First-principles electronic-structure methods

For the electronic ground state, i.e., k = 0, Kohn-Sham (KS) density functional theory is commonly used. In this case, the energy is given by 

Molecular Dynamics Simulation From Ab Initio to Coarse Grained  

The orbitals which minimize the total, many-electron energy (O Eq. 7.53) are obtained by solving self-consistently the one-electron Kohn-Sham equations, 

DFT is exact in principle, provided that Exc [p] is known, in which case (see O Eq. 7.53) is an exact representation of the ground state energy Eo (see O Eq. 7.8). In practice, however, Exc [p] is not - and presumably never will be - known exactly therefore (semiempirical) approximations are used. 

The starting point for most density functionals is the local density approximation (EDA), which is based on the assumption that one deals with a homogeneous electron gas. Exc is split into an exchange term Ex and a correlation term Ec. Within the EDA, the exchange functional is given exactly by Dirac (1930)  

The FP-LMTO and PP methods have been implemented from first principles within the DFT and require only the atomic number and an assumed functional form for the exchange and correlation energy of the electrons as input. Historically, the latter functional has been treated within both the standard local-density 

Dislocations and Plasticity in bcc Transition Metals at High Pressure 

In the PP method applied to transition metals one normally treats only the valence s, p, and d electrons, which total five per atom in V and Ta, and six per atom in Mo. Here special pseudopotentials in the Troulher-Martins form [48] have been constructed from scalar-relativistic atomic calculations to be accurate in the pressure range below 400 GPa. An important advantage of the PP method is that it provides accurate forces so that fuUy relaxed atomic configurations can be considered. We have used this capabihty here to obtain accurate relaxed 110 and 211 y surfaces for Ta, Mo, and V. It is also possible to use relaxed PP configurations to perform vahdating FP-LMTO calculations on relaxed defects and y surfaces, as was done previously at ambient pressure [13,45]. 

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Equation (2) is an example of a sum-over-states (SOS) expression of a molecular response property. It suggests an easy way of computing / , but in practice the SOS approach is rarely taken because of its very slow convergence, i.e., because of the need to compute many excited states wavefunctions. The summation goes over all excited states and also needs to include, in principle, the continuum of unbound states. As it will be shown below, there are more economic ways of computing [1 within approximate first-principles electronic structure methods. 

Huge systems like DNA are not accessible by traditional first-principles algorithms as employed in electronic structure theory. However, first-principles electronic structure methods are often needed in order to achieve the necessary level of accuracy for either benchmark calculations that may serve as a reference or in cases where a detailed molecular picture is mandatory. It is therefore desirable to further develop ab initio and DFT methods in the context of multiscale modeling [147]. Examples for extended first-principles CPMD calculations on electronic and optical properties of DNA and on the reactivity of radical cations can be found in Refs. [148-150]. 

We show two examples of the combination of statistical mechanics with first principles electronic structure methods. Although first principles molecular dynamics has been applied for some time to the study of relatively simple systems, its application to Earth materials is more recent. These examples illustrate the power of modem density functional theory and the ability that now exists to treat large systems at high temperature. 

The most common form of AIMD simulation employs DFT (see section First Principles Electronic Structure Methods ) to calculate atomic forces, in conjimction with periodic boundary conditions and a plane wave basis set. Using a plane wave basis has two major advantages over atom-centered basis functions (1) there is no basis set superposition error (Boys and Bernardi 1970 Marx and Hutter 2000) and (2) the Pulay correction (Pulay 1969,1987) to the HeUmann-Feynman force, due to basis set incompleteness, vanishes (Marx and Hutter 2000, 2009). 

The above mentioned potentials can be classified into the empirical ones, which may not be sufficiently accurate to reproduce the dynamics of molecular systems in some cases. There are also a wide variety of semiempirical potentials, known as TB potentials, which use QM matrix representation whose elements are obtained through empirical formulae. For more accurate cases, ab initio QM methods are used to calculate the potential energy of the system on the fly, which is the combination of first principles electronic structure methods with MD based on Newton s equations of motion. 

CPMD has combined first principles electronic structure methods with MD based on Newton s equations of motion. Grand-state electronic structures were described according to DFT in plane-wave pseudopotential framework. 

Our work demonstrates that EELS and in particular the combination of this technique with first principles electronic structure calculations are very powerful methods to study the bonding character in intermetallic alloys and study the alloying effects of ternary elements on the electronic structure. Our success in modelling spectra indicates the validity of our methodology of calculating spectra using the local density approximation and the single particle approach. 

