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

Summary The basis set polarization method is used to derive the first-order polarized basis sets for Ge through Br for calculations of atomic and molecular electric properties. The performance of the [15.12.9/9.7.4] GTO/CGTO basis sets generated in this study is verified in calculations of atomic dipole polarizabilities and dipole moments and polarizabilities of the third-row atom hydrides. Whenever accurate reference data are available for comparison, the excellent performance of the derived first-order polarized basis sets is demonstrated. The role of the core polarization and relativistic contributions to atomic and molecular is also investigated. The detailed basis set data for Ge through Br are given in Appendix.     

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

Summary The first-order polarized basis sets for the use in high-level-correlated investigations of molecular electric properties have been generated for Pb, Bi, Po, and At. The performance of the standard [10.17.14.5/13.11.8.2] and extended [20.17.14.9/13.11.8.4] basis sets has been examined in nonrelativistic and quasirelativistic calculations for atoms and simple closed-shell hydrides. The relativistic contributions to electric dipole properties of those systems have been evaluated by using the recently developed quasirelativistic scheme. The predicted dipole polarizability of At is in good agreement with the results of other relativistic calculations. The calculated quasirelativistic dipole moments of BiH₃ (–0.499 a.u.), PoH₂ (–0.207 a.u.), and AtH (+0.036 a.u.) involve a significant relativistic contribution which amounts to —0.230 a.u., –0.177 a.u., and –0.097 a.u., respectively. The basis set details append this paper. They are also available as a part of the basis set library of the MOLCAS system.     

Standardized basis sets for high-level-correlated relativistic calculations of atomic and molecular electric properties in the spin-averaged Douglas-Kroll (no-pair) approximation I. Groups Ib and IIb

Summary The technique developed earlier for the generation of the so-called first-order polarized basis sets for accurate non-relativistic calculations of molecular electric properties is used to obtain similar basis sets suitable for calculations in the Douglas-Kroll no-pair approximation. The corresponding (relativistic) basis sets are devised for atoms of the Groups Ib and IIb of the periodic table and tested in calculations of atomic polarizabilities and dipole moments of the coinage metal hydrides. Excellent performance of these basis sets has been found in the case of molecular calculations.     

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.     

Reduced–size polarized basis sets for calculations of molecular electric properties. III. Second–row atoms

Reduced–size polarized (ZmPolX) basis sets are developed for the second–row atoms X = Si, P, S, and Cl. The generation of these basis sets follows from a simple physical model of the polarization effect of the external electric field which leads to highly compact polarization functions to be added to the chosen initial basis set. The performance of the ZmPolX sets has been investigated in calculations of molecular dipole moments and polarizabilities. Only a small deterioration of the quality of the calculated molecular electric properties has been found. Simultaneously the size of the present reduced–size ZmPolX basis sets is about one-third smaller than that of the usual polarized (PolX) sets. This reduction considerably widens the range of applications of the ZmPolX sets in calculations of molecular dipole moments, dipole polarizabilities, and related properties.     

Communication: convergence of anharmonic infrared intensities of hydrogen fluoride in traditional and explicitly correlated coupled cluster calculations

It is shown that the convergence of anharmonic infrared spectral intensities with respect to the basis set size is much enhanced in explicitly correlated calculations as compared to traditional configuration interaction type wave function expansion. Explicitly correlated coupled cluster (CC) calculations using Slater-type geminal correlation factor (CC-F12) yield well-converged dipole derivatives and vibrational intensities for hydrogen fluoride with basis set involving f functions on the heavy atom. Combination of CC-F12 with singles, doubles, and non-iterative triples (CCSD(T)-F12) with small corrections due to quadruple excitations, core-electron correlation, and relativistic effects yields vibrational line positions, dipole moments, and transition dipole matrix elements in good agreement with the best experimental values.     

Reduced-size polarized basis sets for calculations of molecular electric properties. IV. First-row transition metals

Recent studies of the perturbation-dependent basis sets have indicated the possibility of a significant reduction of the size of the usual CGTO sets without considerable loss of accuracy in calculations of molecular electric properties. The resulting (ZPolX) basis sets have been developed for several atoms of the first and second row of the Periodic Table. The same method of the ZPolX basis set generation is extended for the first-row transition metals and the corresponding contracted ZPolX basis sets of the size [6s5p3d1f] are determined for both nonrelativistic and scalar relativistic calculations. The performance of the ZPolX basis sets is verified in calculations on the first-row transition metal oxides at the level of the ROHF, ROHF/CASPT2, and ROHF/CCSD(T) approximations. Also the study of the dipole polarizability of TiCl₄ confirms the excellent features of these very compact basis sets. The ZPolX basis sets for nonrelativistic and relativistic calculations of molecular electric properties are available on the web page http://www.chem.uni.torun.pl/zchk/basis-sets.html.     

