Basis sets for geometry optimizations of second-row transition metal inorganic and organometallic complexes

Modest-sized basis sets for the second-row transition metal atoms are developed for use in geometry optimization calculations. Our method is patterned after previous work on basis sets for first-row transition metal atoms. The basis sets are constructed from the minimal basis sets of Huzinaga and are augmented with a set of diffuse p and d functions. The exponents of these diffuse functions are chosen to minimize both the difference between the calculated and experimental equilibrium geometries and the total molecular energies for several second-row transition metal inorganic and organon etallic complexes. Slightly smaller basis sets, based on the same Huzinaga minimal sets but augmented with a set of diffuse s and p functions rather than diffuse p and d functions, are also presented. The performance of these basis sets is tested on a wide variety of second-row transition metal inorganic and organometallic complexes and is compared to pseudopotential basis sets incorporating effective core potentials.     

Basis sets for transition metals: Optimized outer p functions

Although the (n + 1)p orbital is unoccupied in transition-metal ground-state configurations which are all nd^x(n + 1)s^y, these (n + 1)p functions play a crucial role in the structure of transition metal complexes. As we show here, the usual solution, adding one or more diffuse functions, can be insufficient to create an orbital of the correct energy. The major problem appears to be due to the incorrect placement of the (n + 1)p orbital's node. Even splitting the most diffuse component of the np orbital and adding a second diffuse function does not completely solve this problem. Although one can usually solve this deficiency by further uncontracting of the np function, here we offer a set of properly optimized (n + 1)p functions that offer a more compact and satisfactory solution to the proper placements of the node. We show an example of the common deficiencies seen in typical basis sets, including standard basis sets in GAUSSIAN94, and show that the new optimized (n + 1)p function performs well compared to a fully uncontracted basis set. © 1996 by John Wiley & Sons, Inc.     

Infinite Basis set extrapolation for Double Hybrid Density Functional Theory 1: effect of applying various extrapolation functions

We applied the Infinite Basis (IB) set extrapolation and Double Hybrid Density Functional Theory (DHDF) to calculate the databases of atomization energies, ionization energies, electron affinities, reaction barrier heights, proton affinities, alkyl bond dissociation energies, and noncovalent interactions. The Complete Basis Set (CBS) limit is estimated by extrapolating the hybrid density functional theory and PT2 energies using extrapolation functions including exponential, inverse power, modified exponential, and the combination of the these functions. We found that the combination of B2KPLYP/cc-pV[D|T]Z (which is the extrapolation based on the energies calculated in cc-pVDZ and cc-pVTZ) gives results in quadruple-ζ quality. However, if we want to reach the ～2 kcal/mol chemical accuracy limit, the cc-pV[T|Q]Z is required. Similar results with various extrapolation functions obtained, because the IB parameters were determined by minimizing the averaged mean unsigned error of the calculated databases. We generalized the IB set extrapolation to include more than two basis sets, but we found that extrapolation with two basis sets is satisfactory to give reasonable results. The largest error occurred in the databases of the electron affinities and the weak interactions between the noble gas and the nonpolar molecules. We expect that performing the DHDF-IB scheme with the basis sets augmented by diffuse basis functions will further improve the results.     

On the validity of complete basis set extrapolation formula optimized for the equilibrium distance applied to the potential energy surface for the correlation energy of the helium dimer

Full configuration interaction calculations are performed for He₂ using various orbital basis sets of the aug‐cc‐pVXZ type, with the correlation energies being extrapolated to the complete basis set (CBS) limit. A two‐point CBS extrapolation formula has been utilized for such a purpose. It is shown that the extrapolation formula with the offset parameter k(R) optimized for the equilibrium distance is not uniformly applicable to He He distances in the very short region of the potential energy curve. The offset parameter k(R) in the repulsive region of the potential energy curve can be largely different with the one in the long‐range distances especially in the cases of basis‐sets with large cardinality number. It is also noticed that the accuracy of this extrapolation scheme may not be improved with the increasing of the cardinality number.     

