# Gaussian basis sets

In Chapter IX, Liang et al. present an approach, termed as the crude Bom-Oppenheimer approximation, which is based on the Born-Oppen-heimer approximation but employs the straightforward perturbation method. Within their chapter they develop this approximation to become a practical method for computing potential energy surfaces. They show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of the Coulomb interaction with respect to nuclear coordinates is essential. For this purpose, they study a diatomic molecule, and by doing that demonstrate the basic skill to compute the relevant matrix elements for the Gaussian basis sets. Finally, they apply this approach to the H2 molecule and show that the calculated equilibrium position and foree constant fit reasonable well those obtained by other approaches. [c.771]

The application of density functional theory to isolated, organic molecules is still in relative infancy compared with the use of Hartree-Fock methods. There continues to be a steady stream of publications designed to assess the performance of the various approaches to DFT. As we have discussed there is a plethora of ways in which density functional theory can be implemented with different functional forms for the basis set (Gaussians, Slater type orbitals, or numerical), different expressions for the exchange and correlation contributions within the local density approximation, different expressions for the gradient corrections and different ways to solve the Kohn-Sham equations to achieve self-consistency. This contrasts with the situation for Hartree-Fock calculations, wlrich mostly use one of a series of tried and tested Gaussian basis sets and where there is a substantial body of literature to help choose the most appropriate method for incorporating post-Hartree-Fock methods, should that be desired. [c.157]

In addition to the mixed results in Table 10-1, the G2 calculation for H2 produces an energy that is lower than the experimental value, in contradiction to the rule that variational procedures reach a least upper bound on the energy. Some new factors are at work, and we must look into the stmcture of the G2 procedure in temis of high-level Gaussian basis sets and electron correlation. [c.309]

Gaussian Basis Sets [c.309]

COMPUTER PROJECT 10-1 Gaussian Basis Sets The HF Limit [c.311]

The values of the orbital exponents ( s or as) and the GTO-to-CGTO eontraetion eoeffieients needed to implement a partieular basis of the kind deseribed above have been tabulated in several journal artieles and in eomputer data bases (in partieular, in the data base eontained in the book Handbook of Gaussian Basis Sets A. Compendium for Ab initio Moleeular Orbital Caleulations, R. Poirer, R. Kari, and I. G. Csizmadia, Elsevier Seienee Publishing Co., Ine., New York, New York (1985)). [c.469]

When dealing with anions or Rydberg states, one must augment the above basis sets by adding so-ealled diffuse basis orbitals. The eonventional valenee and polarization funetions deseribed above do not provide enough radial flexibility to adequately deseribe either of these eases. Energy-optimized diffuse funetions appropriate to anions of most lighter main group elements have been tabulated in the literature (an exeellent souree of Gaussian basis set information is provided in Handbook of Gaussian Basis Sets, R. [c.473]

R. Poirer, R. Kari, I. G. Csizmadia, Handbook of Gaussian Basis Sets A Compendium for Ah Initio Molecular Orbital Calculations Elsevier Science Publishing, New York (1985). [c.90]

Gaussian basis sets for molecular calculations S. Huzinaga, Ed., Elsevier, Amsterdam (1984). [c.90]

McLean, A.D. Chandler, G.S. Contracted Gaussian basis sets for molecular calculations. I. Second row atoms, Z=ll-18 J. Chem. Phys. 72 5639-5648, 1980. [c.110]

Although most calculations on molecules are now perfonned using Gaussian orbitals (STOs are still coimnonly employed in atomic calculations), it should be noted that other basis sets can be used as long as they span enough of the region of space (radial and angular) where significant electron density resides. In fact. [c.2170]

Atomic natural orbital (ANO) basis sets [44] are fonned by contracting Gaussian fiinctions so as to reproduce the natural orbitals obtained from correlated (usually using a configuration interaction with [c.2171]

The basis sets that we have considered thus far are sufficient for most calculations. However, for some high-level calculations a basis set that effectively enables the basis set limit to be achieved is required. The even-tempered basis set is designed to achieve this each function m this basis set is the product of a spherical harmonic and a Gaussian function multiplied [c.91]

