronic-structure calculations [2]. However, it may be extremely time-consuming and prohibitively expensive in acquiring the interatomic potentials for many-electron systems or weakly bound van der Waals complexes [7]. Nevertheless, advanced experimental techniques, with the help of semi-empirical or empirical analytical potential functions [1], provide another efficient and direct approach to determine very accurate interatomic potentials from the collected spectroscopy, scattering data, or other measurements [1], [7].
To date, many interatomic pair-potential functions (see section B.2 List of Pair-Potential Functions in Appendix A) have been reported. All of them can be roughly summarized in five kinds of analytical forms: (i) Dunham-like Taylor expansions, (ii) suitable mathematical functional expressions, (iii) polynomials, (iv) hybrid, and (v) piecewise. The forms (i–iv) with potential parameters calibrated for one property predict other properties inadequately. They focus on describing either strongly or weakly, covalent or ionic bound, neutral, singly-, doubly-, or multiply-charged molecules, and often lose their validity for either small or relatively large internuclear distances. The form (v) uses piecewise analytical forms, in which different potential functions in different ranges of the internuclear distance R are splined together to give a continuous, multi-parameter function defined for all R. Multi-parameter splined functions lack a certain uniqueness [7]. One must make several arbitrary decisions as to where one function ends and the next begins.
On the other hand, an interatomic potential can be expressed in many different analytical functional forms, but all accomplish the same results that are in agreement with experiments [1], [2]. In this sense, the agreement between experiment and theory is not a sufficient sign of the correctness and good accuracy of a constructed pair-potential function, but only a necessary condition [1], [2], although higher degree of the said agreement may entail much better theory. This is supported by two known facts. The magnitude of the second virial coefficient is not sensitive to the form of the potential-curve shape and its minimum position, but depends only on the ratio between its well width and depth [2]. In the same way, the viscosity coefficient is not sensitive to the dependence of the potential on the separation distance at all [2]. Thus, for practical applications [1], [2], [3], [4], [5], is it possible to construct a unique pair-potential function that is able to describe adequately and accurately the interatomic potential for a wide range of separations and diatomic systems? In this Letter, we are going to demonstrate the possibility of constructing a generalized interatomic pair-potential function.
Section snippets
Generalized pair-potential function
A simple picture of the interatomic potential for a stable diatomic system [1] presents a function curve with a minimum at the equilibrium internuclear distance , a very sharp rise towards the infinity as , and a less sharp rise towards the dissociation limit as . This establishes the basic criteria [1] that a good interatomic potential must satisfy. In addition, a desirable characteristics of a good potential function is that its analytical formula is flexible enough to
Results and discussions
In Appendix A, we provide details on the case study and Fortran 90 source codes for determining the potential parameters. All parameters for the case study are summarized in Appendix A (Table A1, A2, A3, A4). To be noted, for cases that are not fitted in any of the five cases, the generalized function form Eq. (2) can be applied directly.
Conclusions
In conclusion, we have accomplished the goal of this Letter, successfully constructing a generalized interatomic pair-potential function that is able to describe accurately and adequately the potentials for a range of diatomic systems. Very recently, Marques et al. [50] have implemented Rydberg-London potential [19] in their simulation software and demonstrated that Rydberg-London potential is more reliable than the Lennard-Jones potential [23] to be used as starting geometries to obtain global
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