Common Basis Sets

LANL2DZ Available for H(4v) through Vu ls6p2d2f), this is a collection of double-zeta basis sets, which are all-electron sets prior to Na. 

Dolg Also called Stuttgart sets, this is a collection of ECP sets currently under development by Dolg and coworkers. These sets are popular for heavy main group elements. 

This section gives a listing of some basis sets and some notes on when each is used. The number of primitives is listed as a simplistic measure of basis set accuracy (bigger is always slower and usually more accurate). The contraction scheme is also important since it determines the basis set flexibility. Even two basis sets with the same number of primitives and the same contraction scheme are not completely equivalent since the numerical values of the exponents and contraction coefficients determine how well the basis describes the wave function. 

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. 

CRENBL Available for H(45) through Hs(053p6J5/), this is a collection of shape-consistent sets, which use a large valence region and small core region. 

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The ah initio module can run HF, MP2 (single point), and CIS calculations. A number of common basis sets are included. Some results, such as population analysis, are only written to the log file. One test calculation failed to achieve SCF convergence, but no messages indicating that fact were given. Thus, it is advisable to examine the iteration energies in the log file. 

Some common basis sets, and some special-purpose ones... 

Most of the common basis sets do not form a well-defined sequence. 

How can a group of compounds, made from a common basis set of amino acids, be so remarkably heterogeneous and exhibit such varied yet specific functions Clearly, the primary structure and the presence or absence of special functional groups, metals, and so on, are of paramount importance. Of complementary importance are the three-dimensional structures of proteins, which are dictated not just by the primary structure but by the way the primary structure is put together biochemically. The polypeptide chains are seldom, if ever, fully extended, but are coiled and folded into more or less stable conformations. As a result, amino-acid side chains in distant positions in the linear sequence are brought into close proximity, and this juxtaposition often is crucial for the protein to fulfill its specific biological function. 

The Is and 2s orbitals which are affected by neither the photoionization nor the Auger process are omitted for simplicity.) If these wavefunctions are constructed from single-electron orbitals of a common basis set (the frozen atomic structure approximation), the photon operator as a one-particle operator allows a change of only one orbital. Hence, the photon operator induces the change 2p to r in these matrix elements ... 

Table 3 displays also a comparison of a full Cl calculation by Bauschlicher and Taylor [32] with the best BOVB levels using a common basis set. Once again the SD-BOVB level is entirely sufficient, while its extended version leads to a meager improvement. In any case, both levels are in excellent agreement with the full Cl results. 

The approaches described or mentioned to obtain model coefficients in Equation 5.7 can be expressed using a common basis set. For example, the literature commonly... 

Some other examples of less common basis set functions are elliptical 9-12... 

Thus, a common basis set for all subsystems will recover the conventional KS method. In this case the divide-and-conquer method will deliver the conventional KS solution, including the KS eigenvalues and the KS orbitals. The computational efficiency associated with the divide-and-conquer method arises from different basis sets for different subsystems. The KS orbitals are avoided in this case. 

Basis sets affect the performance of P ( r) in a subtle way. In fact, the requirement for (g (r) to give a good matchup is that g (r) decays much faster than the partial molecular density contributed by the basis functions centered at atoms in subsystem a. The bigger the basis sets are the less important the matchup will be. The extreme case will be that all subsystem basis sets are complete. In this case the matchup problem disappears. This is the KS limit solution. Or, all subsystems use a common basis set. The divide-and-conquer method reduces to the conventional KS method. The projection weights do not play any role in this situation. 

Several common basis sets are built in GAUSSIAN 90, which is capable of handling both Cartesian (such as 6d) and spherical (such as 5d) Gaussian basis functions. Molecular geometries can be input in the form of Cartesian coordinates or the Z-matrix. Geometry optimization to both minima and transition states is possible. The HF analytical energy second derivatives needed for the vibrational frequencies calculations can be computed with either a standard or a direct CPHF program. 

The atomic charges were determined using the MuUiken population analysis. The MulUken definition has been shown to suffer from being basis-set dependent and it sometimes gives unreasonable results with diffuse basis functions. This latter defect can manifest itself as a negative electron population. However, for a series of compounds in a common basis set with no especially diffuse basis functions, as is the case here, trends in atomic charges are expected to be reliable. 

To illustrate the size of typical NLO basis sets in use, we show the number of Gaussian functions for several of the common basis sets for two molecules acetylene and p-nitroaniline (Table 5). Most MO programs in use are capable of implementing 5 d functions and 7 f functions, except for GAMESS, which uses 6 d functions and 10 f functions. The difficulty of predicting accurate NLO properties is clearly apparent when calculations on the fairly small molecule nitroaniline could require around 1000 basis functions to overcome basis set deficiencies. 

Gaussian-Type Orbitals. The original Slater-type orbitals were eventually abandoned, and simulated STOs built from Gaussian functions were used. The most common basis set of this kind is the STO-3G basis set, which uses three Gaussian functions (3G) to simulate each one-electron orbital. A Gaussian function is of the type R r) =... 

Common Basis Sets—Modeling Atomic Orbitals... 

A common basis set used in early ab initio calculations is STO-3G, an STO mimic created by a linear combination of three GTOs (Eq. 14.34). Here the a s are coefficients that simply reflect the extent to which each G is added to create the atomic orbital . These a s are not changed during the SCF calculation, but rather they define the basis set. The a s are therefore completely different than the C/ s used in the LCAO-MO method (Eq. 14.33), which are optimized during the SCF method. The a s were optimized to fit experimental data by computational chemist Pople, who won the 1998 Nobel Prize in Chemistry for the development of many of the essential components of modem ofc initio theory. 

Another common basis set is 4-31G, an extended basis set. For each core orbital (Is on C Is, 2s, and 2p on Si ...), a linear combination of four Gaussians is used instead of the three used for STO-3G. More importantly, each valence AO is split into two functions (0, and 0, ). The functions 0, and 0, are a linear combination of three Gaussians and a single diffuse Gaussian, respectively. This is thus referred to as a split valence basis set, denoted by the symbolism 31G. 

In principle, the full NRT variational procedure (equation 24) would require numerically intensive matrix transformations of all possible to a common basis set (e.g.,... 

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