Car-Parrinello dynamics

Despite the fact that the present textbook assumes that the reader has completed a basic quantum chemistry course, the author (according to his declaration in the Introduction) does not profit from this very extensively. Car-Parrinello dynamics is an exception. It positively belongs to the present chapter, while borrowing heavily from the results of Chapter 8. If the reader feels uncomfortable with this, this section may just be omitted. 

We have already listed some problems associated with the otherwise nice and powerful MD. We have also mentioned that the force field parameters (e.g., the net atomic charges) do not change when the conformation changes or when two mole- 

Let us assume the one-electron approximation. Then the total electronic energy q(/ ) is (in the adiabatic approximation) not only a function of the positions of the nuclei, but also a functional of the spinorbitals V = V(R, / / ) = 

The function V = V(R, / / ) will be minimized with respect to the positions R of the nuclei and the spinorbitals i depending on the electronic coordinates. 

If we are going to change the spinorbitals, we have to take care of their orthonormality at all stages of the change. For this reason Lagrange multipliers appear in the equations of motion (Appendix N). We obtain the following set of Newton equations for the motion of M nuclei 

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Semiclassical techniques like the instanton approach [211] can be applied to tunneling splittings. Finally, one can exploit the close correspondence between the classical and the quantum treatment of a harmonic oscillator and treat the nuclear dynamics classically. From the classical trajectories, correlation functions can be extracted and transformed into spectra. The particular charm of this method rests in the option to carry out the dynamics on the fly, using Born Oppenheimer or fictitious Car Parrinello dynamics [212]. Furthermore, multiple minima on the hypersurface can be treated together as they are accessed by thermal excitation. This makes these methods particularly useful for liquid state or other thermally excited system simulations. Nevertheless, molecular dynamics and Monte Carlo simulations can also provide insights into cold gas-phase cluster formation [213], if a reliable force field is available [189]. 

N. L. Doltsinis and M. Sprik (2003) Theoretical pKa estimates for solvated P(0H)6 from coordination constrained Car-Parrinello dynamics. Phys. Chem,. Chem. Phys. 5, p. 2612... 

Asvany, O. Kumar, P Redlich, B. Hegemann, I. Schlemmer, S. Marx, D. Understanding the infrared spectrum of bare CH5-I-. Science 2005, 309, 1219-1222. Gregoire, G. Gaigeot, M.P Marinica, D.C. Lemaire, J. Schermann, J.P Desfrancois, C. Resonant infrared multiphoton dissociation spectroscopy of gas-phase protonated peptides. Experiments and Car-Parrinello dynamics at 300 K. Phys. Chem. Chem.Phys. 2007, 9, 3082-3097. 

Car-Parrinello dynamics allows for the electron structure to be changed in flight , when the nuclei move. 

The already mentioned recent overviews of Barone and co-workers [541, 544] also contain information about recent computations of vibrationaUy resolved absorption spectra including environmental effects. Recent developments and applications of TD-DFT in combination with Car-Parrinello dynamics for the description of photochemical processes in complex systems were described by Moret et al. [116, 847] and Buda [848]. We have also already mentioned recent works of Bearpark, Robb et al. [50, 134-136] and Martinez and co-worker [103,131,133]. For recent applications concerning biologically oriented questions we again refer to the excellent review of Seim and Thiel [60] and some other works [702-704]. 

Specific solute-solvent interactions involving the first solvation shell only can be treated in detail by discrete solvent models. The various approaches like point charge models, siipennoleciilar calculations, quantum theories of reactions in solution, and their implementations in Monte Carlo methods and molecular dynamics simulations like the Car-Parrinello method are discussed elsewhere in this encyclopedia. Here only some points will be briefly mentioned that seem of relevance for later sections. 

Figure B3.3.12. Sulphur atoms in liquid iron at the Earth s core conditions, simnlated by first-principle Car-Parrinello molecular dynamics, (a) Initial conditions, showing a mannally-prepared initial cluster of snlphur atoms, (b) A short tune later, indicating spontaneous dispersal of the snlphur atoms, which mingle with the surroundmg iron atoms. Thanks are dne to D Alfe and M J Gillan for this figure. For fiirtlier details see [210. 211].

Remler D K and Madden P A 1990 Molecular dynamics without effective potentials via the Car-Parrinello approach Mol. Phys. 70 921-66... 

Abstract. We present novel time integration schemes for Newtonian dynamics whose fastest oscillations are nearly harmonic, for constrained Newtonian dynamics including the Car-Parrinello equations of ab initio molecular dynamics, and for mixed quantum-classical molecular dynamics. The methods attain favorable properties by using matrix-function vector products which are computed via Lanczos method. This permits to take longer time steps than in standard integrators. 

Car-Parrinello Equations of Ab Initio Molecular Dynamics, Constrained Newtonian Dynamics... 

In the Car-Parrinello method [6] (and see, e.g., [24, 25, 16, 4]), the adiabatic time-dependent Born-Oppenheimer model is approximated by a fictitious Newtonian dynamics in which the electrons, represented by a set of... 

Abstract. This paper presents results from quantum molecular dynamics Simula tions applied to catalytic reactions, focusing on ethylene polymerization by metallocene catalysts. The entire reaction path could be monitored, showing the full molecular dynamics of the reaction. Detailed information on, e.g., the importance of the so-called agostic interaction could be obtained. Also presented are results of static simulations of the Car-Parrinello type, applied to orthorhombic crystalline polyethylene. These simulations for the first time led to a first principles value for the ultimate Young s modulus of a synthetic polymer with demonstrated basis set convergence, taking into account the full three-dimensional structure of the crystal. 

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

A key feature of the Car-Parrinello proposal was the use of molecular dynamics a simulated annealing to search for the values of the basis set coefficients that minimise I electronic energy. In this sense, their approach provides an alternative to the traditioi matrix diagonalisation methods. In the Car-Parrinello scheme, equations of motion ... 

Although constrained dynamics is usually discussed in the context of the geometrically constrained system described above, the same techniques can have many other applications. For instance, constant-pressure and constant-temperature dynamics can be imposed by using constraint methods [33,34]. Car and Parrinello [35] describe the use of the extended Lagrangian to maintain constraints in the context of their ab initio MD method. (For more details on the Car-Parrinello method, refer to the excellent review by Gain and Pasquarrello [36].)... 

A successful tool to describe and interpret experimental findings of liquids is to perform ab initio molecular dynamics (MD) simulations for the particular systems. We performed such simulations for 5 different compositions of NaSn - ranging from 20% to 80% of sodium - applying the Car-Parrinello technique [5]. 

Thar J, Reckien W, Kirchner B (2007) Car-Parrinello Molecular Dynamics Simulations and Biological Systems. 268 133-171... 

Markwick PRL, Doltsinis NL, Schlitter J (2007) Probing irradiation induced DNA damage mechanisms using excited state Car-Parrinello molecular dynamics. J Chem Phys 126 045104... 

The Kohn-Sham theory made a dramatic impact in the field of ab initio molecular dynamics. In the 1985, Car and Parrinello38 introduced a new formalism to study dynamics of molecular systems in which the total energy functional defined as in the Kohn-Sham formalism proved to be instrumental for practical applications. In the Car-Parrinello method (CP), the equations of motion are based on a Lagrangian (Lcp) which includes fictitious degrees of freedom associated with the electronic state. It is defined as ... 

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