Ab initio and DFT Software

Some of these software packages also have semiempirical or molecular mechanics functionality. However, the primary strength of each is ah initio calculation. There are also ah initio programs bundled with the Unichem, Spartan, and Hyperchem products discussed previously in this appendix. 

ADF (we tested Version 1999.02) stands for Amsterdam density functional. This is a DFT program with several notable features, including the use of a STO basis set and the ability to perform relativistic DFT calculations. Both LDA and 

ADF uses a STO basis set along with STO fit functions to improve the efficiency of calculating multicenter integrals. It uses a fragment orbital approach. This is, in essence, a set of localized orbitals that have been symmetry-adapted. This approach is designed to make it possible to analyze molecular properties in terms of functional groups. Frozen core calculations can also be performed. 

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. 

A number of molecular properties can be computed. These include ESR and NMR simulations. Hyperpolarizabilities and Raman intensities are computed using the TDDFT method. The population analysis algorithm breaks down the wave function by molecular fragments. IR intensities can be computed along with frequency calculations. 

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Robert s team [76-78] performed ab initio and DFT calculations using Gaussian 03W v6.0 [80] on various amineboranes (Table 13.3). In Gaussian 03W, the aqueous media was modeled using a continuum of constant dielectric constant the Polarizable Continuum Model (PCM) solvation method in its lEFPCM (Integral Equation Formalism) version [81]. The latest version of HyperChem (v7.51) [19] was also used to perform PM3 calculations since this software does contain the parameters for the boron atom, as opposed to the original PM3 model. Ab initio and DFT calculations were also performed directly in HyperChem without any add-on. In HyperChem,... 

Currently there are numerous software packages that perform the ab initio or DFT calculations introduced in this section. Most of these programs are available commercially, but there are a few distributed to the scientific community free of charge. Some popular programs are briefly described below, and the list is by no means exhaustive. 

Recently, due to both availability of the Fourier transform VCD spectrometers (FT-VCD) and DFT software for predicting the VCD spectra, the VCD technique has become widely recognized and used [108-110]. DFT has been accepted by the ab initio quantum chemistry community as a cost-effective approach to computations of molecular structures and spectra (vibrational and NMR) of molecules of chemical interest. Many studies have shown that vibrational frequencies and VCD intensities calculated by means of DFT methods are more reUable than those obtained at the MP2 level [87]. 

Recently, quantum chemical computational techniques, such as density functional theory (DFT), have been used to study the electrode interface. Other methods ab initio methods based on Hartree-Fock (HF) theory,65 such as Mollcr-PIcsset perturbation theory,66,67 have also been used. However, DFT is much more computationally efficient than HF methods and sufficiently accurate for many applications. Use of highly accurate configuration interaction (Cl) and coupled cluster (CC) methods is prohibited by their immense computational requirements.68 Advances in computing capabilities and the availability of commercial software packages have resulted in widespread application of DFT to catalysis. 

One interesting scheme based on density functional theory (DFT) is particularly appealing, because with the current power of the available computational facilities it enables the study of reasonably extended systems. DFT has been applied with a variety of basis sets (atomic orbitals or plane-waves) and potential formulations (all-electron or pseudopotentials) to complex nu-cleobase assemblies, including model systems [90-92] and realistic structures [58, 93-95]. DFT [96-98] is in principle an ab initio approach, as well as MP2//HF. However, its implementation in manageable software requires some approximations. The most drastic of all the approximations concerns the exchange-correlation (xc) contribution to the total DFT functional. 

The decision of which quantum mechanical model to use boils down to what size molecule you want to calculate, how reliable an answer you want, and how much time are you willing to wait for the results. Fortunately, as software and hardware improve, the tipping point of the balance weighing the pros and cons of semiempirical vs. DFT vs. ab initio is shifting such that larger molecules can be handled by the better methods. In special situations, a molecule with a couple of hundred atoms can be treated by an ab initio method (46,47), but the typical molecule of interest to theorists, spectrosco-pists, and physicists is smaller than what a pharmaceutical chemist usually wants to treat. Large molecular systems are often best left to one of the FF approaches (see next section). 

To solve the problem put by the Hartree-Fock method with ab initio qrproximation (non-empirical calculations) was chosen. All calculations have been done with the assistance of Gaussian 98/A7 software and use the extended valence-splitting basis, which included diffusive and polarized d- and p-functions — 6-31G(d,p). The correlation amendments were performed with use of Density Functional Theory (DFT) in B3LYP approximation. 

The connecting link between ab initio calculations and vibrational spectra is the concept of the energy surface. In harmonic approximation, usually adopted for large systems, the second derivatives of the energy with respect to the nuclear positions at the equilibrium geometry give the harmonic force constants. For many QM methods such as Hartree-Fock theory (HF), density functional methods (DFT) or second-order Moller-Plesset pertiubation theory (MP2), analytical formulas for the computation of the second derivatives are available. However, a common practice is to compute the force constants numerically as finite differences of the analytically obtained gradients for small atomic displacements. Due to recent advances in both software and computer hardware, the theoretical determination of force field parameters by ab initio methods has become one of the most common and successful applications of quantum chemistry. Nowadays, analysis of vibrational spectra of wide classes of molecules by means of ab initio methods is a routine method [85]. 

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