The structure and dynamics of clean metal surfaces are also of importance for understanding surface reactivity. For example, it is widely held that reactions at steps and defects play major roles in catalytic activity. Unfortunately a lack of periodicity in these configurations makes calculations of energetics and structure difficult. When there are many possible structures, or if one is interested in dynamics, first-principle electronic structure calculations are often too time consuming to be practical. The embedded-atom method (EAM) discussed above has made realistic empirical calculations possible, and so estimates of surface structures can now be routinely made. 

Electronic Structure Calculations. We have used first-principles electronic structure calculations as manifest in the (spin) density functional linearized muffin-tin orbital method to examine whether the asymmetry in properties is reflected in a corresponding asymmetry in the one-electron band structure. While in a more complete analysis explicit electron correlation of the Hubbard U type would be intrinsic to the calculation,17 we have taken the view that one-electron bandwidths point to the possible role that correlation might play and that correlation could be a consequence of the one-electron band structure rather than an integral part of the electronic structure. We have chosen the Lai- Ca,Mn03 system for our calculations to avoid complications due to 4f electrons in the corresponding Pr system. 

In addition to the development in the methodology to compute electronic structures, there have been several attempts to handle the simulation of a chemical event in a system with a large number of degrees of freedom. The Car-Parrinello (CP) approach [5], often referred to as first-principles molecular dynamics (FPMD) method, opened the way to the molecular dynamics simulations based on the first-principles electronic structure calculations. The point of the method is to circumvent the explicit... 

In the first part of this work, a brief overview over several strategies to combine such time domain transport simulations with first principles electronic structure theory is given. For the latter, we restrict ourselves to a discussion of time dependent density functional theory (TDDFT) only. This method is by far the most employed many body approach in this field and provides an excellent ratio of accuracy over computational cost, allowing for the treatment of realistic molecular devices. This digest builds on the earlier excellent survey by Koentopp and co-workers on a similar topic [13]. Admittedly and inevitably, the choice of the covered material is biased by the authors interests and background. 

The Amsterdam Density Functional package (ADF) is software for first-principles electronic structure calculations (quantum chemistry). ADF is often used in the research areas of catalysis, inorganic and heavy-element chemistry, biochemistry, and various types of spectroscopy. ADF is based on density functional theory (DFT) (see Chapter 2.39), which has dominated quantum chemistry applications since the early 1990s. DFT gives superior accuracy to Hartree-Fock theory and semi-empirical approaches, especially for transition-metal compounds. In contrast to conventional correlated post-Hartree-Fock methods, it enables accurate treatment of systems with several hundreds of atoms (or several thousands with QM/MM)." ... 

In contrast to the case of bulk properties, very few ab initio calculations have been done for lanthanide or actinide surfaces. Although there has been much interest in the valence state at the surface of lanthanides, this has been treated by other means than first-principles electronic-structure calculations (Johansson and Martensson 1987). However, Hong et al. (1992) considered the Sm surface and applied the FLAPW method to a five-layer fee (100) slab in order to investigate theoretically the possibility of a valence change relative to the bulk. Although the results were not conclusive, this demonstrates the type of problems which can now be addressed by means of the present computational techniques. 

Ffom a theoretical point of view, stacking fault energies in metals have been reliably calculated from first-principles with different electronic structure methods [4, 5, 6]. For random alloys, the Layer Korringa Kohn Rostoker method in combination with the coherent potential approximation [7] (LKKR-CPA), was shown to be reliable in the prediction of SFE in fcc-based solid solution [8, 9]. 

Vibrational spectroscopy is of utmost importance in many areas of chemical research and the application of electronic structure methods for the calculation of harmonic frequencies has been of great value for the interpretation of complex experimental spectra. Numerous unusual molecules have been identified by comparison of computed and observed frequencies. Another standard use of harmonic frequencies in first principles computations is the derivation of thermochemical and kinetic data by statistical thermodynamics for which the frequencies are an important ingredient (see, e. g., Hehre et al. 1986). The theoretical evaluation of harmonic vibrational frequencies is efficiently done in modem programs by evaluation of analytic second derivatives of the total energy with respect to cartesian coordinates (see, e. g., Johnson and Frisch, 1994, for the corresponding DFT implementation and Stratman etal., 1997, for further developments). Alternatively, if the second derivatives are not available analytically, they are obtained by numerical differentiation of analytic first derivatives (i. e., by evaluating gradient differences obtained after finite displacements of atomic coordinates). In the past two decades, most of these calculations have been carried... 

In this chapter, I have provided a brief overview of the QMC method for electronic structure with emphasis on the more accurate diffusion Monte Carlo (DMC) variant of the method. The high accuracy of the approach for the computation of energies is emphasized, as well as the adaptability to large multiprocessor computers. Recent developments are presented that shed light on the capability of the method for the computation of systems larger than those accessible by other first principles quantum chemical methods. 

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