Augmented Gaussian basis sets of double and triple zeta valence qualities for the atoms K and Sc–Kr: Applications in HF, MP2, and DFT calculations of molecular electric properties

Augmented Gaussian basis sets of double and triple zeta valence qualities plus polarization functions for the atoms K and from Sc to Kr are presented. They were generated from the all-electron unaugmented sets by addition of diffuse functions (s, p, d, f, and g symmetries) that were optimized for the anion ground states. From these sets, Hartree–Fock, second-order Møller–Plesset perturbation theory, and density functional theory electric dipole moment and dipole polarizability calculations for a sample of molecules were carried out. Comparison with theoretical and experimental values available in the literature was done.     

Augmented Gaussian basis set of quintuple zeta valence quality for H and from Li to Ar: Applications in DFT calculations of molecular electric properties

Augmented Gaussian basis set of quintuple zeta valence quality plus polarization functions (A5ZP) for H and Li–Ar is presented. It was determined from the 5ZP basis set by addition of diffuse (s and p symmetries) and polarization (p, d, f, g, and h symmetries) functions that were optimized for the anion at the Hartree–Fock and Mller–Plesset second-order levels, respectively. It was shown that in general this basis set in combination with the density functional theory can be used with success to predict electric properties for a sample of molecules. Comparison with theoretical and experimental values available in the literature is done.     

Multipole polarizabilities of Ar

The four lowest multipole polarizabilities of Ar have been calculated by using the complete fourth-order many-body perturbation theory approach and a large GTO/CGTO basis set including a number of diffuse and polarization functions. The present results for the dipole polarizability (α =11.23 au), quadrupole polarizability (C= 26.79 au), dipole-quadrupole polarizability (B = -164.3), and the dipole hyperpolarizability (γ =1329 au) are compared with other theoretical data and experimental values.     

Efficient polarized basis sets for evaluation of static and dynamic molecular electric properties

New medium size Gaussian‐type basis set R‐ORP for evaluation of static and dynamic electric properties in molecular systems is presented. It is obtained in a close resemblance to the original ORP basis set, from the source basis set through addition of two first‐order polarization functions whose exponent values are optimized with respect to the finite field restricted open‐shell Hartree–Fock (ROHF) atomic polarizabilities. As the source set the VTZ basis set of Ahlrichs and coworkers, augmented with additional diffuse functions and contracted to the form [6s/3s] for hydrogen and [11s7p/4s3p] for carbon through fluorine, is chosen. The resulting basis set is of the form [6s2p/3s2p] for hydrogen and [11s7p2d/4s3p2d] for other atoms. Presented basis set is next tested in the CCSD static and dynamic molecular polarizability and hyperpolarizability calculations for a set of ten and four test molecules, respectively, for which very accurate reference data exist. Additionally, the recently developed ORP basis set is employed in the calculations to examine the limits of its applicability. Results are compared to the literature data obtained in both, large and diffuse, as well as reduced‐size basis sets. In the case of polarizability calculations, the aug‐pc‐1 and R‐ORP are the optimal choices among the investigated smaller basis sets, with the overall performance of the aug‐pc‐1 set being better. Among the larger sets, the ORP performs better in the case of average polarizability, while the RMSE values for polarizability anisotropy are practically identical for d‐aug‐cc‐pVDZ and ORP sets. Finally, the R‐ORP and ORP basis sets compete other small bases in the evaluation of the first hyperpolarizability in investigated systems. © 2016 Wiley Periodicals, Inc.     

Ab initio dipole polarizability surfaces of water molecule: static and dynamic at 514.5 nm

Coupled cluster calculations with a carefully designed basis set have been performed to obtain both static, alpha, and dynamic at 514.5 nm, alpha(514.5 nm), dipole polarizability surfaces of water. We employed a medium size basis set (13s10p6d3f9s6p2d1f)[9s7p6d3f6s5p2d1f] consisting of 157 contracted Gaussian-type functions that yields values near the Hartree-Fock limit for alpha [G. Maroulis, J. Chem. Phys. 94, 1182 (1991)]. The alpha and alpha(514.5 nm) surfaces were able to reproduce all the experimentally available information about the dipole polarizability of water, especially the Raman spectra of gaseous H(2)O, D(2)O, and HDO. Vibrational averages for the dipole polarizability of water molecule are also reported.     