There is no definitive method for generating basis sets, and the construction of a new basis set is very much an art. Nevertheless, there are a number of well-established approaches that have resulted in widely used basis sets. We have already seen how linear combinations nf Gaussian functions can be fitted to Slater type orbitals by minimising the overlap (see Figure 2.6 and Table 2.3). The Gaussian exponents and coefficients are derived by lea.st-squares fitting to the desired functions, such as Slater type orbitals. When using basis sets that have been fitted to Slater orbitals it is often advantageous to use Slater exponents that are different to those obtained from Slater s rules. In general, better results for molecular calculations are obtained if larger Slater exponents are used for the valence electrons I hi has the effect of giving a smaller, less diffuse orbital. For example, a value of 1.24 is widely used for the Slater exponent of hydrogen rather than the 1.0 that would be suggested by Slater s rules. It is straightforward to derive a basis set for a different Slater exponent if the Gaussian expansion has been fitted to a Slater type orbital with ( = 1.0. If the Slater exponent is replaced by a new value, then the respective Gaussian exponents a and a are related by [c.92]

A doubling of the Slater exponent thus corresponds to a quadrupling of the Gaussian exponent. The expansion coefficients remain the same. For example, to obtain the exponent of the Gaussian functions for hydrogen in the STO-3G basis set we need to multiply llic appropriate values in Table 2.3 by 1.24, giving exponents of 0.168856, 0.623913 and 3.42525. This strategy can be quite powerful the STO-nG basis sets were originally defined with exponents that reproduce best atom values for the core orbitals, but the exponents lor the valence electrons were values that give optimal performance for a selected set of sn. dll molecules. For example, the suggested exponent for the valence orbitals in carbon was 1.72 rather than the 1.625 predicted by Slater s rules. The core orbitals have a Slater exponent "I 5.67. [c.92]

Minimal basis sets in which 3, 4 etc, Gaussian functions are used to represent the atomic orbitals on an atom [c.124]

In Computer Projects 8-1 and 8-2, we used the STO and CBS basis sets stored as part of the data base of GAUSSIAN. The general basis case (keyword gen) in GAUSSIAN permits us to bypass the stored basis sets (there is no stored STO-IG basis set) and make our own basis functions. To run GAUSSIAN under the general basis input to determine the SCF output for the ground state of the hydrogen atom using a single Gaussian trial function, the input file is [c.244]

We now have two ways of inserting the correct parameters into the STO-2G calculation. We can write them out in a gen file like Input File 8-1 or we can use the stored parameters as in Input File 8-2. You may be wondering where all the parameters come from that are stored for use in the STO-xG types of calculation. They were determined a long time ago (Hehre et al, 1969) by curve fitting Gaussian sums to the STO. See Szabo and Ostlund (1989) for more detail. There are parameters for many basis sets in the literature, and many can be simply called up from the GAUSSIAN data base by keywords such as STO-3G, 3-21G, 6-31G, etc. [c.247]

Flelgaker T and Taylor P R 1995 Gaussian basis sets and molecular integrals Modem Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) section 5.4, pp 725-856 [c.2195]

Flelgaker T and Taylor P R 1995 Gaussian basis sets and molecular integrals Modern Electronic Structure Theory yo 2, ed D R Yarkony (Singapore World Scientific) section 5.3, pp 725-856 [c.2195]

In this chapter, we demonstrate the approach of the CBOA, and show that to carry out different orders of perturbation, the ability to calculate the matrix elements of the derivatives of Coulomb interaction with respect to nuclear coordinates is essential. Therefore, we studied the case of the diatomic molecule, and here we demonstrate the basic skill of computing the relevant matrix elements in Gaussian basis sets. The formulas for diatomic molecules, up to the second derivatives of the Coulomb interaction, are shown here to demonstrate that some basic techniques can be developed to cany out the calculation of the matrix elements of even higher derivatives. The formulas obtained may be complicated. First, they are shown to be nonsingular. Second, the Gaussian basis set with angular momentum can be dealt with in similar ways. Thud, they are expressed as multiple finite sums of certain simple functions, of order up to the angular momentum of the basis functions, and thus they can be computed efficiently and accurately. We show the application of this approach on the H2 molecule. The calculated equilibrium position and force constant seem to be reasonable. To obtain more reliable results, we have to employ a larger basis set to higher orders of perturbation to calculate the equilibrium geometiy and wave functions. [c.401]

