An efficient methodology to study cyclodextrin clusters: application to α-CD hydrated monomer, dimer, trimer and tetramer

The hydrated α-cyclodextrin (α-CD) clusters resulting from the following process: nα-CD + n(H₂O)₆ → α-CD_n · 6nH₂O, with n = 1, 2, 3, 4, have been investigated using semiempirical (PM3), ab initio Hartree-Fock and Density Functional Theory (BLYP functional) levels of theory. The largest structure containing 576 atoms and 5,760 contracted basis functions (6-31G(d,p) basis set) poses as a considerable hard task for quantum chemical calculations. As the number of basis function increases rapidly with the cluster size, an alternative procedure to make the calculations feasible is certainly welcome, in order to perform BLYP calculations with an adequate basis set. Through the aid of a computer program that we developed, it became of practical use the selection of atom by atom basis sets, using the common chemical sense, enabling quantum mechanical calculations to be performed for very large molecular interacting systems (inclusion complexes), at an affordable computational cost. In this article we show how an appropriate selection of basis functions, leaving the CH_n groups with a minimal basis set and the oxygen atoms (and OH groups) with a better quality basis set, lower considerably the computational cost with no significant loss in the calculated interaction energies. A regular pattern is observed for α-CD hydrated monomer, dimer, trimer and tetramer, therefore adding support to the use of this procedure when studying larger hydrogen bonded clusters where electron correlation effects are important. We show that the procedure reported here enables DFT calculations for hydrated cyclodextrin using basis set up to the 6-311++G(3df,3pd) triple zeta quality .     

Gegenbauer polynomials in a theoretical study of the vibrational structure of the Ca+–H2 system

This work presents an application of Gegenbauer polynomials in vibrational calculations. We illustrated that by example calculations of vibrational structure of the Ca⁺–H₂ exciplex, in the state correlated with 3D calcium ion state. For this case Gegenbauer polynomials are used for formation of a basis set for a bending mode. We showed that this basis set leads to a faster convergence of results than a basis set formed from Legendre polynomials. Additionally we compared vibrational structure obtained in this manner with results of discrete variable representation-distributed Gaussian basis (DVR–DGB) method.     

Anab initio potential energy surface and dynamics calculations for vibrational excitation of I2 by He

We present newab initio calculations of the interaction potential and the elastic and inelastic cross sections for He scattering by I₂. The electronic structure calculations of the interaction potential are based on an extensive one-electron basis set (triple zeta plus ad set on each I, ans function plus ap set at the I₂ bond center, and quadruple zeta plus twop sets on He), a two-configuration-SCF orbital set, and a configuration interaction calculation based on all single and double excitations out of the two-configuration reference space. The calculations are performed at 16He-I₂ distances for nine combinations of I₂ vibrational displacement and orientation. A new form of analytic representation is presented that is particularly well suited to efficient and accurate fitting ofab initio interaction potentials that include vibrational displacements. Scattering calculations are performed by the vibrational close-coupling, rotational-infinite-order-sudden approximation with a converged vibrational basis.     

Cubic force constants of the FH⋯OH2 and FH⋯O(CH3)2hydrogen-bonded complexes. An analyses of computed Ab initio SCF values

Ab intio SCF MO calculations of quadratic and cubic force constants of the FH? OH₂ and FH?O(CH₃)₂ dimers have been carried out, using a split-valence (6-31G) basis set. For the former complex, the effects of H₂O relaxation and of extension of the basis set (triple-zeta and triple-zeta plus polarization basis functions on the FH?O hydrogen bond) have been evaluated With the most extended basis set, the equilibrium geometry of the FH?OH₂ complex does not have a definite C_2v character, in contrast to previous calculations.     

The error due to neglecting the core spin–orbit splitting in valence ZORA calculations with frozen core approximation and its elimination

In valence zeroth-order regular approximation (ZORA) calculations with frozen core approximation, when the basis set optimized to the related scalar relativistic ZORA calculations is used, neglecting the core spin–orbit splitting may result in additional basis set truncation errors. It is found that the error is negligible for most elements except the 6p-block elements. When the basis set is extended by a p-type STO function put on the 6p element atoms with the ζ value proper to 5p_1/2 orbitals, the error can be reduced to be negligible. The calculated atomic properties related to valence orbitals can be improved greatly by use of this extended basis set. The frozen core approximation calculations of some molecules containing Tl, Pb and Bi with closed shells show that neglecting the core spin–orbit splitting only slightly affects the calculated bond lengths and bond energies, and the calculated molecular property can also be improved slightly by use of the extended basis sets.     

