cc-pVTZ Set Research Articles

Vibrational Spectra of Cyclopentadienylphosphine: Infrared and Theoretical Studies from DFT Anharmonic Potentials

Both experimental and theoretical infrared investigations of cyclopentadienylphosphine (CpP) are reported. The infrared spectra (3500-500 cm(-1)) in the gas phase have been recorded at 0.5 cm(-1) resolution. Infrared absorptions bands of the two lowest stable conformers were observed and assigned. Average integrated intensities of isolated and overlapping vibrational bands were also determined experimentally. The vibrational frequencies of the CpP system and its P-dideuterated isotopologue have been calculated by means of density functional theory. The Becke exchange functional and Lee-Yang-Parr correlation functional method with a combination of the two basis sets, namely 6-31+G(d,p) and the correlation-consistent triple-zeta cc-pVTZ set of Dunning, were used. Hybrid B3LYP/B3LYP//cc-pVTZ/6-31+G(d,p) anharmonic frequencies of the fundamental, overtone, and combination transitions were calculated in the 3500-200 cm(-1) area with the use of a variational approach, implemented in the P_Anhar_v1.1 code, to assign the experimental data for each conformer.

Binding energies of hydrogen-bonded complexes from extrapolation with localized basis sets

By incorporating effective basis sets containing diffuse functions only in the interaction region of hydrogen-bonded complexes into the simple extrapolation scheme suitable for such basis sets, an accurate estimation of the MP2 basis set limit hydrogen-bonding energies of formic acid tetramer, formamide tetramer, alanine-water, phenol-water, and guanine-cytosine base pair is made with all estimates falling within 0.1-0.3 kcalmol of the reference basis set limits. The basis sets for extrapolation are composed of the cc-pVDZ and cc-pVDZ plus highest polarization functions from the cc-pVTZ set, or cc-pVDZ and cc-pVTZ set, all of which are augmented by the diffuse functions of the atoms in the interaction region of hydrogen bond. In contrast to the extrapolated estimates by this method, density functional theory binding energies with B3LYP, B971, and TPSS methods yield the differences from the reference values as large as 3.9 kcalmol with much higher computational cost in most cases, signifying the efficacy of the employed extrapolation scheme for study of large hydrogen-bonded complexes.

MP2 Basis Set Limit Binding Energy Estimates of Hydrogen-bonded Complexes from Extrapolation-oriented Basis Sets

By use of a simple two-point extrapolation scheme estimating the correlation energies of the molecules along with the basis sets specifically targeted for extrapolation, we have shown that the MP2 basis set limit binding energies of large hydrogen-bonded complexes can be accurately predicted with relatively small amount of computational cost. The basis sets employed for computation and extrapolation consist of the smallest correlation consistent basis set cc-pVDZ and another basis set made of the cc-pVDZ set plus highest angular momentum polarization functions from the cc-pVTZ set, both of which were then augmented by diffuse functions centered on the heavy atoms except hydrogen in the complex. The correlation energy extrapolation formula takes the (X+1) -3 form with X corresponding to 2.0 for the cc-pVDZ set and 2.3 for the other basis set. The estimated MP2 basis set limit binding energies for water hexamer, hydrogen fluoride pentamer, alanine-water, phenol-water, and guanine-cytosine base pair complexes of nucleic acid by this method are 45.2(45.9), 36.1(37.5), 10.9(10.7), 7.1(6.9), and 27.6(27.7) kcal/mol, respectively, with the values in parentheses representing the reference basis set limit values. A comparison with the DFT results by B3LYP method clearly manifests the effectiveness and accuracy of this method in the study of large hydrogen-bonded complexes.

Accurate ab Initio Binding Energies of Alkaline Earth Metal Clusters

The effects of basis set superposition error (BSSE) and core-correlation on the electronic binding energies of alkaline earth metal clusters Y(n) (Y = Be, Mg, Ca; n = 2-4) at the Moller-Plesset second-order perturbation theory (MP2) and the single and double coupled cluster method with perturbative triples correction (CCSD(T)) levels are examined using the correlation consistent basis sets cc-pVXZ and cc-pCVXZ (X = D, T, Q, 5). It is found that, while BSSE has a negligible effect for valence-electron-only-correlated calculations for most basis sets, its magnitude becomes more pronounced for all-electron-correlated calculations, including core electrons. By utilizing the negligible effect of BSSE on the binding energies for valence-electron-only-correlated calculations, in combination with the negligible core-correlation effect at the CCSD(T) level, accurate binding energies of these clusters up to pentamers (octamers in the case of the Be clusters) are estimated via the basis set extrapolation of ab initio CCSD(T) correlation energies of the monomer and cluster with only the cc-pVDZ and cc-pVTZ sets, using the basis set and correlation-dependent extrapolation formula recently devised. A comparison between the CCSD(T) and density functional theory (DFT) binding energies is made to identify the most appropriate DFT method for the study of these clusters.

Binding energies of hydrogen-bonded clusters from extrapolation-oriented basis sets

The MP2 and CCSD(T) basis set limit binding energies of various hydrogen-bonded clusters were estimated via basis set extrapolation employing the correlation consistent aug-cc-pVDZ and modified aug-cc-pVDZ set containing extra polarization functions from cc-pVTZ set. By adopting the optimal interval for the difference between the cardinal numbers (X) corresponding to two basis sets in the X−3 type extrapolation scheme the estimated binding energies for (H2O)n and (HF)n (n=3−5) are shown to be close to the reference basis set limit values within the error bounds in many cases, manifesting the significance of these basis sets in studying the structures and binding of large hydrogen-bonded clusters.

Benchmark calculations with correlated molecular wave functions. VIII. Bond energies and equilibrium geometries of the CHn and C2Hn (n=1–4) series

Using systematic sequences of correlation consistent basis sets, the accuracy of calculated bond energies De(CH) and equilibrium geometries (re, θe) has been investigated for the CHn and C2Hn series (n=1–4). Perturbation theory (MP2, MP3, MP4), coupled cluster [CCSD, CCSD(T)], and single and multireference configuration interaction (HF+1+2, CAS+1+2) methods have been investigated. Except for the vinyl radical, all of the calculated bond energies showed significant basis set dependence with average errors (standard deviations) of 5.6 (±3.0) kcal/mol for the cc-pVDZ set, 1.4 (±0.8) kcal/mol for the cc-pVTZ set, and 0.5 (±0.4) kcal/mol for the cc-pVQZ set with CCSD(T) wave functions. For the vinyl radical the total variation with basis set was just 0.6 kcal/mol. Strong basis set dependence was also observed for the equilibrium geometries, e.g., for re(CH) the average error decreased from 0.020 Å (cc-pVDZ) to 0.003 Å (cc-pVTZ) to 0.002 Å (cc-pVQZ). The effect of including the core electrons in the correlated calculations was also investigated for the two series. Inclusion of core correlation in the CHn series increased De(CH) by 0.13 (CH) to 0.61 kcal/mol (CH2) and decreased the equilibrium CH bond lengths by approximately 0.0015 Å. For the C2Hn series, correlation of the core electrons increased De(CH) by 0.18 (C2H4) to 1.01 (C2H) kcal/mol, but decreased De(CH) in C2H2 by 0.25 kcal/mol. Predictions are also made for the equilibrium geometries of C2H, H2CC, and C2H3, as well as the CH bond strength of vinylidene and the acetylene–vinylidene isomerization energy.