Truncation of the correlation consistent basis sets: extension to third-row (Ga-Kr) molecules

The systematic reduction of the commonly used correlation consistent basis sets [cc-pVnZ where n=D(2), T(3), Q(4), and 5] as a means to reduce computational cost has been extended to hydrogen-containing third-row (Ga-Kr) molecules of the G2 test suite. Coupled cluster with singles, doubles, and quasiperturbative triple excitations [CCSD(T)] calculations were performed using both the full correlation consistent basis sets and a series of truncated basis sets in order to assess the impact of basis set reduction upon the structures and energies of the species. The impact that truncation of the basis sets for hydrogen has upon extrapolation of energies to the complete basis set limit also has been examined, and the cost savings that can be achieved are discussed. Overall, basis set reduction can be accomplished which preserves the systematic convergence behavior of the full correlation consistent basis sets.     

H3PAuR型单核Au(Ⅰ)配合物的结构和非线性光学系数的量子化学计算比较

采用量子化学ab initio和DFT中的不同方法和基组对H3PAuR型单核Au(Ⅰ)配合物结构和二阶NLO系数进行计算, 探讨不同计算方法和Au基组对计算结果产生的影响. 对计算结果分析表明, 不同计算方法对Au(Ⅰ)配合物结构和二阶NLO系数影响较大, 其中用考虑电子相关效应的DFT-B3LYP和MP2方法优化得到的Au—P配键长比用HF方法的短, 相应的二阶NLO系数比HF方法的大2倍左右; 同一计算方法下, Au基组中d轨道个数增加优化得到的Au—P配键键长减小; 随着Au基组的增大, 前线分子轨道能级差减小, 其中SDD和CEP-121G基组之间的变化更明显. 基组变化对分子二阶NLO系数的影响较小, 多数分子Au取不同基组计算的βμ值相差在10%以内.     

Truncation of the correlation consistent basis sets: an effective approach to the reduction of computational cost?

The systematic reduction of commonly used basis sets as a means to reduce computational cost is examined for a small test set of molecules, which includes H(2), CH(4), NH(3), H(2)O, HF, and HCN. Coupled cluster with single, double, and quasiperturbative triple excitations calculations were performed using both the correlation consistent basis sets, and a set of systematically reduced basis sets to examine both the impact of the reduction upon the accuracy of the structures and energies, and the computational cost savings achieved. The effect of several truncation scenarios upon basis set convergence is also examined. Overall, for the systems studied, a reduction can occur which preserves the well-established systematic convergence behavior of the correlation consistent basis sets.     

Quantum-chemical investigation of the structures and electronic spectra of the nucleic acid bases at the coupled cluster CC2 level

We study the ground-state structures and singlet- and triplet-excited states of the nucleic acid bases by applying the coupled cluster model CC2 in combination with a resolution-of-the-identity approximation for electron interaction integrals. Both basis set effects and the influence of dynamic electron correlation on the molecular structures are elucidated; the latter by comparing CC2 with Hartree-Fock and M?ller-Plesset perturbation theory to second order. Furthermore, we investigate basis set and electron correlation effects on the vertical excitation energies and compare our highest-level results with experiment and other theoretical approaches. It is shown that small basis sets are insufficient for obtaining accurate results for excited states of these molecules and that the CC2 approach to dynamic electron correlation is a reliable and efficient tool for electronic structure calculations on medium-sized molecules.     

Auxiliary basis sets for density fitting-MP2 calculations: Nonrelativistic triple-zeta all-electron correlation consistent basis sets for the 3d elements Sc-Zn

Auxiliary basis sets for density fitting second-order Moller-Plesset perturbation theory (DF-MP2) have been optimized for use with the triple-zeta nonrelativistic all-electron correlation consistent orbital basis sets, cc-pVTZ-NR and aug-cc-pVTZ-NR, for the 3d elements Sc-Zn. The relative error in using these auxiliary basis sets is found to be around four orders of magnitude smaller than that from utilizing triple-zeta orbital basis sets rather than corresponding quadruple-zeta basis sets, in calculation of the correlation energy for a test set of 54 small to medium sized transition metal complexes.     

Ab initio characterization of XH3 (X=N, P). I. Ammonia, phosphine and their related ions and radicals: structure and thermochemistry

Ammonia, phosphine and their related cations, anions and radicals have been investigated at a high level of accuracy. The singles and doubles coupled cluster method including a perturbational correction for connected triple excitations, CCSD(T), in conjunction with correlation consistent basis sets ranging in size from triple to sextuple zeta have been employed. Extrapolation to the complete basis set limit has been used with accurate treatments of core–valence correlation effects in order to accurately predict structures, ionization potentials, electron affinities as well as N–H and P–H bond dissociation energies. For all the species studied, harmonic vibrational frequencies have also been evaluated in order to obtain zero-point corrections.     