Compact basis sets for LCAO-LSD calculations. Part II: Tests for Cr2 and Ni4

The compact orbital and auxiliary basis sets for LCAO-LSD calculations introduced in Part I are tested in molecular calculations on Cr₂ and Ni₄. The present results for spectroscopic constants and valence orbital energies obtained using medium size orbital expansions with a double-zeta representation for valence orbitals are in very good agreement with those previously calculated with very extended sets. Since the computational time of the present calculations is reduced severalfold compared with the extended basis set calculations, the present basis sets allow increased efficiency of the LCAO-LSD calculations and allow the method to be extended to larger systems.     

Optimization of Gaussian basis sets for Dirac-Hartree-Fock calculations

We investigate the optimization of Gaussian basis sets for relativistic calculations within the framework of the restricted Dirac-Hartree-Fock (DHF) method for atoms. We compare results for Rn of nonrelativistic and relativistic basis set optimizations with a finite nuclear-size. Optimization of separate sets for each spin-orbit component shows that the basis set demands for the lower j component are greater than for the higher j component. In particular, the p _1/2 set requires almost as many functions as the s _1/2 set. This implies that for the development of basis sets for heavy atoms, the symmetry type for which a given number of functions is selected should be based on j, not on l, as has been the case in most molecular calculations performed to date.     

A non-empirical molecular orbital study of valence tautomers of C2H3N

The valence tautomers of C₂H₃N have been examined by non-empirical molecular orbital calculations using two split-valence shell basis sets. All geometries were fully optimized using the 4–31G basis set and these structures were then used in 6–31G basis set calculations. The order of stability of the three possible cyclic isomers is 1-azirine > cyclic carbene > 2-azirine. The profiles for conversion of vinylmethylene into cyclopropene, vinylnitrene into 1-arizine, and iminomethylene into 2-azirine have all been shown to have barriers.     

The electronic structure of small sodium clusters

Ab initio molecular orbital calculations using the STO3-21G basis set has been carried out for the cluster series Na _n ⁺ , Na _n , and Na _n ^– (wheren=2–7). The basis set is shown to be reliable compared with more extensive basis sets at the Hartree-Fock level. Thirty-one optimized structures are reported and discussed, many of which (especially for the anions) have not been considered. The STO3-21G//STO3-21G calculations suggest that for most of the species the optimum geometries are planar. In particular, the optimized structures for the anionic species should provide a starting point for more sophisticated configuration interaction calculations.     

Some theoretical aspects of vibrational fine structure accompanying core ionizations in N2 and CO

Ab initio calculations have been carried out on CO and N₂ and the relevant core hole states with different basis sets to investigate differences in geometries and force constants. From these calculations vibrational band profiles of the core level ESCA spectra for these molecules have been interpreted, obviating the need to rely on data pertaining to the equivalent core species. The agreement with experimental profiles is excellent. The O_1s level of CO which has not been subjected to detailed theoretical analysis previously, is predicted to show substantial vibrational structure in excellent agreement with recently acquired experimental data. The effect of temperature on the band profiles has also been considered. Theoretically derived core binding and relaxation energies of these systems have been investigated both as a function of basis set, and of internuclear distance. Density difference contours have been computed and give a straightforward pictorial representation of the substantial electron reorganizations accompanying core ionizations. Small basis sets with valence exponents appropriate to the equivalent core species when used in hole state calculations describe bond lengths, force constants, core binding energies and relaxation energies with an accuracy comparable to that appropriate to the corresponding extended basis set calculations.     

The mechanism of carbonyl reduction by LiBH4: An ab initio investigation

The minimum energy path and the geometry of the transition state for the first stage of the reduction by LiBH₄ of R₂CO (RH, CH₃) to alcohol have been determined by ab initio SCF calculations using a small basis set and subsequently confirmed by further calculations using a larger basis set and CI methods. Attention has been focused on the changes of electron distribution during the reaction, the nature of the bonding, and the effect of chemical substituents. The results lend support to one of the proposed reaction mechanisms. Some supplementary data concerning the role of the solvent are also discussed.     

