Computer codes GAUSSIAN

The main purpose of quantum-chemical modeling in materials simulation is to obtain necessary input data for the subsequent calculations of thermodynamic and kinetic parameters required for the next steps of multiscale techniques. Quantum-chemical calculations can also be used to predict various physical and chemical properties of the material in hand (the growing film in our case). Under quantum-chemical, we mean here both molecular and solid-state techniques, which are now implemented in numerous computer codes (such as Gaussian [25], GAMESS [26], or NWCHEM [27] for molecular applications and VASP [28], CASTEP [29], or ABINIT [30] for solid-state applications). 

Brent s and Brown s methods are variations of Newton s method that improve convergence. The calculation of the elements in in Eq. (L.ll) and the solving of the linear equations are intermingled. Each row of Jt is obtained as needed using the latest information available. Then one more step in the solution of the linear equations is executed. Brown s method is an extension of Gaussian elimination Brent s method is an extension of QR factorization. Computer codes are generally implemented by using numerical approximations for the partial derivatives in J. ... 

The computer codes of Sambe and Felton (SF) and Dunlap et al. (DCS) are based on the choice of a Hermite-Gaussian expansion set. Applying the variational theorem with the trial function of Eq. (37) and the LSD Hamiltonian of Eq. (36) leads to the usual matrix pseudo-eigenvalue problem ... 

Despite the huge increase in computational effort, this direct symmetry-adapted LCAO method was used to study ozone [22], tetrahedral Ni4 [23], and D5h-symmetric ferrocene (Fe(C5H5)2) [24] using molecular orbital (MO) contraction coefficients in the linear-combination-of-Gaussian-type orbital (LCGTO) computer code of [25]. Obviously, symmetry-adapted calculations are important enough to pay an order-TV computational price. The reasons are first, and foremost, that the calculations converge, and second that the wavefunction and one-electron orbitals can be used to address experiment, which typically must first determine the symmetry of the molecule. 

All the calculations we report in the following sections have been performed with two quantum mechanical computional codes, Gaussian and GAMESS, ° in which the PCM solvation method has been implemented. 

The calculation of the has been implemented at different levels of theory in several computer codes of widespread use. The HFF, APT and AAP tensors, as derivatives of energies and wave functions with respect to the proper perturbations, can be evaluated using either numerically (finite differences of gradients) or directly, analytically. Software packages that are capable of VCD spectra calculations are available commercially. Here, we present, in alphabetical order, the most popular software packages implementing analytical derivatives in the calculations of the HHF, APT and AAP tensors (a) Amsterdam Density Functional, ADF [103] (b) CADPAC [104] (c) DALTON [105] and (d) GAUSSIAN, G03, G09 release [106, 107]. 

The U. S. Enviromnental Protection Agency (EPA) has developed a set of computer codes based on the Gaussian model which carry out the calculations needed for regulatory purposes. These models are available from the Applied Modeling Research Branch, Office of Air Quality Planning and Standards, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711. 

The analysis can also be carried out using the standard computer code. However, the procedure for analysis is the same as described earlier. PIXEF (for PIXE-fit) the Livermore PIXE spectrum analysis package has been developed by Antolak and Bench (1994). This software initially computes an approximation to the background continuum, subtracts from the raw spectral data and the resulting X-ray peaks are then fitted to either Gaussian or Hy > ermet distributions. The energy dependent ionization cross-sections for each element s K-shell or L-subshell are procured from the analytical functional fit, while the subshell and total photoelectric cross-sections are determined directly from the Dirac-Hartree-Slater calculations of Scofield. Schematic of a typical PIXE spectrum is as shown in Fig. 1.16. 

Theoretical studies have been based on ab-initio molecular orbital calculations performed using either the Gaussian 86 code or, earlier, Gaussian codes on a Cray 1 Computer. The majority of calculations employed a modestly sized basis set (6-31G)to save computational time but a few have been carried out using a larger (6-311G ) basis set and using Moller-Plesset (MP) many-body perturbation theory to second or fourth order. 

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