Configuration interaction simulation techniques

A theoretical justification of the scaling procedure was given by Pupyshev et al [14]. They compared the force field Fhf obtained in the Hartree-Fock (HF) limit with the force-field Fa obtained in the configuration interaction (Cl) technique, where the electron correlation effects are taken into account by mixing the HF ground state function with electronic excitations from the occupied one-electron HF states to the virtual (unoccupied) HF states. It was assumed that the force constants F01 obtained in the Cl approximation simulate the exact harmonic force field while those, extracted from the HF approximation FHF cast the quantum-mechanical force field F1-"1. It was demonstrated that under conditions listed below ... 

Both MD and MC techniques evolve a finite-sized molecular configuration forward in time, in a step-by-step fashion. (In this context, MC simulation time has to be interpreted liberally, but there is abroad connection between real time and simulation time (see [i, chapter 2]).) Common features of MD and MC simulation techniques are that there are limits on the typical timescales and length scales that can be investigated. The consequences of finite size must be considered both in specifying the molecular interactions, and in analysing the results. 

Ab initio simulation techniques derive interactions within the system from quantum mechanical principles, computing forces that act on the atomic nuclei in the system by solving the electronic structure problem on the fly , that is, at each nuclear configuration (Marx and Hutter, 2009). Ab initio techniques are highly accurate. However, this accuracy comes at the cost of excessive computational requirements. Their range of applicability is limited to a narrow window of lengths and times that corresponds to the microscopic scale (sizes of 1 nm and time spans of 100 ps). The size of systems that is required for meaningful structural studies of hydrated ionomer systems limits the utility of ab initio simulations. 

The past three decades have witnessed the development of three broad techniques—molecular dynamics (MD), Monte Carlo (MC), and cellular automata simulations—that approach the study of molecular systems by simulating submicroscopic chemical events at this intermediate level. All three methods focus attention on a modest number of molecules and portray chemical phenomena as being dependent on dynamic, and interactive events (a portrayal consistent with our scientific intuition and a characteristic not intrinsic to either thermodynamics or the traditional deterministic approach based on differential equations). These techniques lend themselves to a visual portrayal of the evolution of the configurations of the systems under study. Because each approach has its own particular advantages and shortcomings, one must take into consideration the pros and cons of each, especially in light of the nature of the problem to be solved. 

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