Full CI benchmark calculations for molecular properties

Full CI calculations of first- and second-order properties are presented to provide benchmark results for comparisons with other methods, such as multireference CI(MRCI). The full CI(FCI) polarizability of F^– is computed using a double zeta plus polarization plus diffuse basis set. These FCI results are compared to those obtained at other levels of theory; the CASSCF/MRCI with Davidson correction results are in excellent agreement with the FCI. Differences between the polarizability results computed as a (numerical) second derivative of the energy or as an induced dipole moment are also discussed. FCI calculations are presented for the dipole moment and polarizability of HF, CH₂ and SiH₂ using a DZP basis set. Again, the CASSCF/MRCI values are in excellent agreement with the FCI results, whereas SDCI values, whether computed as an expectation value or as an energy derivative, are much worse. The results obtained using the CPF approach are in considerably better agreement with the FCI results than SDCI, and are similar in quality to the SDCI energy derivative results with the inclusion of Davidson's correction.     

Dipole preserving and polarization consistent charges

A method for estimating dipole preserving and polarization consistent (DPPC) charges is described, which reproduces exactly the molecular dipole moment as well as the local, atomic hybridization dipoles determined from the corresponding wave function and can yield accurate molecular polarization. The method is based on a model described by Thole and van Duijnen and a new feature is introduced to treat molecular polarization. Thus, the DPPC method offers a convenient procedure to describe molecular polarization in applications using semiempirical models and ab initio molecular orbital theory with relatively small basis functions such as 6‐31+G(d,p) or without inclusion of electron correlation; these methods tend to underestimate molecular polarizability. The trends of the DPPC partial atomic charges are found to be in good accord with those of the CM2 model, a class IV charge analysis method that has been used in a variety of applications. The DPPC method is illustrated to mimic the correct molecular polarizability in a water dimer test case and in water‐halide ion complexes using the explicit polarization (X‐Pol) potential with the Austin model 1 Hamiltonian. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

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.     

Molecular energies and properties from density functional theory: Exploring basis set dependence of Kohn—Sham equation using several density functionals

The performance of four commonly used density functionals (VWN, BLYP, BP91, and Becke's original three-parameter approximation to the adiabatic connection formula, referred to herein as the adiabatic connection method or ACM) was studied with a series of six Gaussian-type atomic basis sets [DZP, 6–31G**, DZVP, TZVP, TZ2P, and uncontracted aug-cc-pVTZ (UCC)]. The geometries and dipole moments of over 100 first-row and second-row molecules and reaction energies of over 300 chemical reactions involving such molecules were computed using each of the four density functionals in combination with each of the six basis sets. The results were compared to experimentally determined values. Based on overall mean absolute theory versus experiment errors, it was found that ACM is the best choice for predictions of both energies of reaction [overall mean absolute theory versus experiment error (MATvEE) of 4.7 kcal/mol with our most complete (UCC) basis set] and molecular geometries (overall MATvEE of 0.92 pm for bond distances and 0.88° for bond angles with the UCC basis set). For routine calculations with moderate basis sets (those of double-ζ type: DZP, 6–31G**, and DZVP) the DZVP basis set was, on average, the best choice. There were, however, examples of reactions where significantly larger basis sets were required to achieve reasonable accuracy (errors ≤ 5 kcal/mol). For dipole moments, ACM, BP91, and BLYP performed comparably (overall MATvEE of 0.071, 0.067, and 0.059 debye, respectively, with the UCC basis set). Basis sets that include additional polarization functions and diffuse functions were found to be important for accurate density functional theory predictions of dipole moments. © 1997 by John Wiley & Sons, Inc.     

Medium-size polarized basis sets for high-level-correlated calculations of molecular electric properties

Summary The basis set polarization approach is employed for the generation of medium-size polarized GTO/CGTO basis sets for calculations of molecular dipole moments and polarizabilities. The excellent performance of the [13.10.4/7.5.2] GTO/CGTO polarized basis sets derived for Si through Cl is illustrated by the atomic polarizability results and SCF and MBPT data for dipole moments and polarizabilities of the second-row atom hydrides. The possible applications of the electric-property oriented polarized basis sets are discussed. The basis set data for Si through Cl are those for H and C through F append the paper.     

Effect of secondary basis-set superposition error upon calculated vibrational intensities

The calculated dipole moment and polarizability of a molecule are affected by the position of the ghost orbitais of its partner subunit within a molecular complex. The IR and Raman intensities, evaluated in terms of the derivatives of these properties with respect to an intermolecular motion, are hence subject to a secondary basis-set superposition error (BSSE), here calculated for (HF)₂ with a variety of basis sets. Whereas the IR intensity is only slightly affected, the BSSE introduces enormous errors into the Raman intensities. These errors can be reduced if two sets of polarization functions are included in the basis set.     

