Ab initio MD

A group of theoretical methods exists where the electronic wavefuntion is computed, and the atomic nuclei are propagated (using classical equations of motion). The Car-Parrinello MD method is one of this type [22-24]. These methods he between the extremes of the classical and ab initio methods, as they include some (quantum) electronic information and some (classical) dynamics information. These methods are called ah initio or first principles MD if you come from the classical community and semi-classical MD if you come firom the quantum community [9], Ah initio MD methods are far more expensive and cannot simulate as many molecules for as long as the classical simulations, but they are more flexible in that structures are not predetermined and information on the electronic structure is retained. Semi-classical MD can be carried out under periodic boundary conditions and thus the local liquid environment, and any extended bonding network, vyill be present. These methods hold a great deal of promise for the future study of ionic liquid systems, the first such calciilations on ionic liquids were reported in 2005 [21,25]. 

Using Ah Initio Quantum Chemical Methods to Study Ionic Liquids 

Unlike the HF method, the MP2 method recovers a good portion of the electron correlation in a system. DFT methods are popular because they recover some of the correlation for approximately the cost of a FI F computation. Correlation is important for describing aromatic systems such as the imidazolium cation, for accurately recovering dispersion effects, and describing hydrogen bonds well. DFT methods, however, lack a dispersion term, and this is problematic for ionic liquids, as Van der Waals interactions between the alkyl chains of the ions are important. Improvements can be made by the use of coupled cluster or multi-configurational methods, however, these require very large basis sets and are computationally very expensive to perform. 

Early computational studies of ionic liquids include semi-empirical methods these have now generally been superseded as advances in computing resources have allowed the routine use of higher level DFT and HF methods. As these methods have not been parameterized for the unusual interactions present in ionic liquids, the level of accuracy is unknovm. For example, early attempts to determine the H-bonding in [BMIM]C1 (Fig. 4.2-1) using the AMI [33] method predicted a very long C -H bond (1.56 A) in favor of a short H-Q bond (1.40 A) [34]. The equivalent interaction calculated at the MP2 level predicts the reverse, a strong C -H bond (1.11 A), and weaker H-Q interaction (2.02 A). 

Early quantum chemical calculations on ionic liquids were focused towards the haloaluminate, and related metal- (Au and Fe) containing melts, these are examined in the foUovying subsection. As the field has developed, this focus has shifted towards imidazolium-based ionic liquids because of their lower melting points and more fevorable physical properties. Imidazolium-based ionic liquids are discussed in the third subsection which examines imidazolium cations with small alkyl chains (methyl, ethyl and butyl). The ionic liquids which can be formed from imidazolium cations and small anions such as halides or [PFe] are then discussed, mention is also made of calculations carried out on a few more diverse systems. The electronic structure of the imidazolium-based ionic liquids is the focus of the fourth and final subsection. 

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As ab initio MD for all valence electrons [27] is not feasible for very large systems, QM calculations of an embedded quantum subsystem axe required. Since reviews of the various approaches that rely on the Born-Oppenheimer approximation and that are now in use or in development, are available (see Field [87], Merz ]88], Aqvist and Warshel [89], and Bakowies and Thiel [90] and references therein), only some summarizing opinions will be given here. 

The second aspect, predicting reaction dynamics, including the quantum behaviour of protons, still has some way to go There are really two separate problems the simulation of a slow activated event, and the quantum-dynamical aspects of a reactive transition. Only fast reactions, occurring on the pico- to nanosecond time scale, can be probed by direct simulation an interesting example is the simulation by ab initio MD of metallocene-catalysed ethylene polymerisation by Meier et al. [93]. 

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].)... 

Furthermore, the electrical conductivities of liquid Na-Sn alloys for the five compositions are determined with the Kubo-Greenwood scheme, using the trajectories from our ab initio MD simulations. The calculated values reproduce the measured strong variation of the conductivity with the Na (or Sn) concentration very well. The small (semimetallic) conductivity of the alloys with nearly equimolar composition can be explained by the position of the Fermi energy between the occupied sp-band of tin and the sp-band of sodium. 