Small basis sets for calculations of barrier heights, energies of reaction, electron affinities, geometries, and dipole moments

Beginning with the MIDI! basis set (also called MIDIX), we introduce the MIDIX+, MIDIY, and MIDIY+ basis sets. Using correlated ab initio and hybrid density functional theory, we compare their performance to that of several existing basis sets for electronic structure calculations. The new basis sets are tested with databases of 358 energies of reactions, 44 barrier heights, 31 electron affinities, 18 geometries, and 29 dipole moments. The MIDI!, MIDIX+, MIDIY, and MIDIY+ basis sets are shown to be cost-efficient methods for calculating relative energies, geometries, and dipole moments. The MIDIX+ basis is shown to be particularly efficient for calculating electron affinities of large molecules.Contribution to the Jacopo Tomasi Honorary Issue     

Basis set convergence studies of Hartree-Fock calculations of molecular properties within the resolution of the identity approximation

Within the resolution of the identity (RI) method, the convergence of the Hartree-Fock (HF) total molecular energy and the multipole moments in the course of the combined regular expansion of the molecular and auxiliary (RI) basis sets is studied. Dunning's cc-pVXZ series is used for both the molecular and the RI basis sets. The results show the calculated quantities converge to the HF limit when both the molecular and the RI basis sets are expanded from correlation-consistent polarized valence double zeta to correlation-consistent polarized valence sextuple zeta. Combinations of molecular/RI basis sets sufficient for convergence of the total energy and of the multipole moments at various accuracy levels have been determined. A measure of the RI basis set incompleteness is suggested and discussed. As it is significantly faster than the standard HF algorithm for small and midsize molecules, the RI-HF method, together with appropriate expanding series of both molecular and RI basis sets, provide an efficient tool to estimate and control the error of the Hartree-Fock calculations due to the finite 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).     

Density functional investigation of high-spin XY (X = Cr, Mo, W and Y = C, N, O) molecules

The performance of a density functional theory approach in calculating the equilibrium bond length, dipole moment, and harmonic vibrational frequency in a series of group 6 (Cr, Mo, W) transition metal-containing diatomic molecules is evaluated. Using flexible basis sets comprised of Slater type functions, a wide range of exchange-correlation functionals is investigated. Comparing with known experimental values and published results from high-level theoretical calculations, the most suitable functional form is selected. The importance of relativistic effects is checked, and predictions are made for several unknown dipole moments. The best agreement with experimental parameters is obtained when using a general gradient approximation, while special and hybrid functional forms give less accurate results.     

Quality of contracted Gaussian-type function basis sets

The valence quality of contracted (C) Gaussian-type function (GTF) basis sets in molecular calculations is discussed for the first- through fourth-row atoms. The split-valence basis sets derived from minimal-type CGTF sets are compared with those derived from primitive (P) GTF sets. Using F, Cl, Br, and I atoms and their homonuclear diatomics as test species, we find that the split-valence CGTF sets have almost the same quality as PGTF sets with larger s and p expansion terms: for example, the (53/5), (533/53), (5333/533/5), and (53 333/5333/53) CGTF sets correspond approximately to the [9/5], [15/9], [19/15/5], and [22/18/7] PGTF sets for the first- to fourth-row atoms, respectively, where the slash separates the s, p, and d symmetries. For the main group atoms of the four rows, we recommend using the above-mentioned CGTFs or larger.     

Utilizing relativistic effective core potentials for accurate calculations of molecular polarizabilities on transition metal compounds

The requirements necessary to extend an ECP basis set for the calculation of electric and linear optical properties to the transition metals are studied. Previously an augmentation of the SBK basis set for 39 elements with s and p electron only valences (H-Rn, excluding Ga, In, and Tl) [J. Comput. Chem., 2005, 26, 1464-1471] was presented. In this work, electric dipole moments, polarizabilities, and anisotropies of selected metal hydrides, sulfides, and bromides, cisplatin, and the Fe, Ru, and Os metallocene derivatives along with many other systems are calculated and discussed. ECP calculations of molecules containing 3d and 4d metal centers among main group atoms have good agreement, often within 1-2% of the all-electron result at the time-dependent Hartree-Fock (TDHF)/Sadlej level of theory. Molecules with a 5d metal center have a large difference from and are more accurate than the all-electron results due to the inclusion of relativistic effects in the ECPs. The polarizability as calculated with and without ECPs of metallic clusters and surfaces is increasingly different as atomic number increases, again due to a lack of relativistic effects in the all-electron calculations. The augmented ECP calculations are consistent with relativistic all-electron results, while the Sadlej calculations are consistent with other nonrelativistic results. Both relativistic and basis set effects are less noticeable when the metal is in a formally positive state.     