Density functional theory and the correlation consistent basis sets: the tight d effect on HSO and HOS

The HSO and HOS isomers have been revisited using the DFT functionals, B3LYP, B3PW91, and PBE, in combination with tight d-augmented correlation consistent basis sets, cc-pV(x+d)Z and aug-cc-pV(x+d)Z for second-row atoms. Structures, vibrationally averaged structures, relative energies, harmonic and anharmonic frequencies, enthalpies of formation of HSO and HOS, and the barrier for the HSO/HOS isomerization have been determined. These results were compared with results from previous DFT and ab initio studies in which the standard correlation consistent basis sets were used. The relative energies of the two isomers converge more rapidly and smoothly with respect to increasing basis set size for the tight d-augmented sets than for the standard basis sets. Our best calculations, B3PW91/aug-cc-pV(5+d)Z, for the relative energy of the isomers are in excellent agreement with previous CCSD(T) results given by Wilson and Dunning.     

Light-dependent isomeric effects of polycyclic aromatic hydrocarbons on the predication of DNA cleavage factor efficiency

PAHs, short for polycyclic aromatic hydrocarbons, are a ubiquitous group of chemically related, environmentally persistent organic compounds having diverse structures and varied toxicity. They have been shown to cause mutagenic and carcinogenic effects on organisms and are quite immunosuppressive. Time-dependent density functional theory (TD-DFT) offers a practical means of understanding the behavior of excitation energies for PAHs. Here, we examined the performance of the long-range corrected Coulomb-attenuating functional (CAM-B3LYP) in relation to four different basis sets, determining which basis set compliments the functional better in identifying the most reactive atomic site on six isomeric PAH compounds. Condensed Fukui function indices were used to compare the performance of applied basis sets in identifying the most reactive atomic site on six isomeric PAHs compounds, assessing which basis set would be more appropriate in determining the site where free-radical formation would occur after light irradiation. Dunning’s correlation consistent triple-zeta (cc-pVTZ) basis set was determined to have the best PAH characterization performance, concluding the need for application of a higher-level basis set with the long-range corrected Coulomb-attenuating functional. Although each compound was a structural isomer of the other, the reactive atomic sites varied for each molecule with the use of an applied basis set. It was concluded that structural shape has some influence on the calculation of PAH characteristics. Lastly, in order to predict DNA single-stranded cleavage factor for the compounds proposed here, we have used the quantitative structure-activity relationship (QSAR). The cleavage factor values for the set of aromatic molecules with similar structures have been collected from the literature for a total number of 22 compounds.     

Basis set and electron correlation effects on the polarizability and second hyperpolarizability of model open-shell pi-conjugated systems

The basis set and electron correlation effects on the static polarizability (alpha) and second hyperpolarizability (gamma) are investigated ab initio for two model open-shell pi-conjugated systems, the C(5)H(7) radical and the C(6)H(8) radical cation in their doublet state. Basis set investigations evidence that the linear and nonlinear responses of the radical cation necessitate the use of a less extended basis set than its neutral analog. Indeed, double-zeta-type basis sets supplemented by a set of d polarization functions but no diffuse functions already provide accurate (hyper)polarizabilities for C(6)H(8) whereas diffuse functions are compulsory for C(5)H(7), in particular, p diffuse functions. In addition to the 6-31G(*)+pd basis set, basis sets resulting from removing not necessary diffuse functions from the augmented correlation consistent polarized valence double zeta basis set have been shown to provide (hyper)polarizability values of similar quality as more extended basis sets such as augmented correlation consistent polarized valence triple zeta and doubly augmented correlation consistent polarized valence double zeta. Using the selected atomic basis sets, the (hyper)polarizabilities of these two model compounds are calculated at different levels of approximation in order to assess the impact of including electron correlation. As a function of the method of calculation antiparallel and parallel variations have been demonstrated for alpha and gamma of the two model compounds, respectively. For the polarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset methods bracket the reference value obtained at the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples level whereas the projected unrestricted second-order M?ller-Plesset results are in much closer agreement with the unrestricted coupled cluster singles and doubles with a perturbative inclusion of the triples values than the projected unrestricted Hartree-Fock results. Moreover, the differences between the restricted open-shell Hartree-Fock and restricted open-shell second-order M?ller-Plesset methods are small. In what concerns the second hyperpolarizability, the unrestricted Hartree-Fock and unrestricted second-order M?ller-Plesset values remain of similar quality while using spin-projected schemes fails for the charged system but performs nicely for the neutral one. The restricted open-shell schemes, and especially the restricted open-shell second-order M?ller-Plesset method, provide for both compounds gamma values close to the results obtained at the unrestricted coupled cluster level including singles and doubles with a perturbative inclusion of the triples. Thus, to obtain well-converged alpha and gamma values at low-order electron correlation levels, the removal of spin contamination is a necessary but not a sufficient condition. Density-functional theory calculations of alpha and gamma have also been carried out using several exchange-correlation functionals. Those employing hybrid exchange-correlation functionals have been shown to reproduce fairly well the reference coupled cluster polarizability and second hyperpolarizability values. In addition, inclusion of Hartree-Fock exchange is of major importance for determining accurate polarizability whereas for the second hyperpolarizability the gradient corrections are large.     