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.     

Prediction of water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) using correlation‐consistent and polarization‐consistent basis sets in the Kohn–Sham basis set limit

Density functional theory (DFT) was used to estimate water's isotropic nuclear shieldings and indirect nuclear spin–spin coupling constants (SSCCs) in the Kohn–Sham (KS) complete basis set (CBS) limit. Correlation‐consistent cc‐pVxZ and cc‐pCVxZ (x = D, T, Q, 5, and 6), and their modified versions (ccJ‐pVxZ, unc‐ccJ‐pVxZ, and aug‐cc‐pVTZ‐J) and polarization‐consistent pc‐n and pcJ‐n (n = 0, 1, 2, 3, and 4) basis sets were used, and the results fitted with a simple mathematical formula. The performance of over 20 studied density functionals was assessed from comparison with the experiment. The agreement between the CBS DFT‐predicted isotropic shieldings, spin–spin values, and the experimental values was good and similar for the modified correlation‐consistent and polarization‐consistent basis sets. The BHandH method predicted the most accurate ¹H, ¹⁷O isotropic shieldings and ¹J(OH) coupling constant (deviations from experiment of about ? 0.2 and ? 1 ppm and 0.6 Hz, respectively). The performance of BHandH for predicting water isotropic shieldings and ¹J(OH) is similar to the more advanced methods, second‐order polarization propagator approximation (SOPPA) and SOPPA(CCSD), in the basis set limit. Copyright © 2008 John Wiley & Sons, Ltd.     

Comparison of large basis set DFT and MP2 calculations in the study of the barrier for internal rotation of 2,3,5,6‐tetrafluoroanisole

The barrier for internal rotation around the ? OCH₃ bond in 2,3,5,6‐tetrafluoroanisole was calculated using the density functional theory (DFT) and second‐order Møller–Plesset (MP2) methods with Pople's basis sets up to 6‐311++G(3df,2p) and Jensen basis sets up to pc‐3. The results are converged only if fairly large basis sets are used (at least 6‐311++G(3df,2pd) or pc‐2). Both the DFT and MP2 potential energy curves show internal structure. Two minima and three maxima are observed on the curves, arising from the interplay between lone‐pair delocalization and changes in the hybridization around the oxygen atom, together with the attraction between the positively polarized hydrogens in the methyl group and the negatively polarized fluorine atom at the ortho position. These critical points are somehow ironed out by the addition of zero‐point and thermal corrections to the energy curves. At this level, the MP2 method can describe reasonably well the previously determined single‐well experimental rotational barrier, 2.7 ± 2.0 kcal/mol at 298 K, while all DFT methods yield a much smaller result. As observed experimentally, the ? OCH₃ group is perpendicular to the aryl ring in the equilibrium structure, although two very close minima with an intermediate hump at 90° are still observable. The theoretical free energy barrier of rotation at the MP2(full)/pc‐2 level is 2.0 ± 1.0 kcal/mol, in reasonable agreement with the experimental determination. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Basis sets for the evaluation of van der Waals complex interaction energies: Ne–N2 intermolecular potential and microwave spectrum

In order to obtain efficient basis sets for the evaluation of van der Waals complex intermolecular potentials, we carry out systematic basis set studies. For this, interaction energies at representative geometries on the potential energy surfaces are evaluated using the CCSD(T) correlation method and large polarized LPol‐n and augmented polarization‐consistent aug‐pc‐2 basis sets extended with different sets of midbond functions. On the basis of the root mean square errors calculated with respect to the values for the most accurate potentials available, basis sets are selected for fitting the corresponding interaction energies and getting analytical potentials. In this work, we study the Ne–N₂ van der Waals complex and after the above procedure, the aug‐pc‐2–3321 and the LPol‐ds‐33221 basis set results are fitted. The obtained potentials are characterized by T‐shaped global minima at distances between the Ne atom and the N₂ center of mass of 3.39 Å, with interaction energies of ?49.36 cm^?1 for the aug‐pc‐2–3321 surface and ?50.28 cm^?1 for the LPol‐ds‐33221 surface. Both sets of results are in excellent agreement with the reference surface. To check the potentials further microwave transition frequencies are calculated that agree well with the experimental and the aV5Z‐33221 values. The success of this study suggests that it is feasible to carry out similar accurate calculations of interaction energies and ro‐vibrational spectra at reduced cost for larger complexes than has been possible hitherto. © 2013 Wiley Periodicals, Inc.     

