Density-based methods adjustable parameter

The time-dependent theory of spectroscopy bridges this gap. This approach has received less attention than the traditional time-independent view of spectroscopy, but since 1980, it has been very successfully applied to the field of coordination chemistry.The intrinsic time dependence of external perturbations, for example oscillating laser fields used in electronic spectroscopy, is also expKdtly treated by modern computational methods such as time-dependent density functional theory, a promising approach to the efficient calculation of electronic spectra and exdted-state structures not based on adjustable parameters, as described in Chapter 2.40. In contrast, the time-dependent theory of spectroscopy outlined in the following often relies on parameters obtained by adjusting a calculated spectrum to the experimental data. It provides a unified approach for several spectroscopic techniques and leads to intuitive physical pictures often qualitatively related to classical dynamics. The concepts at its core, time-dependent wave functions (wave packets) and autocorrelation functions, can be measured with femtosecond (fs) techniques, which often illustrate concepts very similar to those presented in the following for the analysis of steady-state spectra. The time-dependent approach therefore unifies spectroscopic... 

Electronic structure calculations may be carried out at many levels, differing in cost, accuracy, and reliability. At the simplest level, molecular mechanics (this volume, Chapter 1) may be used to model a wide range of systems at low cost, relying on large sets of adjustable parameters. Next, at the semiempirical level (this volume, Chapter 2), the techniques of quantum mechanics are used, but the computational cost is reduced by extensive use of empirical parameters. Finally, at the most complex level, a rigorous quantum mechanical treatment of electronic structure is provided by nonempirical, wave function-based quantum chemical methods [1] and by density functional theory (DFT) (this volume, Chapter 4). Although not treated here, other less standard techniques such as quantum Monte Carlo (QMC) have also been developed for the electronic structure problem (for these, we refer to the specialist literature, Refs. 5-7). 

In computational organometallic chemistry, the density functional must often be viewed as an adjustable parameter. If similar and chemically reasonable results are obtained with different functionals, and with different wave function-based methods, this is typically a good indication that the computational techniques are reliably describing the underlying chemistry of the system at hand. In short, B3LYP is an excellent functional, but in the absence of literature precedence for its utility for the organometallic system of interest, it cannot be assumed to be infallible. 

Unlike most materials simulation methods that are based on classical potentials, the main advantages of Ab initio methods, which is based on first principles density functional theory (without any adjustable parameters), are the generality, reliability, and accuracy of these methods. They... 

Statement 4 was an important guiding principle in the early days of the theory of atomic and molecular structure. Results based entirely on group theory were very helpful. It also turned out to be necessary to formulate approximative theories in terms of empirically adjustable parameters. A nice example of a theory in line with Dirac s suggestion is Slater s theory of complex atoms [6] in which certain parameters Fk or Gjt, appeared, that could, in principle, be calculated, but which were rather evaluated from spectral data to get better agreement with experiment. Semiempirical adjustments of theoretical parameters was also essential in Hiickel s molecular orbital theory of 7c-electron systems [7] in order for it to be practically useful. Although the recent developments of ab initio theory make semiempirical parameters obsolete, the trend to oversimplified theories that need to be calibrated by experiment or by benchmark calculations is tending to return, as is demonstrated by the apparent success of modern density functional methods [8, 9]. 

First prindple quantum chemical methods, whether wave function based ( ab initio ) or density based, are aimed at solving the electronic Schrddinger equation without any reference to adjustable parameters or empirical data. In their standard form, they invoke the Bom-Oppenhdmer separation of electronic and nuclear motion and employ a nonrelativistic Hamiltonian which does not include any explicit reference to spin-dependent terms. Many quantum chemical methods are based on the variational prindple which, for computational convenience, is implemented in algebraic form via either one-electron functions built from linear combinations of atomic orbitals or n-electron functions constructed from Slater determinants. [11, 12]... 

The density functional (DF) formalism [14] is the most widely used method for determining electronic and structural properties of condensed matter that does not require adjustable parameters. It is based on the electron density n(r) and reduces the problem of determining ground state properties of an interacting system of electrons and ions to the solution of single-particle Schrodinger-Uke equations. An approximation... 

The atom-centered models do not account explicitly for the two-center density terms in Eq. (3.7). This is less of a limitation than might be expected, because the density in the bonds projects quite efficiently in the atomic functions, provided they are sufficiently diffuse. While the two-center density can readily be included in the calculation of a molecular scattering factor based on a theoretical density, simultaneous least-squares adjustment of one- and two-center population parameters leads to large correlations (Jones et al. 1972). It is, in principle, possible to reduce such correlations by introducing quantum-mechanical constraints, such as the requirement that the electron density corresponds to an antisymmetrized wave function (Massa and Clinton 1972, Frishberg and Massa 1981, Massa et al. 1985). No practical method for this purpose has been developed at this time. 

The attitude of most users is pragmatic. One does not worry why DF methods work and uses them as one uses other methods implemented in the same black box. There are quite a few different functionals available and one can choose between them depending on the problem that one wants to solve, where the superiority of one functional over another is usually based on statistical comparison with experiment rather than on formal arguments. This pragmatic attitude is encouraged by the fact that some of the density functionals in current use, contain parameters that were adjusted to fit experimental data. This - in order not to say more - puts DF schemes in the neighborhood of semiempirical methods. 

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