Predicting new molecular species of potential interest to atmospheric chemistry: the isomers HSBr and HBrS

Coupled cluster singles and doubles with perturbative contributions of connected triples CCSD(T) theory with a series of correlation consistent basis sets was used to predict the existence and characterize for the first time the structures, harmonic frequencies, and energetic quantities of the isomeric species HSBr and HBrS, as well as the transition state connecting them. These calculations consider extrapolation to the complete basis set (CBS) limit, corrections for scalar relativistic effects using the second-order Douglas-Kroll-Hess Hamiltonian, and also correlation of the bromine d electrons in addition to the 14 valence electrons. The species HSBr was found to be more stable than HBrS by 50.93 kcal/mol, with a high barrier height of 60.00 kcal/mol for the interconversion into HBrS. The smaller barrier of 7.90 kcal/mol (ZPE included) for the reverse process, however, should favor a rapid interconversion of HBrS into HSBr if HBrS can also be initially present in a potential synthetic route. If trapped in a matrix, their harmonic frequencies will allow for an unambiguous distinction between the two species. Scalar relativistic corrections and correlation of 24 electrons, although minor for the present purpose of a first time, but accurate, characterization of these species, are needed if chemical accuracy is also pursued. A test of the DFT/B3LYP approach in describing this type of system resulted in good energetic quantities, but geometric parameters and frequencies still lack spectroscopic accuracy. Whether HSBr can act as a temporary bromine reservoir and/or a source of reactive bromine and HS radicals requires further studies that are underway in our group.     

Intramolecular basis set superposition errors

The effects of intramolecular basis set superposition errors are less well documented than the corresponding intermolecular effects. The intramolecular basis set superposition errors are examined, using the approach of Jensen, for several basis sets developed by Pople and his co‐workers, which are widely used in studies of larger molecules. Prototype calculations are reported for the ground state of the water molecule using both the matrix Hartree–Fock method and the many‐body perturbation expansion for the correlation energy taken through second order. A similar investigation is carried out for some of the correlation consistent basis sets published by Dunning and his collaborators. Specifically, the following aspects are investigated: (i) the magnitude of the intramolecular basis set superposition error, (ii) the nonadditivity of intramolecular counterpoise corrections when applied in a pairwise fashion, and (iii) the use of multiple “ghost” centers. © 2001 John Wiley & Sons, Inc. Int J Quant Chem 82: 282–292, 2001     

Auxiliary basis sets for density fitting second-order Møller-Plesset perturbation theory: correlation consistent basis sets for the 5d elements Hf-Pt

Auxiliary basis sets specifically matched to the correlation consistent cc-pVnZ-PP, cc-pwCVnZ-PP, aug-cc-pVnZ-PP, and aug-cc-pwCVnZ-PP orbital basis sets (used in conjunction with pseudopotentials) for the 5d transition metal elements Hf-Pt have been optimized for use in density fitting second-order M?ller-Plesset perturbation theory and other correlated ab initio methods. Calculations of the second-order M?ller-Plesset perturbation theory correlation energy, for a test set of small to medium sized molecules, indicate that the density fitting error when utilizing these sets is negligible at three to four orders of magnitude smaller than the orbital basis set incompleteness error.     

Systematically convergent basis sets for explicitly correlated wavefunctions: the atoms H, He, B-Ne, and Al-Ar

Correlation consistent basis sets have been optimized for use with explicitly correlated F12 methods. The new sets, denoted cc-pVnZ-F12 (n=D,T,Q), are similar in size and construction to the standard aug-cc-pVnZ and aug-cc-pV(n+d)Z basis sets, but the new sets are shown in the present work to yield much improved convergence toward the complete basis set limit in MP2-F12/3C calculations on several small molecules involving elements of both the first and second row. For molecules containing only first row atoms, the smallest cc-pVDZ-F12 basis set consistently recovers nearly 99% of the MP2 valence correlation energy when combined with the MP2-F12/3C method. The convergence with basis set for molecules containing second row atoms is slower, but the new DZ basis set still recovers 97%-99% of the frozen core MP2 correlation energy. The accuracy of the new basis sets for relative energetics is demonstrated in benchmark calculations on a set of 15 chemical reactions.     