Study on the behavior of energy convergence in ab initio crystal orbital calculations

Summary This article studies the dependence on the cutoff scheme of ab initio crystal orbital calculations with no long-range correction. We have thoroughly studied the Namur cutoff and cell-wise cutoff schemes through calculations of polyethylene and LiH chains. The Namur cutoff gives the fastest energy convergence with respect to the number of neighbors (N ₀). The energy convergence behavior with respect to N ₀ depends on the basis set. The Namur cutoff shows the fastest convergence with the STO-3G basis set, intermediate convergence with the MINI basis set, and the slowest convergence with the (7s4p/3s) basis set. The cell-wise cutoff shows exactly the reverse order of the Namur cutoff. The Namur cutoff destroys the translational symmetry. Both the Namur cutoff and cell-wise cutoff schemes introduce slight asymmetry on the two equivalent C-C bonds of polyethylene when calculating with a C₂H₄ unit cell. The asymmetry with the Namur cutoff can be made to disappear by increasing N ₀ a little. The calculations on two different unit-cell structures of trans-polyacetylene show the effect of the cutoff scheme on the total energy. Only the symmetric cutoff energies are the same. Disagreement related to the Namur cutoff disappears at N ₀ = 20, however, that related to the cell-wise and modified symmetric cutoff schemes remains at N ₀ 20. The optimized geometry and vibrational frequency are not as sensitive to the cutoff method except with the symmetric cutoff. A compilation of all results shows that the Namur cutoff is the superior cutoff scheme when calculating the insulator using the minimal basis set, especially the STO-3G basis set.     

Electrically polarized valence basis sets for the SBKJC effective core potential developed for calculations of dynamic polarizabilities and Raman intensities

Sadlej’s electric polarization method of Gaussian basis functions was applied to the double-zeta effective core potential basis sets of Stevens, Basch, Krauss, Jasien and Cundari to generate a new augmented polarized valence double-zeta set, named as pSBKJC, which is appropriate for the calculation of dynamic polarizabilities and Raman intensities. The pSBKJC basis set was developed for the atoms of families 14–17 (from C to F, Si to Cl, Ge to Br and Sn to I). In order to assess the performance of this new basis set, these properties were compared to those evaluated using Sadlej’s set, available in the EMSL online library under the name of Sadlej-pVTZ. In these tests, Hartree-Fock/pSBKJC calculations have proved to be less demanding of the computer than the Hartree-Fock/Sadlej-pVTZ ones but give results in excellent agreement with those from the Sadlej-pVTZ basis set. Since the Stevens et al. pseudopotential can represent the scalar relativistic effects, the results obtained at the Hartree-Fock/pSBKJC level show a better agreement with the results of Dirac-Hartree-Fock/Sadlej-pVTZ relativistic calculations using Dyall’s spin-free Hamiltonian. When comparing Hartree-Fock/pSBKJC data of Raman scattering activities, at the excitation wavelength of 488 nm, with those of spin-free Dirac-Hartree-Fock/Sadlej-pVTZ calculations, a very good agreement is observed, where the RMS error is 8.5 Å⁴a.m.u.^?1 and the averaged percentage error is 3.4%. In terms of computer savings in calculations of dynamic Raman intensities, a 20% reduction in the CPU time in the coupled cluster singles and doubles intensities of C₆H₆ and about 40% reduction in the time-dependent Hartree-Fock intensities for C₆F₆ molecules were attained.     

Theoretical studies of organometallic compounds. I. All electron and pseudopotential calculations of Ti(CH3)nCl4 − n (n = 0–4)

The performance of effective core potentials (ECP) and model potentials (MP) has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules Ti(CH₃)_nCl_{4 ? n} (n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G basis set from Hehre and a (53321/521/41) basis set from Huzinaga. For the ECP calculations the potentials developed by Hay and Wadt, and for the MP calculations, the model potentials developed by Sakai and Huzinaga, are employed. © 1992 by John Wiley & Sons, Inc.     

