Basis sets Gaussian

Dunning T FI Jr and Flay P J 1977 Gaussian basis sets for moleoular oaloulations Methods of Electronic Structure Theory vo 3, ed FI F III Sohaefer (New York Plenum) pp 1-27... 

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... 

The picture here is of uncoupled Gaussian functions roaming over the PES, driven by classical mechanics. The coefficients then add the quantum mechanics, building up the nuclear wavepacket from the Gaussian basis set. This makes the treatment of non-adiabatic effects simple, as the coefficients are driven by the Hamiltonian matrices, and these elements couple basis functions on different surfaces, allowing hansfer of population between the states. As a variational principle was used to derive these equations, the coefficients describe the time dependence of the wavepacket as accurately as possible using the given... 

In modem quantum chemistry packages, one can obtain moleculai basis set at the optimized geometry, in which the wave functions of the molecular basis are expanded in terms of a set of orthogonal Gaussian basis set. Therefore, we need to derive efficient fomiulas for calculating the above-mentioned matrix elements, between Gaussian functions of the first and second derivatives of the Coulomb potential ternis, especially the second derivative term that is not available in quantum chemistry packages. Section TV is devoted to the evaluation of these matrix elements. 

In the work of King, Dupuis, and Rys [15,16], the mabix elements of the Coulomb interaction term in Gaussian basis set were evaluated by solving the differential equations satisfied by these matrix elements. Thus, the Coulomb matrix elements are expressed in the form of the Rys polynomials. The potential problem of this method is that to obtain the mabix elements of the higher derivatives of Coulomb interactions, we need to solve more complicated differential equations numerically. Great effort has to be taken to ensure that the differential equation solver can solve such differential equations stably, and to... 

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. 

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. 

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. 

COMPUTER PROJECT 10-1 Gaussian Basis Sets The HF Limit... 

In hybrid DET-Gaussian methods, a Gaussian basis set is used to obtain the best approximation to the three classical or one-election parts of the Schroedinger equation for molecules and DET is used to calculate the election correlation. The Gaussian parts of the calculation are carried out at the restiicted Hartiee-Fock level, for example 6-31G or 6-31 lG(3d,2p), and the DFT part of the calculation is by the B3LYP approximation. Numerous other hybrid methods are currently in use. 

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)). 

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). 

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

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. 

Ref. 29. MO-SCF calculations using medium-size contracted Gaussian basis set. 

F. B. van Duijneveldt, Gaussian basis sets for the atoms H - Ne for use in molecular calculations, Technical Report Report RJ 945, IBM Research Laboratory San Jose, 1971. 

S.Huzinaga. Gaussian basis sets For molecular calculations. Physical Sciences data 16, Elsevier, 1984. 

To appreciate this point somewhat better it is useful to compare three types of Gaussian basis sets, (a) a set of Gaussians with common orbital exponents (for one 1) but a sequence of principle quantum-numbers... 

R. Poirier, R. Kari and LG. Csizmadia, Handbook of gaussian basis sets, Elsevier, Amsterdam, 1985. 

Table 5.3 Contributions of -orbitals to the total electron density at the iron nucleus (in a.u. ) as a function of oxidation state and configuration. Calculations were done with the spin-averaged Hartree-Fock method and a large uncontracted Gaussian basis set. (17 1 Ip 5d If)... 

Schaefer, A. Huher, C. Ahlrichs, R. Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr. J. Chem. Phys. 1994, 100, 5829-5835. 

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