Two-photon absorption cross sections: an investigation of the accuracy of calculated absolute and relative values

We have studied the basis set and electron correlation effects on the ab initio calculations of two-photon absorption cross sections of water. Various series of correlation consistent basis sets up to triply augmented basis sets of valence pentuple zeta level as well as the popular 6-31G(d) basis set have been employed in combination with several coupled cluster, configuration interaction, and density functional theory methods. We find that it is very difficult to obtain converged values of the cross sections for even a small molecule such as water. Acknowledging these difficulties in obtaining a fully converged cross section for a given state, we also investigated the possibility of determining relative cross sections for a series of organic molecules. However, we did not find consistency between the relative cross sections calculated at the Hartree-Fock level and several coupled-cluster methods using the 6-31G(d) and aug-cc-pVDZ basis sets. However, we could reproduce the relative ordering of the two-photon absorption cross sections of the molecules studied at the Hartree-Fock level.     

Relativistic effects determined using the Douglas-Kroll contracted basis sets and correlation consistent basis sets with small-core relativistic pseudopotentials

The coupled cluster approximation with single, double, and quasiperturbative triple excitations [CCSD(T)] was used in combination with the Douglas-Kroll contracted correlation consistent basis sets [cc-pVnZ-DK, where n = D(2), T(3), Q(4), and 5] and small-core relativistic pseudopotentials (PP) with correlation consistent polarized valence basis sets (cc-pVnZ-PP and aug-cc-pVnZ-PP) to investigate the impact of scalar relativistic corrections on energetic and structural properties of small molecules containing third-row (Ga-Kr) atoms. These molecules were taken from the Gaussian-2 extended test set for third-row atoms. Atomization energies, ionization energies, electron affinities, and proton affinities for molecules in the test set were determined and compared with nonrelativistic results which were obtained in a recent study in which the standard and augmented correlation consistent basis sets were used in combination with CCSD(T). Several schemes were used to extrapolate the energies to the complete basis set limit.     

Improved efficiency of focal point conformational analysis with truncated correlation consistent basis sets

It has been suggested that the computational cost of correlated ab initio calculations could be reduced efficiently by using truncated basis sets on hydrogen atoms (Mintz et al., J Chem Phys 2004, 121, 5629). We now explore this proposal in the context of conformational analysis of small molecules, such as hydrogen peroxide, dimethyl ether, ethyl methyl ether, formic acid, methyl formate, and several small alcohols. It is found that truncated correlation consistent basis sets that lack certain higher angular momentum functions on hydrogen atoms offer accuracy similar to traditional Dunning's basis sets for conformational analysis. Combination of such basis sets with the basis set extrapolation technique to estimate Hartree-Fock and M?ller-Plesset second order energies provides composite extrapolation model chemistries that are significantly more accurate and faster than analogous single point calculations with traditional correlation consistent basis sets. Root mean square errors of best composite extrapolation model chemistries on the used set of molecules are within 0.03 kcal/mol of traditional focal point conformational energies. The applicability of composite extrapolation methods is illustrated by performing conformational analysis of tert-butanol and cyclohexanol. For comparison, conformational energies calculated with popular molecular mechanics force fields are also given.     

Conformations of allyl amine: theory vs experiment

The relative stabilities of the five conformers of allyl amine, a medium-size aliphatic molecule, were estimated by applying ab initio quantum mechanical methods at several levels of theory. The second-order M?ller-Plesset perturbation method (MP2), quadratic configuration interaction including single and double excitations (QCISD), coupled-cluster with single and double excitations (CCSD) and CCSD plus perturbative triple excitations [CCSD(T)] were applied. The Dunning correlation consistent basis sets (through aug-cc-pVQZ and cc-pV5Z) were employed. The MP2 energies relative to the energy of the cis-trans conformer reported here appear to approach the basis set limit. The predicted allyl amine conformer energies approaching the Hartree-Fock basis set limit are 158 cm-1 (cis-gauche), -5 cm-1 (gauche-trans), and -146 cm-1 (gauche-gauche). The same three relative energies near the MP2 basis set limit are 135, 103, and 50 cm-1, respectively. The analogous energies deduced from experiment are 173 +/- 12, 92 +/- 8, and 122 +/- 5 cm-1. The theoretical results obtained in the present study suggest that satisfactory predictions of the conformer energetics of allyl amine may be achieved only by theoretical methods that incorporate consideration of correlation effects in conjunction with large basis sets. Evaluation of the zero-point vibrational energy corrections is critical, due to the very small classical energy differences between the five conformers of allyl amine. Agreement between theory and experiment for the gauche-gauche conformational energy remains problematical.     

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.