In addition, for the sodium-antimony alloy, where the Zintl anions are Sb spiral chains, ab initio MD simulations are in progress. 

An important advance in making explicit polarizable force fields computationally feasible for MD simulation was the development of the extended Lagrangian methods. This extended dynamics approach was first proposed by Sprik and Klein [91], in the sipirit of the work of Car and Parrinello for ab initio MD dynamics [168], A similar extended system was proposed by van Belle et al. for inducible point dipoles [90, 169], In this approach each dipole is treated as a dynamical variable in the MD simulation and given a mass, Mm, and velocity, p.. The dipoles thus have a kinetic energy, JT (A)2/2, and are propagated using the equations of motion just like the atomic coordinates [90, 91, 170, 171]. The equation of motion for the dipoles is... 

Tab. 1.1 Comparison of the properties of quantum chemical electronic structure calculations (QC methods), classical molecular dynamics (Classical MD) based on empirical force fields and first-principles molecular dynamics (ab initio MD) simulations.

A proposal for the comprehensive study of chemical processes in a variety of important condensed-phase systems using modern theoretical methodology has been presented. The primary goals of the research are to provide microscopic information on the mechanisms and structural and dynamical properties of the chemical systems proposed for investigation, to test the applicability of modern ab initio molecular dynamics (MD) by comparison with experiment, and to develop and apply novel ab initio MD techniques in simulating complex chemical systems. The proposed research will contribute to the forefront of modern theoretical chemistry and address a number of important technological issues. The PI has carefully attempted to demonstrate his knowledge, ability, and resources to carry out the proposed research projects. 

To understand the main ideas that define ab initio MD, it is useful to first review some concepts from classical mechanics. Classical MD is a well-developed approach that is widely used in many types of computational chemistry and... 

The explanation of classical MD given above was meant in part to emphasize that the dynamics of atoms can be described provided that the potential energy of the atoms, U U(ru. .., r3N), is known as a function of the atomic coordinates. It has probably already occurred to you that a natural use of DFT calculations might be to perform molecular dynamics by calculating U U(r, ..., r3N) with DFT. That is, the potential energy of the system of interest can be calculated on the fly using quantum mechanics. This is the basic concept of ab initio MD. The Lagrangian for this approach can be written as... 

To conclude our brief overview of ab initio MD, we note that the dynamics defined by Eq. (9.16) define a microcanonical ensemble. That is, trajectories defined by this Lagrangian will conserve the total energy of the system. Similar to the situation for classical MD simulations, it is often more useful to calculate trajectories associated with dynamics at a constant temperature. One common and effective way to do this is to add additional terms to the Lagrangian so that calculations can be done in the canonical ensemble (constant N, V, and T) using the Nose-Hoover thermostat introduced in Section 9.1.2. 

Figure 9.5 Five configurations of a Pt13 cluster that are local minima on this cluster s potential energy surface as characterized by GGA DFT calculations. The three clusters in the upper part of the figure were generated by hand based on symmetry considerations. The two clusters in the lower part of the figure were obtained using ab initio MD as described in the text. The energy of each cluster is defined relative to the lowest energy cluster.

Figure 9.6 Energy of the Pt13 nanocluster simulated with ab initio MD using the methods...

For further details on the algorithms underlying ab initio MD, see M. C. Payne, M. P. Teter, D. C. Allan, T. A. Arias, and J. D. Joannopoulos, Rev. Mod. Phys. 64 (1992), 1045, and R. M. Martin, Electronic Structure Basic Theory and Practical Methods, Cambridge University Press, Cambridge, 2004. 

The development of improved ab initio MD algorithms using DFT remains an active area. For one example of work in this area, see T. D. Kiihne, M. Krack, F. R. Mohamed, and M. Parrinello, Phys. Rev. Lett. 98 (2007), 066401. Similar work exists for performing MD using high-level quantum chemistry techniques, as described, for example, in J. M. Herbert and M. Head-Gordon, Phys. Chem. Chem. Phys. 7 (2005), 3629. 

