Semi-empirical and ab initio methods

On the other hand, ab initio (meaning from the beginning in Latin) methods use a correct Hamiltonian operator, which includes kinetic energy of the electrons, attractions between electrons and nuclei, and repulsions between electrons and those between nuclei, to calculate all integrals without making use of any experimental data other than the values of the fundamental constants. An example of these methods is the self-consistent field (SCF) method first introduced by D. R. Hartree and V. Fock in the 1920s. This method was briefly described in Chapter 2, in connection with the atomic structure calculations. Before proceeding further, it should be mentioned that ab initio does not mean exact or totally correct. This is because, as we have seen in the SCF treatment, approximations are still made in ab initio methods. 

Another approach closely related to the ab initio methods that has gained increasing prominence in recent years is the density functional theory (DFT). This method bypasses the determination of the wavefunction //. Instead, it determines the molecular electronic probability density p directly and then calculates the energy of the system from p. 

Ab initio and DFT calculations are now routinely applied to study molecules of increasing complexity. Sometimes the results of these calculations are valuable in their own right. But more often than not these results serve as a guide or as a complement to experimental work. Clearly computational chemistry is revolutionizing how chemistry is done. In the remaining part of this chapter, the discussion will be devoted to ab initio and DFT methods. 

---

Applications of semi-empirical and ab initio methods frequently follow the course of chemical reactions that break and form covalent bonds. You must take care in choosing a method for these applications. 

Semi-empirical methods could thus treat the receptor portion of a single protein molecule as a quantum mechanical region but ab mdio methods cannot. However, both semi-empirical and ab initio methods could treat solvents as a perturbation on a quantum mechanical solute. In the future, HyperChem may have an algorithm for correctly treating the boundary between a classical region and an ab mdio quantum mechanical region in the same molecule. For the time being it does not. 

Semi-empirical and ab initio methods differ in the trade-off made between computational cost and accuracy of result. Semi-empirical calculations are relatively inexpensive and provide reasonable qualitative descriptions of molecular systems and fairly accurate quantitative predictions of energies and structures for systems where good parameter sets exist. 

The aim is to give a general approach which can be followed when total energies are calculated by both semi-empirical and ab initio methods. 

Spectroscopic methods such as IR and Raman have proven to be exceptionally powerful methods for solving many chemistry problems . However, the vibrational assignment, as well as the understanding of the relationship between the observed spectral features and molecular structure or reactivity of the sample, can be very difficult. Theoretical methods can certainly assist to obtain a deeper understanding of the vibrational spectra of new compounds. These are the well-established force field calculations, semi-empirical and ab initio methods . 

Calculations of the properties of nitrenium ions continue to be performed by semi-empirical and ab initio methods, in an effort to provide information concerning ... 

In the final exploration of the quantum chemistry unit students use a computational chemistry package (eg. Spartan, Gaussian, CaChe, etc.) to calculate the ground state energies, molecular orbitals, and in some cases the excited state energies, of two proton transfer tautomers. Calculations are performed at several different levels of theory, and use both semi-empirical and ab initio methods. Several different basis sets are compared in the ab initio calculations. The students use the results of these calculations to estimate the likelihood of excited state proton transfer. The calculations require CPU time ranging from a couple of minutes to a couple of hours on the PCs available to the students in the laboratory. 

The properties of oligomers of thiophene at the ground and excited states have been investigated by semi-empirical and ab initio methods. Semi-empirical calculations for the ground state of thiophene involve the QCFF/PI -f CISD method, while ab initio calculations are carried out at the HF/6-31G and the CASSF/3-21G" levels and also at the SCF and the averaged coupled-pair functional (ACPF) levels, with (basis set I) and without (basis set II) the sulfur 3d-orbitals. 

Because of the complexity of some conjugated TTF derivatives, electron charge density distribution was calculated applying combined semi-empirical and ab initio methods <1997MCH135>. 

This paper will discuss the state of the art in 3D structure refinement using empirical, semi-empirical and ab initio methods. We believe that the success story of liquid state NMR in protein structure elucidation is going to continue within the solid state (or membrane environment) if chemical shifts can be successfully exploited. Neutron and X-ray diffraction methods owe their success to a simple formula that connects the measured reflex intensities with the nuclear positions or the electron density, respectively. The better we understand how chemical shifts change with the three-dimensional arrangement of atoms, the more reliably we can construct molecular models from our NMR experiments. As we can in principle determine up to six numbers per nucleus if we perform a full chemical shift tensor analysis, we need to address the question whether whole CS tensor or at least its principal values can be used in structure calculations. 

On the Bridge between Semi-Empirical and Ab-Initio Methods in Atomic and Molecular Quantum Theory. 

One approach to the problem of the size of the calculation which may be performed has been introduced both for semi-empirical and ab initio methods , and this embeds the fragment under consideration within a cluster of point charges which are taken to represent a greater portion of the zeolite. No substantial increase in computer time is caused by this addition, as only the one-electron integrals will be affected the more computationally expensive two-electron... 

Section 2.15) but exchange and correlation typically serve as to characterize the worth of the computational approach the (sometimes questionable) distinction between (semi-)empirical and ab initio methods also goes back - to some extent - to this question. Let us group the different approaches, a bit simplified, and see how they relate with each other. 

There are two methods, semi-empirical and ab initio methods, for continuing the quantum chemical calculations. In the semi-empirical method, many of the integrals are estimated by using spectroscopic data or physical properties. On the other hand, in the ab initio method, all the integrals in the secular determinant are attempted to be directly calculated. 

Relativistic calculations of a number of polyatomic molecules have been carried out by both semi-empirical and ab initio methods. Many of the earlier calculations have been reviewed by Pyykko" as well as by Christiansen, Ermler and Pitzer. The semi-empirical methods include the relativistic extended Hiickel method, relativistic Xa method, etc. Most of the ab initio calculations on polyatomics initially omit the spin-orbit interaction. This is introduced at a later stage as a perturbation or by a semi-empirical scheme. 

For the calculation of one may apply one out of several different methods. At first one may choose between semi-empirical and ab initio methods. Ab initio methods are, in principle, exact, at least in the sense that they contain no parameters that have been obtained by fitting to experimental or theoretical findings, although they are based on various approximations. Thereby, they provide, in principle, exact results but suffer simultaneously from the problem that they are computationally much more costly than the semi-empirical methods. These, in turn, contain parameters whose values have been obtained by fitting to results from experimental or theoretical studies on simple systems. The price to be paid for their computational simplicity is that the results obviously never are better than the values of the parameters entering these methods. 

---