New global potential energy surface of the MgH2 system and dynamics studies of the reaction H + MgH → Mg + H2

A new global potential energy surface for the ground state of MgH₂ was constructed using the permutation invariant polynomial neural network method. About 70 000 ab initio energy points were calculated via the multi‐reference configuration interaction method method with aug‐cc‐pVTZ and aug‐cc‐pVQZ basis sets, and these points were used to construct the potential energy surface (PES). To avoid basis set superposition error, the basis set was extrapolated to the complete basis set limit using the two point energy extrapolation formula. The root mean square error of the present PES is only 8.85 meV. Initial state (v = 0, j = 0) dynamics studies were performed using the time‐dependent wave packet method with a second‐order split operator for the total angular momentum J up to a value of 50. Furthermore, the reaction probability, integral cross section, and thermal rate constant are reported and compared with available theoretical studies.     

TiCl, TiH, and TiH+ bond energies: a test of a correlation-consistent Ti basis set

Correlation-consistent basis sets are developed for the Ti atom. The polarization functions are optimized for the average of the ³F and ⁵F states. One series of correlation-consistent basis sets is for 3d and 4s correlation, while the second series includes 3s and 3p correlation as well as 3d and 4s correlation. These basis sets are tested using the Ti ³F–⁵F separation and the dissociation energies of TiCl X⁴Φ, TiH X⁴Φ, and TiH⁺ X³Φ. The CCSD(T) complete basis set limit values are determined by extrapolation. The Douglas–Kroll approach is used to compute the scalar relativistic effect. Spin-orbit effects are taken from experiment and/or are computed at the CASSCF level. The Ti³F–⁵F separation is in excellent agreement with experiment, while the TiCl, TiH, and TiH⁺ bond energies are in good agreement with experiment. Extrapolation with the valence basis set is consistent with other atoms, while including 3s and 3p correlation appears to make extrapolation more difficult. Received: 20 January 1999 / Accepted: 26 February 1999 / Published online: 7 June 1999     

Computer simulation of trifluoromethane properties with ab initio force field

Intermolecular interaction potentials of the trifluoromethane dimer in 15 orientations have been calculated using the Hartree‐Fock (HF) self‐consistent theory and the second‐order Møller‐Plesset (MP2) perturbation theory. Single point energies at important geometries were also calibrated by the coupled cluster with single and double and perturbative triple excitation [CCSD(T)] calculations. We have employed Pople's medium size basis sets [up to 6‐311++G(3df,3pd)] and Dunning's correlation consistent basis sets (up to aug‐cc‐pVQZ). Basis set limit potential values were obtained through well‐studied extrapolation methods. The calculated MP2 potential data were employed to parameterize a 5‐site force field for molecular simulations. We performed molecular dynamics simulations using the constructed ab initio force field and compared the simulation results with experiments. Quantitative agreements for the atom‐wise radial distribution functions and the self‐diffusion coefficients over a wide range of experimental conditions can be obtained, thus validating the ab initio force field without using experimental data a priori. © 2011 Wiley Periodicals, Inc. J Comput Chem, 2011     

High-quality Gaussian basis sets for fourth-row atoms

Summary Energy-optimized Gaussian basis sets of triple-zeta quality for the atoms Rb-Xe have been derived. Two series of basis sets are developed; (24s 16p 10d) and (26s 16p 10d) sets which we expand to 13d and 19p functions as the 4d and 5p shells become occupied. For the atoms lighter than Cd, the (24s 16p 10d) sets with triple-zeta valence distributions are higher in energy than the corresponding double-zeta distribution. To ensure a triple-zeta distribution and a global energy minimum the (26s 16p 10d) sets were derived. Total atomic energies from the largest basis sets are between 198 and 284E _H above the numerical Hartree-Fock energies.     