Ab initio SCF calculations on hydrogen bonded cresol isomers

Ab initio GAUSSIAN 80 calculations with two different basis sets (STO-3G and 4–31 G*) were performed on hydrogen bonded cresol isomers for comparison with experimental data from free jet fluorescence excitation spectroscopy. Form-cresol, the calculated barriers for hindered internal rotation of the OH-group and the CH₃-group are in good agreement with experiment. The calculations show the trans-linear configuration ofp-cresol·B-clusters (B = H₂O, CH₃OH) to be more stable than the all-planar configuration. This agrees with CI calculations and microwave spectroscopic investigations of the water dimer. Calculations of both the intermolecular stretch and bend frequencies ofp-cresol·B-clusters show little dependence on the all-planar or trans-linear configuration but a strong dependence on the choice of the basis set. With the minimal basis set STO-3G, the vibrational energies are generally too high. The agreement between the calculated vibrational frequencies from the 4–31 G* basis set and the experimental values is fair.     

Theoretical studies of organometallic compounds. II. All electron and pseudopotential calculations of M(CH3)nCl4 − n (M = C,Si, Ge,Sn, Pb; n = 0–4)

The performance of effective core potentials (ECP) for the main group elements of group IV has been studied by calculating the geometries and reaction energies of isodesmic reactions for the molecules M(CH₃)_nCl_{4 ? n} (M = C, Si, Ge, Sn, Pb; n = 0–4) at the Hartree–Fock level of theory. The results are compared with data from all electron calculations and experimental results as far as available. The all electron calculations were performed with a 3-21G(d) and a 6-31G(d) basis set for Si, a (43321/4321/41) basis set for Ge, and a (433321/43321/431) basis set for Sn. For the ECP calculations the potentials developed by Hay and Wadt with a configuration (n)s^a(n)p^b and the valence basis set (21/21), extended by a set of d functions, are employed. © 1992 by John Wiley & Sons, Inc.     

Complete active-space configuration interaction with optimized orbitals: Application to Li2

We performed CAS –CI calculations on Li₂ using a set of molecular orbitals (MO ) optimized with a procedure that, in the case of highly symmetric molecules, permits extraction of a small set of MO out of a large set of atomic orbitals (AO ). The dimension of the CAS –CI space was of about 12 million symmetry-adapted determinants. We determined some spectroscopic constants of Li₂ with three different atomic basis sets of increasing quality. The values obtained with the largest atomic basis set are very close to the experimental results. © 1995 John Wiley & Sons, Inc.     

Minimal basis study of inner-shell ionization potentials for molecules containing sulfur: S,S-Diphenyl-N-p-Tolylsulfonyl-Sulfilimine

Ab initio calculations with a minimal (STO -3G) basis set on a number of sulfur-containing molecules are used to show that Koopmans' theorem and minimal basis calculations may be a simple but adequate way of obtaining inner-shell ionization potentials and chemical shifts of large molecules. The x-ray photoelectron spectrum of (C₆H₅)₂SNSO₂C₆H₄CH₃ is discussed with reference to an ab initio SCF minimal basis calculation on the model molecule H₂SNSO₂H.     

Computational convergence of electronic structure calculations of transition metal ligand complexes

Calculations of binding energies and optimum geometries of compounds of the series M(H₂O)⁺ with M = Sc to Zn have been carried out and compared with gas-phase experimental data and with the Rosi and Bauschlicher MCPF calculations. Hartree–Fock calculations and correlated calculations at MP2, MP4, and QCISD(T) levels were used to test the dependence of the results upon the level of correlation. A test of basis set dependence was also carried out, using parallel calculations on four basis sets ranging in size from a small DZ set to a TZ contraction. Correlation levels above MP2 and elaboration of the metal d-function basis set to (4d/3d) size or greater were both necessary for convergence with the most uniformly reliable results obtained from QCISD(T) calculations on a basis set with a (6d/4d) contraction for the d-function space. However, MP2 or higher-level calculations with a contracted four or five d function set [(5d/3d) or (4d/3d)] are capable of yielding results on binding energies and geometries close to the current gas-phase experimental uncertainty on electrostatically bound transition metal complexes. © 1993 John Wiley & Sons, Inc.