Basis set double zeta

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. 

The double zeta basis sets, such as the Dunning-Huzinaga basis set (D95), form all molecular orbitals from linear combinations of two sizes of functions for each atomic orbital. Similarly, triple split valence basis sets, like 6-3IIG, use three sizes of contracted functions for each orbital-type. 

Optimize these three molecules at the Hartree-Fock level, using the LANL2DZ basis set, LANL2DZ is a double-zeta basis set containing effective core potential (ECP) representations of electrons near the nuclei for post-third row atoms. Compare the Cr(CO)5 results with those we obtained in Chapter 3. Then compare the structures of the three systems to one another, and characterize the effect of changing the central atom on the overall molecular structure. 

We refer to such a basis set as a double zeta basis set. Where the minimal basis set for atomic lithium had a 1 s exponent of 2.6906, the double zeta basis set has two Is orbitals with exponents 2.4331 and 4.5177 (the outer and inner orbitals). 

A selection of dementi s double zeta basis sets is given in Table 9.4. 

Barone also introduces two new basis sets, EPR-Il and EPR-llI. These are optimized for the calculation of hyperfine coupling constants by density functional methods. EPR-Il is a double zeta basis set with a single set of polarization functions and an enhanced s part. EPR-III is a triple zeta set including diffuse functions, double d polarization functions and a single set off functions. 

The calculations were performed using a double-zeta basis set with addition of a polarization function and lead to the results reported in Table 5. The notation used for each state is of typical hole-particle form, an asterisc being added to an orbital (or shell) containing a hole, a number (1) to one into which an electron is promoted. In the same Table we show also the frequently used Tetter symbolism in which K indicates an inner-shell hole, L a hole in the valence shell, and e represents an excited electron. The more commonly observed ionization processes in the Auger spectra of N2 are of the type K—LL (a normal process, core-hole state <-> double-hole state ) ... 

In a previous work [1,2], we were interested in the calculation of second order hyperpolarizabilities of eonjugated systems including substituted benzenes, pyridine N-oxydes and vinyl oligomers, in relation with non linear optical activity [3]. We showed that MNDO ealeulations were in good agreement with SCF ab initio results obtained using a double zeta basis set plus polarization and diffuse orbitals. 

Andzelm and Wimmer, 1992, published one of the first comprehensive studies on the performance of approximate density functional theory in which optimized molecular geometries were reported. These authors computed the geometries of several organic species containing the atoms C, N, O, H, and F at the local SVWN level, using a polarized double-zeta basis set optimized for LDA computations. Some trends have been discerned... 

For the related [CpIr(PH3)(CH3)]+ system, four basis sets were used. Basis set one (BS1) is the same as the ones described above for Ir and P, but the C and H are described as D95. Basis set two (BS2) is the Stuttgart relativistic, small core ECP basis set (49) augmented with a polarization function for Ir, and Dunning s correlation consistent double-zeta basis set with polarization function (50) for P, C and H. Basis set three (BS3) is the same as BS1 except the d-orbital of Ir was described by further splitting into triple-zeta (111) from a previous double-zeta (21) description and augmented with a f-polarization function (51). Basis set four (BS4) is the same as BS2 for Ir, P, and most of the C and H, but the C and H atoms involved in the oxidative addition were described with Dunning s correlation consistent triple-zeta basis set with polarization. 

In minimal basis sets, each atom is represented by a single orbital of each type. For example, oxygen is represented by Is, 2s, 2p, 2py, and 2p orbitals only. In double zeta basis sets, twice the functions in the minimum basis sets are used. Extended basis sets generally refer to sets that make use of functions that are more than the minimum basis set. 

Figure 1. The shape of the potential curve for nitrogen in a correlation-consistent polarized double-zeta basis set is presented for the variational 2-RDM method as well as (a) single-reference coupled cluster, (b) multireference second-order perturbation theory (MRPT) and single-double configuration interaction (MRCl), and full configuration interaction (FCl) wavefunction methods. The symbol 2-RDM indicates that the potential curve was shifted by the difference between the 2-RDM and CCSD(T) energies at equilibrium.

All methods employ a correlation-consistent polarized double-zeta basis set. 

The A -representability conditions on the 2-RDM can be systematically strengthened by adding some of the 3-positivity constraints to the 2-positivity conditions. For three molecules in valence double-zeta basis sets Table II shows... 

Figure 2. Comparison of the 2-RDM, coupled-cluster, MRPT2, and FCI potential energy surfaces of CO in a valence double-zeta basis set, where all valence electrons are correlated (a) without an electric field and (b) with an electric field of strength 0.10 an apphed in the direction of the permanent dipole moment. The 2-RDM and MRPT2 methods accurately describe the features of the FCI potential energy surface.

For Three Molecules in Valence Double-Zeta Basis Sets, a Comparison of Energies in Hartrees (H) from the 2-RDM Method with the T2 Condition (DQGT2) with the Energies from Second-Order Many-Body Perturbation Theory (MP2), Coupled-Cluster Method with Single-Double Excitations and a Perturbative Triples Correction (CCSD(T)), and Full Configuration Interaction (FCI)... 

With this correction all but one computed electron correlation energy fell within 10% of the exact solution. As Table 11 shows, the very simple scaling correction yields huge improvements on modest initial electron correlations. The use of the correction factor implies the loss of the variational principle and does not account for the use of different basis sets for example, the Dunning double-zeta basis set for Be is different for LiH [24, 25]. 

Alternatively, instead of looking for a significant truncation of the system of equations, one may try to perform multiple but simple calculations hoping for a favorable cancellation of errors. Thus, the idea tested was to start from a set of 2-TRDM s, corresponding to the eigenstates of 5, and then to apply the CLVNE in order to obtain a set of more accurate 1-TRDM s. This kind of calculation was not only carried out for the Beryllium atom but also for the LiH molecule (also with a double zeta basis set). Unfortunately, the results were not encouraging either. 

In general, DFT calculations are known to converge fast with the size of the basis set. Although polarized double-zeta basis sets are a minimum requirement, polarized triple-zeta basis sets are... 

The choice of the exchange correlation functional in the density functional theory (DFT) calculations is not very important, so long as a reasonable double-zeta basis set is used. In general, the parameterized model will not fit the quantum mechanical calculations well enough for improved DFT calculations to actually produce better-fitted parameters. In other words, the differences between the different DFT functionals will usually be small relative to the errors inherent in the potential model. A robust way to fit parameters is to use the downhill simplex method in the parameter space. Having available an initial set of parameters, taken from an analogous ion, facilities the fitting processes. 

---