Double-zeta-valence-with-polarization

Dunning has developed a series of correlation-consistent polarized valence n-zeta basis sets (denoted cc-pVnZ ) in which polarization functions are systematically added to all atoms with each increase in n. (Corresponding diffuse sets are also added for each n if the prefix aug- is included.) These sets are optimized for use in correlated calculations and are chosen to insure a smooth and rapid (exponential-like) convergence pattern with increasing n. For example, the keyword label aug-cc-pVDZ denotes a valence double-zeta set with polarization and diffuse functions on all atoms (approximately equivalent to the 6-311++G set), whereas aug-cc-pVQZ is the corresponding quadruple-zeta basis which includes (3d2flg,2pld) polarization sets. 

An important issue of the application of electronic structure theory to polyatomic systems is the selection of the appropriate basis set. As usual in quantum chemistry, a compromise between precision and computational cost has to be achieved. It is generally accepted that in order to obtain qualitatively correct theoretical results for valence excited states of polyatomic systems, a Gaussian basis set of at least double-zeta quality with polarization functions on all atoms (or at least on the heavy atoms) is necessary. For a correct description of Rydberg-type excited states, the basis set has to be augmented with additional diffuse Gaussian functions. Such basis sets were used in the calculations discussed below. 

For most molecules studied, modest Hartree-Fock calculations yield remarkably accurate barriers that allow confident prediction of the lowest energy conformer in the S0 and D0 states. The simplest level of theory that predicts barriers in good agreement with experiment is HF/6-31G for the closed-shell S0 state (Hartree-Fock theory) and UHF/6-31G for the open-shell D0 state (unrestricted Hartree-Fock theory). The 6-31G basis set has double-zeta quality, with split valence plus d-type polarization on heavy atoms. This is quite modest by current standards. Nevertheless, such calculations reproduce experimental barrier heights within 10%. 

To model the copper (100) surface a two-layer cluster of C4V symmetry, with 5 copper atoms in one layer and 4 copper atoms in the other layer, has been used. In this cluster, all the 9 metal atoms were described by the LANL2DZ basis set. The LANL2DZ basis set treats the 3s 3p 3d 4s Cu valence shell with a double zeta basis set and treats all the remainder inner shell electrons with the effective core potential of Hay and Wadt [33]. The non-metallic atoms (C and H) were described by the 6-3IG basis set of double zeta quality with p polarization functions in... 

One should mention however that our conclusions have been very recently questionned by Axe and Marynick (42) who carried out calculations on the reaction (3) with various basis sets ranging from split valence to double zeta quality, with and without polarization functions on C, O and H atoms. They found a marked increase in the endothermicity value on going from the unpolarized basis sets ( values ranging between 8.7 and 15.2 kcal/mol) to the polarized basis s.ets (with values between 19.5 and 25.2 kcal/mol, i.e. close to our SD-CI values). We have now carried out calculations adding to our original split valence basis set polarization functions on C, O and H. One polarized set includes the two sets of polarization functions ( = 0.920... 

The cluster structures were optimized at the corresponding level of theory employing a double zeta valence polarization (DZVP) basis set (Godbout et al. 1992). For the polarizability calculations a triple zeta valence polarization (TZVP) basis set augmented with field induced polarization (FIP) function was used (Calaminid et al. 1999). All calculations were performed in the framework of auxiliary density fimctional theory (ADFT) (Koster et al. 2004b) with A2 or GEN-A2 auxiliary function sets (Calaminici et al. 2007a). The latter was used in the analytical calculation of the cluster polarizabilities (Flores-Moreno and Koster 2008). 

To illustrate how well DFT or ab initio methods predict the dipole moments. Table 1 illustrates the comparison between theory and experiment for eight small molecules. The error statistics are summarized in Table 2. In general, the quality of the basis set plays an important role in the prediction of dipole moments. We see that the 6-3IG basis set provides poor predictions, even when applied with a QCISD level of theory. The performances of the double-zeta basis set plus polarization functions (6-3IG, DZVPD (double-zeta valence orbitals plus polarization and diffuse functions on heavy atoms), and cc-pVDZ (correlation-consistent polarized valence double-zeta)) are poorer than those from the polarized triple-zeta basis sets. The only exception is B-P/DZVPD (B-P = Becke-Perdew), from which we obtained an average absolute deviation of 0.040 debye, lower than that (0.053 debye) from B-P/TZVPD (triple-zeta valence orbitals plus polarization and diffuse functions on heavy atoms). It can be seen that the inclusion of correlation effects through either ab initio or DFT approaches significantly improves the agreement. 

An older, but still used, notation specihes how many contractions are present. For example, the acronym TZV stands for triple-zeta valence, meaning that there are three valence contractions, such as in a 6—311G basis. The acronyms SZ and DZ stand for single zeta and double zeta, respectively. A P in this notation indicates the use of polarization functions. Since this notation has been used for describing a number of basis sets, the name of the set creator is usually included in the basis set name (i.e., Ahlrichs VDZ). If the author s name is not included, either the Dunning-Hay set is implied or the set that came with the software package being used is implied. 

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 ) ... 

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). 

Related basis sets in common usage include the original Dunning full and valence double-zeta sets, denoted D95 and D95V, respectively (built from nine s-type and five p-type primitives). These sets may be augmented in the usual way with diffuse and/or polarization functions, as in the example D95++ (diffuse and first-polarization sets on all atoms). 

Although there is no strict relationship between the basis sets developed for, and used in, conventional ah initio calculations and those applicable in DFT, the basis sets employed in molecular DFT calculations are usually the same or highly similar to those. For most practical purposes, a standard valence double-zeta plus polarization basis set (e.g. the Pople basis set 6-31G(d,p) [29] and similar) provides sufficiently accurate geometries and energetics when employed in combination with one of the more accurate functionals (B3LYP, PBEO, PW91). A somewhat sweeping statement is that the accuracy usually lies mid-way between that of M P2 and that of the CCSD(T) or G2 conventional wave-function methods. 

In the present work, correlation consistent basis sets have been developed for the transition metal atoms Y and Hg using small-core quasirelativistic PPs, i.e., the ns and (nA)d valence electrons as well as the outer-core (nA)sp electrons are explicitly included in the calculations. This can greatly reduce the errors due to the PP approximation, and in particular the pseudo-orbitals in the valence region retain some nodal structure. Series of basis sets from double-through quintuple-zeta have been developed and are denoted as cc-pVwZ-PP (correlation consistent polarized valence with pseudopotentials). The methodology used in this work is described in Sec. II, while molecular benchmark calculations on YC, HgH, and Hg2 are given in Sec. III. Lastly, the results are summarized in Sec. IV. 

In the early calculations of IR spectra of molecules, small basis sets (e.g., STO-3G, 3-21G, or 4-31G) were used because of limitations of computational power. At present typically a basis set consists of split valence functions (double zeta) with polarization functions placed on the heavy atoms (i.e., non-hydrogens) of the molecule (the so-called DZ+P or 6-31 G basis set). Such basis sets have been... 

---