The ab initio model potential for Age was used in molecular dynamics (MD) simulation of the thermal behavior of different isomers of Age in our studies The advantages of using such kind of potential in MD simulation studies are related to the reliability of the quantitative predictions obtained, due to the use of an accurate model potential at the electron correlation level and to the extended length of the simulation time (comparing with other ab initio MD approaches) during which a good statistics is collected. 

At this point some misleading nomenclature in publications of simulations has to be clarified. Frequently simulations based on DFT functionals are termed ab initio MD and first principle or -empirical. This is indeed not correct as all available density functionals are of a more or less semiempirical nature, as pointed out by their developers themselves, e.g., by Becke in his presentation of the B3LYP functional (15). The term ab initio should be reserved, therefore, for simulations where for the QM part a true ab initio procedure, i.e., HF or correlated methods like MP/2 or better, is employed. Only by this one is also enabled to perform a method-inherent control of accuracy and deficiencies by increasing the level of theory from a one-determinantal to a multi-determinantal method. 

In order to reconcile this discrepancy, dynamics effect was examined by means of ab initio MD simulations at (U)B3LYP/6-31G. 44 Trajectories were initiated at the TS for the denitrogenation from 27 (R = Z = H) to 31 with 353 K Boltzmann distribution for the reaction coordinate translation. Out of 10 trajectories, 1 went back to the reactant, 8 gave 31, and 1 led directly to 29. Thus, the trajectory calculations reproduced experimental trend reported in the literature,45 namely spiropentane is the major product for the reaction of the parent 4-spirocyclopropane-l-pyrazoline. 

Since an early stage of the history of ab initio MD study, many cases have been observed in which the calculated trajectories do not support expectation derived from traditional reaction theories, such as RRKM and TST, and thus the applicability or suitability of these theories has been a matter of argument. In this section examples of one of those dynamics-derived phenomena are shown, namely nonstatistical barrier recrossing. 

Despite the simple form of Equation (1.83), the detailed formulation of an extended Lagrangian for CPCM is not a straightforward matter and its implementation remains challenging from the technical point of view. Nevertheless, is has been attempted with some success by Senn and co-workers [31] for the COSMO-ASC model in the framework of the Car-Parrinello ab initio MD method. They were able to ensure the continuity of the cavity discretization with respect to the atomic positions, but they stopped short of providing a truly continuous description of the polarization surface charge as suggested,... 

This restriction rules out all discrete models exclusively based on semiempirical force fields, leaving among the discrete models the MC/QM and the MD/QM procedures, in which the second part of the acronyms indicates that the solute is described at the quantum mechanical (QM) level, as well as the full ab initio MD description, and some mixed procedures that derive the position of some solvent molecules from semiclassical simulations, replace the semiclassical description with the QM one, and repeat the calculation on these small supermolecular clusters. The final stage is to perform an average on the results obtained with these clusters. These methods can be used also to describe electronic excitation processes, but at present, their use is limited to simple cases, such as vertical excitations of organic molecules of small or moderate size. This limitation is due to the cost of computations, and there is a progressive trend toward calculations for larger systems. 

Very recently, the structure of HDA-Si was experimentally disclosed by means of X-ray diffraction measurements [267, 268]. Daisenberger et al. [267] have attempted to obtain the structure factor S(Q) for the HDA form under pressure. Figure 20 shows the experimentally obtained S(Q) for LDA (3-13.5 GPa) and HDA (16.5 GPa). As the pressure is increased from 13.5 to 16.5 GPa, the first peak becomes more intense than the second peak and shifts to larger Q. The shift of the first peak indicates a large densihcation, and the overall features are in good agreement with the ab initio MD results [265] (Fig.16). Unfortunately, however, g(r) calculated from the S(Q) by Fourier transformation... 

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