Quantum chemical procedures density functional theory

As an alternative to ab initio methods, the semi-empirical quantum-chemical methods are fast and applicable for the calculation of molecular descriptors of long series of structurally complex and large molecules. Most of these methods have been developed within the mathematical framework of the molecular orbital theory (SCF MO), but use a number of simplifications and approximations in the computational procedure that reduce dramatically the computer time [6]. The most popular semi-empirical methods are Austin Model 1 (AMI) [7] and Parametric Model 3 (PM3) [8]. The results produced by different semi-empirical methods are generally not comparable, but they often do reproduce similar trends. For example, the electronic net charges calculated by the AMI, MNDO (modified neglect of diatomic overlap), and INDO (intermediate neglect of diatomic overlap) methods were found to be quite different in their absolute values, but were consistent in their trends. Intermediate between the ab initio and semi-empirical methods in terms of the demand in computational resources are algorithms based on density functional theory (DFT) [9]. 

Abstract We present a general theoretical approach for the simulation and control of ultrafast processes in complex molecular systems. It is based on the combination of quantum chemical nonadiabatic dynamics on the fly with the Wigner distribution approach for simulation and control of laser-induced ultrafast processes. Specifically, we have developed a procedure for the nonadiabatic dynamics in the framework of time-dependent density functional theory using localized basis sets, which is applicable to a large class of molecules and clusters. This has been combined with our general approach for the simulation of time-resolved photoelectron spectra that represents a powerful tool to identify the mechanism of nonadiabatic processes, which has been illustrated on the example of ultrafast photodynamics of furan. Furthermore, we present our field-induced surface hopping (FISH) method which allows to include laser fields directly into the nonadiabatic... 

The focus in this chapter is on quantum chemical methods. These can be classified as semiempirical, ab initio, and density functional theory (DFT) methods. The latter ones usually involve empirical parameterization and, hence, sometimes are also considered as semiempirical methods. Alternatively, a distinction on the basic quantity - wave function (WF) or electronic density - can be made as wave-function-based methods (WFT) and DFT. In this classification scheme, wave-function-based methods include semiempirical as well as ah initio procedures. Although the impact of semiempirical methods on the progress of quantum chemistry can hardly be overestimated [13], their use now is mainly restricted to very large systems [14]. Thus, in the following the description of wave-function-based procedures will be restricted to ah initio methods. 

In some instances, a quantitative understanding of anharmonic effects may be required to acheive a priori accuracies of better than a factor of two. Procedures for incorporating one-dimensional corrections, particularly for hindered rotors are well developed and commonly employed. Increased quantum chemical and computational capabilities should now allow for studies of the fully coupled nonrigid anharmonic state densities and/or partition functions via direct Monte Carlo sampling. Such accurate state density studies are a necessary prerequisite to furthering our understanding of the accuracy limits of both quantum chemical estimates and of RRKM theory itself. 

The phosphane molecule is the subject of numerous quantum-chemical calculations. The methods applied range from simple LCAO MO approaches to high-quality calculations, such as Hartree-Fock (SCF MO), configuration interaction (Cl), perturbation theory (MP, MBPT), and, more recently, density function procedures. 

Developments in ab initio MO quantum chemistry have resulted in theoretical models [41]. These are able to predict the properties of neutral molecules and ions within so-called chemical accuracy (about 2 kcal/mol). This makes these procedures extremely useful in ion chemistry, especially in thermochemical studies. Another approach is DFT that has attracted intense interest. DFT offers the promise of less drastic scaling with the size of the system than traditional ab initio methods. In general, hybrid density functions frequently provide the best overall agreement and surpass MP2 result of ab initio theory. There have been a number of theoretical studies of the structures and binding energies of alkali ions to many bases, including from free radical, biradical, amino acid, and crown ether to DNA bases (see details in Chap. 3). 

In recent years, the topological analysis of the three-dimensional scalar fields [87-95], such as electron density [55, 67, 92, 95-97], the Laplacian of the electron density [68, 92], the electron localization function (ELF) [94, 98], and molecular electrostatic potential, have been widely used to discern chemical structure and reactivity. This procedure, named quanmm chemical topology (QCT) [99] has been utilized for the study of chemical stmcture and reactivity [100-106]. Since its origins, the well-known approach of the atoms in molecules quantum theory (QTAIM), has evolved to be an invaluable tool for the chemical interpretation of quantum mechanical data, which relies on the properties of the electron density p(r) when atoms interact. Excellent reviews on QTAIM methods have been published elsewhere [69, 96, 107-109]. 

---