Equation (3.23) <7 would be the x, y or z coordinate of an atom and Xj would be a irameter such as a basis function coefficient or a basis function exponent. An important suit is that the terms involving variationally determined parameters (such as basis func-)n coefficients) are equal to zero the energy is a minimum when (dE/dCj) is zero. This eatly reduces the computational effort. Most of the numerical work in calculating the adient is due to the various basis set parameters (e.g. orbital centres and exponents) hich require the derivatives of the various electron integrals. For Gaussian basis sets ese derivatives can be obtained analytically and indeed it is relatively straightforward obtain first derivatives for many levels of theory. The time taken to calculate the deriva- es is comparable to that required for the calculation of the total energy. Second (and [c.140]

After expansion of P as a power series (Foresman and Frisch, 1996) Moeller-Plesset theory results in a correction for the wave function and the energy. The energy conection is always negative, which improves our calculation, but the Moeller-Plesset (MP) procedure is not a var iational procedure, does not produce a least upper limit, and can overcorrect the energy. This is pari of the explanation of why the G2 bond energy for H2 in the section on the hydrogen molecule above in this chapter is lower than the experimental value. Gaussian basis sets containing component MP Cl calculations are denoted, for example, MP2/6-31G or, if polarization functions are also included, MP2/6-31G(d,p). [c.313]

Calculations that can be performed are HF, Cl, MRCI, FCI, CC, DFT, MCSCF, CASSCF, ACPF, CEPA, valence bond, and many variations of these. Perturbation theory calculations can be done from single- and multiple-determinant references spaces. The MCSCF and coupled-cluster algorithms have proven to be very efficient. Restricted, unrestricted, and restricted open-shell wave functions are available. The user has a large amount of detailed control over wave function construction. Many one-electron properties can be computed, including relativistic energy corrections, spin-orbit coupling, electric field gradients, and multipoles. A number of options for electronic excited states and transition-structure calculations are also available. It can use Gaussian basis sets with high-angular-momentum functions (spdfghi) and elfective core potentials. [c.339]

Contracted [5s3p] and [5s4p] Gaussian basis sets for the first-row atoms are derived from the (10s6p) primitive basis sets of Huzinaga. Contracted [2s] and [3s] sets for the hydrogen atom obtained from primitive sets ranging from (4s) to (6s) are also examined. Calculations on the water and nitrogen molecules indicate that such basis sets when augmented with suitable polarization functions should yield wavefunctions near the Hartree-Fock limit. [c.169]

Peng Chunyang, Ayala, P. Y. and Schlegel, H. B. (1996) J. Comput. Chem. 17, 49. Poirer, R., Kari, R. and Csizmadia, I. G. (1985) Handbook of Gaussian Basis Sets, Elsevier, Amsterdam. [c.328]

Dunning T FI Jr 1970 Gaussian basis funotions for use in moleoular oaloulations I. Contraotion of (9s 5p) atomio basis sets for the first-row atoms J. Chem. Phys. 53 2823-33 [c.2194]

The major factor determining the level of an ab-initio SCF calculation is the quality of the basis set. It should be dear firom the above discussion that the MOs obtained within the LCAO approximation can only be linear combinations of the AOs used (i.e., of the basis set). If, for instance, our AOs are very compact, we will not be able to describe very diffuse MOs firom them using linear combinations. Therefore, the nature and number of the AOs comprising the basis set ( basis functions ) affects the quality of the LCAO-SCF electron density. Semi-empirical techniques usually use minimal basis sets, as described above (an exception are the methods vdth d-orbitals for Si-Cl). Furthermore, the AOs used by semi-empiri-cal techniques are usually Slater-type orbitals (STOs). This form for the AOs, first proposed by Slater [22], gives a good description of the electron density for many cases. However, it suffers the practical difficulty that integrals involving STOs are very difficult and time

The simplest Gaussian-type orbital (GTO) basis sets are minimal basis sets in which the STO electron density is mimicked by a fixed linear combination of several (usually three to six) Gaussian functions. A typical, and once very popular, minimal basis set is known as STO-3G (Slater-type orbitals approximated by 3 Gaussian junctions) [23]. The STO-3G basis set was determined by fitting three Gaussian functions so that they reproduced the electron density of the corresponding STO as closely as possible. STO-3G, which is almost never used any more, was the standard basis set for geometry optimizations in the early 1970s when ab-initio methods were beginning to become practicable. Minimal basis sets suffer, however, from a major drawback. Because there is only one basis function of each type, they cannot be used to produce either more compact or more diffuse MOs than the constituent AOs. However,

