Dr. Komal Gupta Assistant Professor Department of Chemistry M. M. PG COLLEGE MODINAGR Computational Methods

.The difficulties arising from the severe assumptions of Huckel Metod have been overcome by more sophisticated theories that not only calculate the shapes and enegies of molecular orbitals but also predict with reasonable accuracy the structure and reactivity of molecules.

John Pople and Walter Kohn were awarded the Nobel Prize in Chemistry for 1998 for their contributions to the development of computational techniques for the elucidation of molecular structure and reactivity.

Different computational methods are: (i) Ab initio methods

.Methods that do not include any empirical or semi-empirical parameters in their equations – being derived directly from theoretical principles, with no inclusion of experimental data – are called ab initio methods.

. This does not imply that the solution is an exact one; they are all approximate quantum mechanical calculations.

.In the ab initio methods, an attempt is made to calculate all the integrals that appear in the Fock and overlap matrices

.The Fock matrix has elements that consist of integrals of the form

where A, B, C, and D are atomic orbitals that in general may be centred on different nuclei.

.Commercial packages are available for ab initio calculations. Here the problem is to evaluate as efficiently as possible thousands of integrals. This task is greatly facilitated by expressing the atomic orbitals used in the LCAOs as linear combinations of Gaussian orbitals. . A Gaussian type orbital (GTO) is a function of the form e−ζr2. The advantage of GTOs over the correct orbitals (which for hydrogenic systems are proportional to e−ζr) is that the product of two Gaussian functions is itself a Gaussian function that lies between the centres of the two contributing functions . In this way, the four-centre integrals become two-centre integrals of the form

where X is the Gaussian corresponding to the product AB and Y is the corresponding Gaussian from CD (ii)Semi-empirical methods

Semi-empirical quantum chemistry methods are based on the Hartree–Fock method formalism, but make many approximations and obtain some parameters from empirical data.

They were very important in computational chemistry from the 60s to the 90s, especially for treating large molecules where the full Hartree–Fock method without the approximations were too costly.

The use of empirical parameters appears to allow some inclusion of correlation effects into the methods.

Within the framework of Hartree–Fock calculations, some pieces of information (such as two-electron integrals) are sometimes approximated or completely omitted.  In order to correct for this loss, semi-empirical methods are parametrized, that is their results are fitted by a set of parameters, normally in such a way as to produce results that best agree with experimental data, but sometimes to agree with ab initio results.

 Semi-empirical methods follow what are often called empirical methods where the two-electron part of the Hamiltonian is not explicitly included. For π-electron systems, this was the Hückel method proposed by Erich Hückel. For all valence electron systems, the extended Hückel method was proposed by Roald Hoffmann Density functional theory (DFT)

.Density-functional theory (DFT) is a computational quantum mechanical modelling method used in physics, chemistry and materials science to investigate the electronic structure in particular atoms, molecules, and the condensed phases.

.Its advantages include less demanding computational effort, less computer time, and—in some cases (particularly d-metal complexes)—better agreement with experimental values than is obtained from Hartree–Fock procedures .The central focus of DFT is the electron density, ρ, rather than the wavefunction ψ.

.The ‘functional’ part of the name comes from the fact that the energy of the molecule is a function of the electron density, written E[ρ], and the electron density is itself a function of position, ρ(r), and in mathematics a function of a function is called a functional The exact ground-state energy of an n-electron molecule is

where EK is the total electron kinetic energy, EP;e,N the electron–nucleus potential energy, EP;e,e the electron–electron potential energy, and EXC[ρ] the exchange– correlation energy, which takes into account all the effects due to spin. The orbitals used to construct the electron density from

are calculated from the Kohn–Sham equations, which are found by applying the variation principle to the electron energy, and are like the Hartree–Fock equations except for a term VXC, which is called the exchange–correlation potential: The exchange–correlation potential is the ‘functional derivative’ of the exchange– correlation energy:

the exchange–correlation potential is calculated by assuming an approximate form of the dependence of the exchange–correlation energy on the electron density and evaluating the functional derivative for this step, the simplest approximation is the local-density approximation and to write

where εXC is the exchange–correlation energy per electron in a homogeneous gas of constant density. Next, the Kohn–Sham equations are solved to obtain an initial set of orbitals. This set of orbitals is used to obtain a better approximation to the electron density and the process is repeated until the density and the exchange–correlation energy are constant to within some tolerance. Molecular mechanics

.These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules. .Large molecular systems can be modeled successfully while avoiding quantum mechanical calculations entirely. Molecular mechanics simulations, for example, use one classical expression for the energy of a compound, for instance the harmonic oscillator. All constants appearing in the equations must be obtained beforehand from experimental data or ab initio calculations.

.The database of compounds used for parameterization, i.e., the resulting set of parameters and functions is called the force field, is crucial to the success of molecular mechanics calculations. A force field parameterized against a specific class of molecules, for instance proteins, would be expected to only have any relevance when describing other molecules of the same class.

.These methods can be applied to proteins and other large biological molecules, and allow studies of the approach and interaction (docking) of potential drug molecules. References:

(i) Atkins Physical Chemistry- Eight Edition Page No. 392-395

(ii) https://en.wikipedia.org/wiki/Computational_chemistry