Gaussian-n methods

A variety of compound methods have been developed in an attempt to accurately model the thermochemical quantities we have been considering. These method-s attempt to achieve high accuracy by combining the results of several different calculations as an approximation to a single, very high level computation which is much too expensive to be practical. We will consider two families of methods the Gaussian-n methods and the Complete Basis Set (CBS) methods. 

Gaussian-2 (G2) theory Ideally, a sucessful method for computation of thermochemical data has several features (1) it should be applicable to any molecular system in an unambiguous manner, (2) it must be computationally efficient so that it can be widely applied, (3) it should be able to reproduce known experimental data to a prescribed accuracy, and (4) it should give similar accuracy for species for which the data are not available or for which experimental uncertainties are large. The Gaussian-n methods were developed with these objectives in mind. Gaussian-1 (Gl) theory was the first in this series.27 28 We will not cover Gl theory in this chapter because it was replaced by G2 theory, which eliminated several deficiencies in Gl, and because G2 is currently the most widely used method of this series. 

In addition to the Gaussian-n methods, there is a variety of CBS (complete basis set) methods, including CBS-Q, CBS-q, and CBS-4, which have also enjoyed some popularity among computational chemists. In these methods, special procedures are designed to estimate the complete-basis-set limit energy by extrapolation. Similar to the Gn methods, single-point calculations are also... 

DeYonker, N. J., Cimdari, T. R., Wilson, A. K. (2006). The correlation consistent composite approach ccCA An alternative to the Gaussian-n methods. J Chem Phys 124,114104. 

Both the BO dynamics and Gaussian wavepacket methods described above in Section n separate the nuclear and electronic motion at the outset, and use the concept of potential energy surfaces. In what is generally known as the Ehrenfest dynamics method, the picture is still of semiclassical nuclei and quantum mechanical electrons, but in a fundamentally different approach the electronic wave function is propagated at the same time as the pseudoparticles. These are driven by standard classical equations of motion, with the force provided by an instantaneous potential energy function... 

Finally, can we dare to ask what is the future of first-principle MD It would be hard to be highly predictive. However we would like to quote the following directions of research QM/MM methods to treat quantum systems in an environment [92-94,225,226,269-272], Gaussian basis sets [23,30,38, 63,110,172] or Gaussian augmented plane waves methods [168] in search for order N methods [273,274] etc. Also, in order to go beyond Density Functional Theory, Quantum-Monte Carlo techniques are very attractive [119]. Some of these topics are already well-advanced and are discussed here in this book. 

Liptak, M.D., Shields, G.C. Accurate pKa calculations for carboxylic acids using complete basis set and Gaussian-n models combined with CPCM continuum solvation methods. J. Am. Chem. 

Gaussian elimination method is based upon the principle of converting a set of N equations of N unknowns represented by... 

The Gaussian-n quantum chemical methods reviewed in this chapter have been part of a long-term collaboration with John Pople who passed away this year. We gratefully acknowledge his seminal contributions to the developments covered in this review. We also acknowledge the contributions of many other people who have been co-authors on the papers referenced herein. One of us (LAC) acknowledges support from the LfS Department of Energy, BES-Division of Materials Science under Contract No. W-31-109-ENG-38. 

A detailed explanation of these methods is beyond the scope of this cluq)ter and can be found elsewhere in the literature [210,215-217]. Among the general theoretical models that can be applied for a wide range of molecules, the so-called Gaussian-n theories, the complete basis set models (CBS) and DFT methods have been the most succesful. 

There are methods that automate some of these steps. They are called composite methods because they combine results from several calculations to estimate the result that would be obtained from a more expensive calculation. The most popular families of composite methods are represented by Gaussian-3 (G3) theory [68,109] and CBS-APNO theory [110,111], where CBS stands for complete basis set. Both families of methods, which are considered reliable, include empirical parameters. The CBS theories incorporate an analytical basis set extrapolation based on perturbation theory, which is in contrast to the phenomenological extrapolation mentioned above. When the Gaussian software is used to perform these calculations, steps 2-, above, are performed automatically, with the result labeled G3 enthalpy (or the Hke) in the output file [20,99]. The user must still choose a reaction (step 1) and manipulate the molecular enthalpies (steps 5 and 6). The most precise composite methods are the Weizmann-n methods, which however are very intensive computationally [112]. 

G2 theory is the result of work by Curtiss, Raghavachari, Pople, and co-workers, " who introduced a series of methods termed Gaussian-n theories for the calculation of energies of molecular systems containing the elements H-Cl. The... 

Mineva T, Russo N and Sicilia E 1998 Solvation effects on reaction profiles by the polarizable continuum model coupled with Gaussian density functional method J. Oomp. Ohem. 19 290-9... 

A more general update method, widely used in the Gaussian suite of programs [19], is due to Schlegel [13], In this method, the Hessian in the n-dimensional subspace spaimed by taking differences between the current q... 

Because th e calculation of m n Iti-ceiiter in tegrals that are in evitable for ah iniiio method is very difficult and time-con sum in g. Ilyper-Chem uses Gaussian Type Orbital (GTO) for ah initio methods. In truly reflecting a atomic orbital. STO may he better than GTO. so HyperC hem uses several GTOs to construct a STO. The number of GTOs depends on the basis sets. For example, in the minimum STO-3G basis set IlyperGhem uses three GTOs to construct a STO. 

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