Reduced-size polarized basis sets for calculations of molecular electric properties. I. The basis set generation

Following the recent studies of basis sets explicitly dependent on oscillatory external electric field we have investigated the possibility of some further truncation of the so-called polarized basis sets without any major deterioration of the computed data for molecular dipole moments, dipole polarizabilities, and related electric properties of molecules. It has been found that basis sets of contracted Gaussian functions of the form [3s1p] for H and [4s3p1d] for the first-row atoms can satisfy this requirement with particular choice of contractions in their polarization part. With m denoting the number of primitive GTOs in the contracted polarization function, the basis sets devised in this article will be referred to as the ZmPol sets. In comparison with earlier, medium-size polarized basis sets (PolX), these new ZmPol basis sets are reduced by 2/3 in their size and lead to the order of magnitude computing time savings for large molecules. Simultaneously, the dipole moment and polarizability data remain at almost the same level of accuracy as in the case of the PolX sets. Among a variety of possible applications in computational chemistry, the ZmPolX are also to be used for calculations of frequencies and intensities in the Raman spectra of large organic molecules (see Part II, this issue).     

Application of the coupled-cluster theory to atomic frequency-dependent polarizabilities

Summary A time-dependent coupled-cluster approach may be employed to describe dynamic processes of many-electron systems. Atomic properties, such as the frequency-dependent polarizability, can be treated as a response of the system described by the coupled-cluster expansion to an external radiation field. The major difficulty in the realization of such a formalism is to deal with dynamic pair functions. The procedure reported here is to simplify the full set of single- and pair-excitation expansion equations to a subset of equations which includes polarization and relaxation effects to all orders and is solved by using a complete set of discrete basis functions. Calculations of excitation energies and frequency-dependent electric dipole polarizabilities for helium are presented. Application of the procedure to calculate photoionization cross sections is discussed.     

Reactivity of haloethanes with hydroxyl radicals: Effects of basis set and correlation energy on reaction energetics

Ab initio calculations on fluoroethane reactions with the hydroxyl radical have been carried out at different levels of theory. The convergence of reaction barriers and reaction enthalpies has been systematically investigated with respect to the size and quality of the basis set and the treatment of correlation energy. The G2 and MP2 barrier heights and reaction enthalpies show the best agreement with the experimental data. The split valence basis sets of triple-zeta quality supplemented by diffuse and polarization functions are necessary to reproduce experimental values for barrier heights and reaction enthalpies at the MP2 level of theory. The full counterpoise correction was used to calculate the basis set superposition error for several standard basis sets, including polarization and diffuse functions. The smallest counterpoise corrections are associated with basis sets that contain polarization and diffuse functions, the diffuse functions being the most effective in reducing BSSE. However, in our case, the uncorrected barrier heights are in better agreement with experimental results than the counterpoise-corrected data. Thus, at the MP2 level of theory, which seems to be dictated for larger electronic systems of chemical interest, the optimal approach is to increase the basis set to the maximum size affordable and to use results without counterpoise corrections for the calculation of reaction barriers. A viable alternative is the use of G2 theory because its results for the barrier heights and reaction enthalpies are in excellent agreement with the experimental data. © 1997 John Wiley & Sons, Inc. J Comput Chem 18: 1190–1199     

Collision-induced dipole polarizability of helium dimer from explicitly correlated calculations

Large expansions in basis sets of explicitly correlated Gaussian functions and the variation-perturbation technique were used to calculate the static dipole polarizability of the helium dimer at 16 different internuclear separations from 1.0 to 9.0 bohrs. The convergence towards the complete basis set limit was analyzed in order to estimate uncertainties of all the calculated values. The results are significantly more accurate than literature data. Asymptotically correct analytic fits for the trace and anisotropy of collision-induced polarizability were obtained.     

A new form of electric-field-dependent basis functions for the calculation of electric polarizabilities and dipole moments

An ab-initio molecular orbital theory of electrical polarization is presented in which the molecular orbitals are written as linear combinations of atomic functions which depend explicitly on the strength of a uniform external electric field. The wavefunctions in the presence of such a field are determined using self-consistent field perturbation theory. It is shown that the use of field-dependent atomic functions provides an efficient technique for the calculation of electric polarizability tensors. Polarizability tensors and electric-dipole moments calculated using both a minimal and a split-valence-shell basis set are compared with experimental results. Both polarizability-tensor components and dipole moments are seriously underestimated at the minimal bases-set level. The split-valence basis approach yields substantially better results; the calculated values at this level are in reasonable agreement with the corresponding experimental values. The experimental ordering of isotropic polarizabilities for a set of small molecules is duplicated quite closely by both the minimal and the split-valence-shell calculations.