The influence of basis sets on wave function tails

Wave function tails are analyzed quantitatively by investigating the dependence of exterior electron density (EED ) on basis sets; the EED is defined as the integrated electron density outside the repulsive molecular surface. Ab initio MO calculations with large scale basis sets were performed to establish the benchmark order of EED values for valence orbitals of some simple molecules. It is found that very popular basis sets, such as 4-31G, which are determined by energy optimization, are inferior in describing the wave function tails to some similar size basis sets, such as MIDI -4, which are obtained by least-squares fit to near Hartree-Fock atomic functions. Further the EED values for atomic 2s functions are shown to be unfavorably smaller than those for atomic 2p functions when the same value is used for the exponent α in the GTO basis sets. This indicates that the frequently used constraint α_s = α_p is not appropriate for describing wave function tails with medium-size basis sets. Deficiencies in the energy-optimized basis sets are found to become more serious for molecules including heavier atoms.     

Basis set quality versus size II. Approximate GTO wave functions for second row transition metal atoms

Basis sets ranging in size from (16, 10, 7) to (20, 14, 11) have been derived for the atoms Y–Cd. Separate sets represent the energy optimized wave functions for each of the s²dⁿ, s¹dⁿ⁺¹, and s⁰dⁿ⁺² configurations. The energies from the largest sets are within 3 mhartrees of the values obtained in numerical Hartree–Fock calculations. Reasonable Hartree–Fock s²dⁿ– s¹dⁿ⁺¹ and s²dⁿ– s⁰dⁿ⁺² excitation energies may be obtained either using the largest basis sets, or using d-orbitals optimized for the s⁰dⁿ⁺² configurations. The basis sets are slightly unbalanced in favor of the s-functions and in disfavor of the d-functions, but various alternative basis sets may be derived by combining parts of the five parent sets. The convergence of radial expectation values is discussed.     

Ab initio calculations of the Ar–ethane intermolecular potential energy surface using bond function basis sets

The intermolecular potential energy surface (PES) of argon with ethane has been studied by ab initio calculations at the levels of second‐order Møller–Plesset perturbation (MP2) theory and coupled‐cluster theory with single, double, and noniterative triple configurations (CCSD(T)) using a series of augmented correlation‐consistent basis sets. Two sets of bond functions, bf1 (3s3p2d) and bf2 (6s6p4d2f), have been added to the basis sets to show a dramatic and systematic improvement in the convergence of the entire PES. The PES of Ar–ethane is characterized by a global minimum at a near T‐shaped configuration with a well depth of 0.611 kcal mol^?1, a second minimum at a collinear configuration with a well depth of 0.456 kcal mol^?1, and a saddle point connecting the two minima. It is shown that an augmented correlation‐consistent basis set with a set of bond functions, either bf1 or bf2, can effectively produce results equivalent to the next larger augmented correlation‐consistent basis set, that is, aug‐cc‐pVDZ‐bf1 ≈ aug‐cc‐pVTZ, aug‐cc‐pVTZ‐bf1 ≈ aug‐cc‐pVQZ. Very importantly, the use of bond functions improves the PES globally, resulting accurate potential anisotropy. Finally, MP2 method is inadequate for accurate calculations, because it gives a potentially overestimated well depth and, more seriously, a poor potential anisotropy. © 2012 Wiley Periodicals, Inc.