Basis sets, diffuse triple polarized

Even larger basis sets are now practical for many systems. Such basis sets add multiple polarization functions per atom to the triple zeta basis set. For example, the 6-31G(2d) basis set adds two d functions per heavy atom instead of just one, while the 6-311++G(3df,3pd) basis set contains three sets of valence region functions, diffuse functions on both heavy atoms and hydrogens, and multiple polarization functions 3 d functions and 1 f function on heavy atoms and 3 p functions and 1 d function on hydrogen atoms. Such basis sets are useful for describing the interactions between... 

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. 

Details of the extended triple zeta basis set used can be found in previous papers [7,8]. It contains 86 cartesian Gaussian functions with several d- and f-type polarisation functions and s,p diffuse functions. All cartesian components of the d- and f-type polarization functions were used. Cl wave functions were obtained with the MELDF suite of programs [9]. Second order perturbation theory was employed to select the most energetically double excitations, since these are typically too numerous to otherwise handle. All single excitations, which are known to be important for describing certain one-electron properties, were automatically included. Excitations were permitted among all electrons and the full range of virtuals. 

The ECP basis sets include basis functions only for the outermost one or two shells, whereas the remaining inner core electrons are replaced by an effective core or pseudopotential. The ECP basis keyword consists of a source identifier (such as LANL for Los Alamos National Laboratory ), the number of outer shells retained (1 or 2), and a conventional label for the number of sets for each shell (MB, DZ, TZ,...). For example, LANL1MB denotes the minimal LANL basis with minimal basis functions for the outermost shell only, whereas LANL2DZ is the set with double-zeta functions for each of the two outermost shells. The ECP basis set employed throughout Chapter 4 (denoted LACV3P in Jaguar terminology) is also of Los Alamos type, but with full triple-zeta valence flexibility and polarization and diffuse functions on all atoms (comparable to the 6-311+- -G++ all-electron basis used elsewhere in this book). 

Ab initio density functional theory calculations were also carried out on the CH2=XH(A) and CH(A)=XH2 series of molecules. The basis set used was the CEP-TZDP+ described previously26 and is more extensive than the DZP basis set used in the CAS(4,4)-OVB calculations. In TZDP+ the valence electron wave function is expanded in a triple-zeta sp set of functions plus a double set of polarization d-type functions plus a set of diffuse sp-type functions. The B3LYP exchange-correlation functional20 as defined in the Gaussian 94 program set35 was used in all the DFT calculations. 

With the addition of polarization functions and/or diffuse functions to the basis sets, the Pople notation can become rather cumbersome. For example, the 6-311++G(3df,2pd) set has a single zeta core and triple zeta valence shell, diffuse functions for all the atoms. Regarding polarized functions, there are three sets of d functions and one set of f functions on the non-hydrogens and two sets of p functions and one set of d orbitals on the hydrogens. 

A more sequential approach to the analysis of the systematic error of ab initio methods has been proposed in [14]. The same set of molecules as in [10] has been analyzed there. For this set the series of calculations using the basis sets aug-cc-pVxZ containing both polarization and diffuse functions with the number of exponents x in their respective radial parts up to x = 6 (single zeta x = 1, double zeta - DZ -x = 2, triple zeta - TZ - x = 3, etc.) and with the account of correlation effects in the range of methods from MP2 up to CCSD(T) had been performed and then fitted to the formulae [15-18] ... 

The calculated structures (at the QCISD level with triple- basis sets which include diffuse and polarization functions for Si, Ge and Sn, and ECPs for Pb)168 of D3h MII5 group 14 anions, which are all minima on the PES, are given in Figure 40. The M—H... 

The AO basis set should be of triple zeta or better quality polarization functions are important and additional basis functions with very tight and diffuse exponents are helpful. A good compromise between accuracy and cost is provided by the AO basis set given by Chipman [5], enlarged by an additional tight s function. 

FCI energies of the ground state and several excited states (3 12+, 2 ll, and 2 2A states) were obtained by Olsen et al. [66] in 1989 using a DZP basis set augmented with diffuse functions. These data have been used as tests for a wide variety of EOM/FR-CC methods, including CCSD [20, 24], CCSDT-la [44], CC3 [45], CCSDT-3 [46], and CCSDt [52], Later Hirata et al. [49] obtained FCI results with the 6-31G basis set. Shiozaki et al. [57] have obtained FCI results with the augmented correlation-consistent polarized valence double-zeta (cc-pVDZ) and valence triple-zeta (aug-cc-pVTZ) sets. 

All calculations were performed with the Gaussian 98 suite of programs [4] using the hybrid DFT/HF B3LYP method. The all-electron 6-311+G(2df) basis set was used for H, O, Si, and Ge, whereas the valence triple zeta pseudopotential basis set of Stoll et al. [5] was used for Sn. The Sn basis set was augmented with diffuse function exponents one-third in size of the outermost valence exponents, the two-membered d-polarization set of Huzinaga, [6] and f(QSn = 0.286. This basis set combination will be called (v)TZ throughout this paper. 

There is a general agreement that accurate quantum studies on hydrogen bonds require flexible basis sets, i.e., triple- with at least one set of diffuse and polarization functions (especially on H atoms it is surprisingly frequent to find in the literature calculations that exclude these functions from hydrogens) and treatment of electron correlation by means of either wave function-based or DFT-based methods [34-41]. Since these requirements have rendered useless much of the outdated theoretical material published before 1990, one can consider that the efforts to characterize hydrogen bonding from a quantum viewpoint are more or less 15 years old (see the historical comments in Ref. 5). 

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