Electronic structure calculations with Gaussian basis functions

The electronic structure calculations were carried out using the hybrid density functional method B3LYP [15] as implemented in the GAUSSIAN-94 package [16], in conjunction with the Stevens-Basch-Krauss (SBK) [17] effective core potential (ECP) (a relativistic ECP for Zr atom) and the standard 4-31G, CEP-31 and (8s8p6d/4s4p3d) basis sets for the H, (C, P and N), and Zr atoms, respectively. 

Almost all contemporary ab initio molecular electronic structure calculations employ basis sets of Gaussian-type functions in a pragmatic approach in which no error bounds are determined but the accuracy of a calculation is assessed by comparison with quantities derived from experiment[l] [2]. In this quasi-empirical[3] approach each basis set is calibrated [4] for the treatment of a particular range of atoms, for a particular range of properties, and for a particular range of methods. Molecular basis sets are almost invariably constructed from atomic basis sets. In 1960, Nesbet[5] pointed out that molecular basis sets containing only basis sets necessary to reach to atomic Hartree-Fock limit, the isotropic basis set, cannot possibly account for polarization in molecular interactions. Two approaches to the problem of constructing molecular basis sets can be identified ... 

Although the first proposals(l) (2) to use Gaussian basis functions in molecular electronic structure calculations were made in the late 1940s and early 1950s, in a recent historical review Shavitt(3) records how the first applications met with very limited success because they used rather small numbers of Gaussians, and little additional work was reported in the fifties but then interest in Gaussian basis sets and exploration of variants and extensions increased substantially in the early sixties . In 1960, Nesbet(4) identified two approaches to the design of molecular basis sets ... 

Gaussian basis functions in molecular electronic structure calculations was first suggested by McWeeny115,116 and independently by Boys117 in 1950. However, the supposedly more physical Slater (exponential) Type Orbitals (STO) remained the basis function of choice for many years because they correctly describe not only the cusp associated with the nucleus on which they are centred but also afford a suitable representation of the long range behaviour. Shavitt118 records that... 

Electronic structure calculations were carried out with the Gaussian 94 suite of programs at the levels of second-order Meller-Plesset (MP2) and hybrid density functional theory (B3LYP) with basis sets developed by Pople, McLean, and co-workers. Geometry optimizations with the 6-31G basis set were followed by single-point calculations with the 6-311G basis set. 

The BAC-MP4 method first involves ab initio electronic structure calculations to determine the structure, vibrational frequencies, and electronic energy. These calculations are carried out using the Gaussian 8x series of codes (e.g., G82, G86, G88) developed by Pople et aL The equilibrium geometry of the molecule is determined using the Hartree-Fock method (restricted Hartree-Fock, RHF, for closed shell molecules and unrestricted Hartree-Fock UHF, for open shell molecules). The basis set used to describe the electronic wave function is split-valence with polarization functions on the heavy atoms (denoted 6-3IG ). For a... 

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