Types of Calculation

10-14 kcal/mol less stable than the reactants and there was a 24-28 kcal/mol activation barrier to the formation of the tetrahedral in term ediate. 

---

JlypeK. hem (. ompiUalional (. hem isin-- con Lain s two parts. Part 1. th c rmctiral Guide., contain s an overview an d in trodiicLion to the types of calculation s that yon can perform with IlyperChem. Part 2. rheory and Melhods. provides detailed jnronnation on the specific implementation of calculations in IlyperChein. 

The most straightforward fype of lattice minimisation is performed at constant volume, where the dimensions of the basic imit cell do not change. A more advanced type of calculation is one performed at constant pressure, in which case there are forces on both the atoms and the unit cell as a whole. The lattice vectors are considered as additional variables along with the atomic coordinates. The laws of elasticify describe the behaviour of a material when... 

We now have two ways of inserting the correct parameters into the STO-2G calculation. We can write them out in a gen file like Input File 8-1 or we can use the stored parameters as in Input File 8-2. You may be wondering where all the parameters come from that are stored for use in the STO-xG types of calculation. They were determined a long time ago (Hehre et al, 1969) by curve fitting Gaussian sums to the STO. See Szabo and Ostlund (1989) for more detail. There are parameters for many basis sets in the literature, and many can be simply called up from the GAUSSIAN data base by keywords such as STO-3G, 3-21G, 6-31G, etc. 

A number of types of calculations begin with a HF calculation and then correct for correlation. Some of these methods are Moller-Plesset perturbation theory (MPn, where n is the order of correction), the generalized valence bond (GVB) method, multi-conhgurational self-consistent held (MCSCF), conhgu-ration interaction (Cl), and coupled cluster theory (CC). As a group, these methods are referred to as correlated calculations. 

An MCSCF calculation in which all combinations of the active space orbitals are included is called a complete active space self-consistent held (CASSCF) calculation. This type of calculation is popular because it gives the maximum correlation in the valence region. The smallest MCSCF calculations are two-conhguration SCF (TCSCF) calculations. The generalized valence bond (GVB) method is a small MCSCF including a pair of orbitals for each molecular bond. 

It is possible to construct a Cl wave function starting with an MCSCF calculation rather than starting with a HF wave function. This starting wave function is called the reference state. These calculations are called multi-reference conhguration interaction (MRCI) calculations. There are more Cl determinants in this type of calculation than in a conventional Cl. This type of calculation can be very costly in terms of computing resources, but can give an optimal amount of correlation for some problems. 

The notation for denoting this type of calculation is sometimes more specihc. For example, the acronym MCSCF+1+2 means that the calculation is a MRCI calculation with single and double Cl excitations out of an MCSCF reference space. Likewise, CASSCF+1+2 and GVB+1+2 calculations are possible. 

Density functionals can be broken down into several classes. The simplest is called the Xa method. This type of calculation includes electron exchange but not correlation. It was introduced by J. C. Slater, who in attempting to make an approximation to Hartree-Fock unwittingly discovered the simplest form of DFT. The Xa method is similar in accuracy to HF and sometimes better. 

A basis set is a set of functions used to describe the shape of the orbitals in an atom. Molecular orbitals and entire wave functions are created by taking linear combinations of basis functions and angular functions. Most semiempirical methods use a predehned basis set. When ah initio or density functional theory calculations are done, a basis set must be specihed. Although it is possible to create a basis set from scratch, most calculations are done using existing basis sets. The type of calculation performed and basis set chosen are the two biggest factors in determining the accuracy of results. This chapter discusses these standard basis sets and how to choose an appropriate one. 

There are several types of basis functions listed below. Over the past several decades, most basis sets have been optimized to describe individual atoms at the EIF level of theory. These basis sets work very well, although not optimally, for other types of calculations. The atomic natural orbital, ANO, basis sets use primitive exponents from older EIF basis sets with coefficients obtained from the natural orbitals of correlated atom calculations to give a basis that is a bit better for correlated calculations. The correlation-consistent basis sets have been completely optimized for use with correlated calculations. Compared to ANO basis sets, correlation consistent sets give a comparable accuracy with significantly fewer primitives and thus require less CPU time. 

Many computational chemistry techniques are extremely computer-intensive. Depending on the type of calculation desired, it could take anywhere from seconds to weeks to do a single calculation. There are many calculations, such as ah initio analysis of biomolecules, that cannot be done on the largest computers in existence. Likewise, calculations can take very large amounts of computer memory and hard disk space. In order to complete work in a reasonable amount of time, it is necessary to understand what factors contribute to the computer resource requirements. Ideally, the user should be able to predict in advance how much computing power will be needed. 

This type of calculation does reliably find a transition structure. However, it requires far more computer time than any of the other techniques. As such, this is generally only done when the research requires obtaining a potential energy surface for reasons other than just finding the transition structure. 

It is sometimes desirable to include the effect of the rest of the system, outside of the QM and MM regions. One way to do this is using periodic boundary conditions, as is done in liquid-state simulations. Some researchers have defined a potential that is intended to reproduce the effect of the bulk solvent. This solvent potential may be defined just for this type of calculation, or it may be a continuum solvation model as described in the next chapter. For solids, a set of point charges, called a Madelung potential, is often used. 

One of the simplest ways to model polymers is as a continuum with various properties. These types of calculations are usually done by engineers for determining the stress and strain on an object made of that material. This is usually a numerical finite element or finite difference calculation, a subject that will not be discussed further in this book. 

A number of types of calculations can be performed. These include optimization of geometry, transition structure optimization, frequency calculation, and IRC calculation. It is also possible to compute electronic excited states using the TDDFT method. Solvation effects can be included using the COSMO method. Electric fields and point charges may be included in the calculation. Relativistic density functional calculations can be run using the ZORA method or the Pauli Hamiltonian. The program authors recommend using the ZORA method. 

Alternatively, the user can construct ASCII input files manually. The file format includes many numerical flags to control the type of calculation. The researcher should plan on investing some time in learning to use the program in this way. Jaguar can be executed from the command line, making it possible to use batch processing or job queue systems. 

AMPAC can also be run from a shell or queue system using an ASCII input file. The input file format is easy to use. It consists of a molecular structure defined either with Cartesian coordinates or a Z-matrix and keywords for the type of calculation. The program has a very versatile set of options for including molecular geometry and symmetry constraints. 

HyperChem Computational Chemistry contains two parts. Part 1, the Practical Guide, contains an overview and introduction to the types of calculations that you can perform with HyperChem . Part 2, Theory and Methods, provides detailed information on the specific implementation of calculations in HyperChem. 

---