The solution to this problem is to use more than one basis function of each type some of them compact and others diffuse, Linear combinations of basis Functions of the same type can then produce MOs with spatial extents between the limits set by the most compact and the most diffuse basis functions. Such basis sets arc known as double is the usual symbol for the exponent of the basis function, which determines its spatial extent) if all orbitals arc split into two components, or split ualence if only the valence orbitals arc split. A typical early split valence basis set was known as 6-31G 124], This nomenclature means that the core (non-valence) orbitals are represented by six Gaussian functions and the valence AOs by two sets of three (compact) and one (more diffuse) Gaussian functions. [c.385]

Ihiil arc added lo a basis lo form a star basis arc a simple set of un COM traded 3d primitive Ganssiaus (five Hermiic Gaussians) in S rO-NG basis sets bill Cartesian Gaussian s in th e split-valen ce basis sets. [c.262]

A deficiency of the basis sets described so far is their inability to deal with species such as anions and molecules containing lone pairs which have a significant amount of electron density away from the nuclear centres. This failure arises because the amplitudes of the Gaussian basis functions are rather low far from the nuclei. To remedy this deficiency highly diffuse functions can be added to the basis set. These basis sets are denoted using a thus the 3-21+G basis set contains an additional single set of diffuse s- cind p-type Gaussian functions. ++ indicates that the diffuse functions are included for hydrogen as well as for heavy atoms. At these levels the terminology starts to become a little unwieldy. For example, the 6-311-f- -G(3df, 3pd) basis set uses a single zeta core and triple zeta valence representation with additional diffuse functions on all atoms. The (3df, 3pd) indicates three sets of d functions and one set of f functions for first-row atoms and three sets of p functions and one set of d functions for hydrogen. This latter convention is probably the most generic one commonly encoxmtered example is the 6-31G(d) basis set, which is synonymous with 6-31G. [c.91]

Almost from the dawn of quantum mechanics a great deal of effort has been put into devising better basis sets for molecular orbital calculations (for example, Rosen, 1931 James and Cooledge, 1933). Prominent among more recent work is the long series of GAUSSIAN programs written by John Pople s group (see, for example, Pople et al., 1989) leading to the award of the Nobel prize in chemistry to Pople in 1999. GAUSSIAN consists of a suite of programs from which one can select members by means of keywords. We have already seen the keyword STO-3G used in File 10-1 to select the approximation of Slater-type orbitals by three Gaussian functions. Along with individual calculations, GAUSSIAN also permits you to run sequential calculations by executing a script that specifies the programs to be run, the order in which they are to be run, and how the various outputs are to be combined to give a final result. This technique has been developed to a high degree of accuracy in the GAUSSIAN family of programs, of which we shall use the principal members, G2 and G3. [c.306]

Gaussian-Type Orbitals, GTOs. In G2 and G3, an effort is made to extend the basis set to its practical limit of accuracy. We have seen, in the case of STO-iiG basis sets, that more contr ibuting Gaussian functions make for better agreement between calculated and known energies, but there is a point of diminishing return, beyond which further elaboration produces little gain. The same is true of the Gaussian n-xxG basis sets, for example, 6-3IG, except that there are more of them [c.309]

Run a single point STO-3G calculation of the total energy of H2O at the MM3 geometry in the GAMESS implementation. Compare your result with the identical calculation in the GAUSSIAN implementation. Repeat the calculation using the double zeta valence (DZV) and triple zeta valence (TZV) basis sets in the GAMESS implementations. Comment on the relative energies calculated by single, double, and triple zeta basis sets. [c.317]

See pages that mention the term

**Gaussian basis sets**:

**[c.2194] [c.93] [c.2172] [c.2195] [c.43] [c.258] [c.89] [c.89] [c.90] [c.93] [c.126] [c.152]**

See chapters in:

** Computational chemistry using the PC
-> Gaussian basis sets
**

Computational chemistry using the PC (2003) -- [ c.309 , c.311 ]