Density-functional theory combined with molecular dynamics

Within the na-qmd approach, electronic (quantum) and nuclear (classical) dof are treated by combining time-dependent (td) density functional theory (dft) with molecular dynamics (md). The basic theorem of tddft [24-26] states that for a system of interacting particles the many-particle state and, thus, any observable are uniquely determined by the time-dependent single-particle density p(r, t) which can be written identically as the density... 

Car and Parrinello [97,98] proposed a scheme to combine density functional theory [99] with molecular dynamics in a paper that has stimulated a field of research and provided a means to explore a wide range of physical applications. In this scheme, the energy functional [ (/, , / , ] of the Kohn-Sham orbitals, (/(, nuclear positions, Ri, and external parameters such as volume or strain, is minimized, subject to the ortho-normalization constraint on the orbitals, to determine the Born-Oppenheimer potential energy surface. The Lagrangian,... 

FIGURE 1.1 Number of peer-reviewed publications with topics molecular dynamics or density functional theory combined with either catalysis or corrosion. Data obtained from the Web of Knowledge database by Thomson Reuters, 2013. https //access.webofknowledge.com/. 

The effects of the solvent and finite temperature (entropy) on the Wittig reaction are studied by using density functional theory in combination with molecular dynamics and a continuum solvation model.21 The introduction of the solvent dimethyl sulfoxide causes a change in the structure of the intermediate from the oxaphosphetane structure to the dipolar betaine structure. 

In 1985 Car and Parrinello invented a method [111-113] in which molecular dynamics (MD) methods are combined with first-principles computations such that the interatomic forces due to the electronic degrees of freedom are computed by density functional theory [114-116] and the statistical properties by the MD method. This method and related ab initio simulations have been successfully applied to carbon [117], silicon [118-120], copper [121], surface reconstruction [122-128], atomic clusters [129-133], molecular crystals [134], the epitaxial growth of metals [135-140], and many other systems for a review see Ref. 113. 

The main purpose of this chapter is to present the basics of ab initio molecular dynamics, focusing on the practical aspects of the simulations, and in particular, on modeling chemical reactions. Although CP-MD is a general molecular dynamics scheme which potentially can be applied in combination with any electronic structure method, the Car-Parinello MD is usually implemented within the framework of density functional theory with plane-waves as the basis set. Such an approach is conceptually quite distant from the commonly applied static approaches of quantum-chemistry with atom-centered basis sets. Therefore, a main... 

In the present chapter, we will focus on the simulation of the dynamics of photoexcited nucleobases, in particular on the investigation of radiationless decay dynamics and the determination of associated characteristic time constants. We use a nonadiabatic extension of ab initio molecular dynamics (AIMD) [15, 18, 21, 22] which is formulated entirely within the framework of density functional theory. This approach couples the restricted open-shell Kohn-Sham (ROKS) [26-28] first singlet excited state, Su to the Kohn-Sham ground state, S0, by means of the surface hopping method [15, 18, 94-97], The current implementation employs a plane-wave basis set in combination with periodic boundary conditions and is therefore ideally suited to condensed phase applications. Hence, in addition to gas phase reference simulations, we will also present nonadiabatic AIMD (na-AIMD) simulations of nucleobases and base pairs in aqueous solution. 

First principles approaches are important as they avoid many of the pitfalls associated with using parameterized descriptions of the interatomic interactions. Additionally, simulation of chemical reactivity, reactions and reaction kinetics really requires electronic structure calculations [108]. However, such calculations were traditionally limited in applicability to rather simplistic models. Developments in density functional theory are now broadening the scope of what is viable. Car-Parrinello first principles molecular dynamics are now being applied to real zeolite models [109,110], and the combined use of classical and quantum mechanical methods allows quantum chemical methods to be applied to cluster models embedded in a simpler description of the zeoUte cluster environment [105,111]. 

Molecular dynamics combined with time-dependent density functional theory... 

A promising method, developed in recent years, is the use of first principles molecular dynamics as exemplified by the Car-Parrinello technique (8]. In these calculations the interatomic potentials are explicitly derived from the electronic ground-state within the density functional theory in local or non-local approximation. It combines quantum mechanical calculations with molecular dynamics simulations and, therefore, overcomes the limitations of both methods. Actual computers allow only simulations of aqueous solutions of about 60 water molecules for several ps (10 s). This limit is still at least one order of magnitude shorter than the fastest directly measured water exchange rate, k = 3.5 x 10 s for [Eu(H20)8], i.e. one exchange event every (8 x 3.5 x lO s ) = 36 ps [9]. Nevertheless, several publications appeared in the late 1990s on solvated Be [10], K+ [11] and Cu + [12] presenting mainly structural results. 

An ingenious method of extending the molecular dynamics approach when incorporating quantum mechanics, is given by the scheme of Car and Parri-nello [255]. Their method combines classical MD with parameter-free quantum mechanics to result in an ab initio molecular dynamics method, sometimes also called dynamical simulated annealing. In this approach, the nuclei are treated as classical objects (the Bom-Oppenheimer approximation is still valid) but the electrons are understood from density-functional theory. As we have seen already, the interactions between the electrons and the nuclei can be described satisfactorily by pseudopotentials (see Section 2.15.2), together with plane-wave basis sets, supercells (see Section 2.18), and periodic boundary conditions. 

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