A systematic ab initio study of the group V trihalides MX3 and pentahalides MX5 (M = P?Bi,X = F?I)

Ab initio calculations using effective core potentials and polarized split-valence basis sets are reported for the title compounds. The calculated geometries, vibrational frequencies, infrared intensities, harmonic force fields, dipole moments, relative energies, and barriers to pseudorotation are compared with the available experimental data for the known molecules. Predictions are made for those pentahalides that are still unknown. Trends in the calculated properties are identified and discussed.     

Contracted basis sets for electrical property calculations derived from Second-order Møller–Plesset theory atomic natural orbitals

 Using established methods based on correlated atomic natural orbitals (ANOs), sets of contracted polarization functions are derived for use in calculations of atomic and molecular electrical properties (especially electric moments, dipole polarizabilities and related property hypersurfaces). Through test calculations on Ne, Ar, NH₃ and CO₂, these polarization functions are shown to reproduce the accuracy of larger basis sets, to incorporate dynamical electron correlation effects and are economical to use in conjunction with sophisticated electron-correlation treatments. We also show how triple-zeta polarized ANO and double-zeta polarized ANO basis sets are constructed from these contracted polarization functions for use in the calculation of reliable zero-point vibrational averages of electrical properties. Received: 20 December 1999 / Accepted: 15 February 2000 / Published online: 12 May 2000     

A fully relativistic method for calculation of nuclear magnetic shielding tensors with a restricted magnetically balanced basis in the framework of the matrix Dirac-Kohn-Sham equation

A new relativistic four-component density functional approach for calculations of NMR shielding tensors has been developed and implemented. It is founded on the matrix formulation of the Dirac-Kohn-Sham (DKS) method. Initially, unperturbed equations are solved with the use of a restricted kinetically balanced basis set for the small component. The second-order coupled perturbed DKS method is then based on the use of restricted magnetically balanced basis sets for the small component. Benchmark relativistic calculations have been carried out for the (1)H and heavy-atom nuclear shielding tensors of the HX series (X=F,Cl,Br,I), where spin-orbit effects are known to be very pronounced. The restricted magnetically balanced basis set allows us to avoid additional approximations and/or strong basis set dependence which arises in some related approaches. The method provides an attractive alternative to existing approximate two-component methods with transformed Hamiltonians for relativistic calculations of chemical shifts and spin-spin coupling constants of heavy-atom systems. In particular, no picture-change effects arise in property calculations.     

Polarization consistent basis sets. VII. The elements K, Ca, Ga, Ge, As, Se, Br, and Kr

Polarization consistent basis sets, optimized for density functional calculations, are proposed for the elements K, Ca, Ga, Ge, As, Se, Br, and Kr. The basis set composition in terms of number of primitive functions and the contraction is defined based on energetic analyses of atoms and molecules along the lines used in previous work and on the performance for molecular systems. The performance for atomization energies and dipole moments is compared to other widely used basis sets, and it is shown that the new basis sets allow a systematic reduction of basis set errors and in general perform better than existing ones.     

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.     

Contracted Gaussian-type basis functions revisited. IV. Atoms Rb to Xe

We report minimal-type contracted Gaussian-type function (GTF) sets, #n=(n3333/n33/n3) with n=5 and 6, #7= (74333/743/74), and #8= (84333/843/75), for the fourth-row atoms from Rb to Xe. Test calculations are performed on the Ag₂ molecule. Spectroscopic constants given by split valence sets derived from #5 and #6 are a little contaminated by basis set superposition error. However, we find that the fully valence split #8 set, (8433111/84111/711111), yields essentially the same results as a large GTF set, (22s15p12d), with a general contraction, when p-, d-, and f-type polarization functions are augmented. The present #7 and #8 CGTF sets are recommended for ab initio molecular calculations including fourth-row atoms. Received: 15 January 2002 / Accepted: 16 April 2002 / Published online: 24 June 2002