F-type Polarization Functions Research Articles

The structures of m-benzyne and tetrafluoro-m-benzyne

The structures of m-benzyne and its fluorinated derivative, tetrafluoro-m-benzyne, were investigated using coupled cluster methods including triple excitations [CCSD(T) and CCSDT], different reference wave functions (spin-restricted Hartree-Fock, spin-unrestricted Hartree-Fock, and Brueckner), and different basis sets [6-31G(d,p) and correlation-consistent valence triple-zeta (cc-pVTZ)]. The inclusion of triple excitations in conjunction with d- and f-type polarization functions is paramount to correctly describe through-bond delocalization of the monocyclic form. At the highest level of theory, the C1-C3 distance of the minimum energy form of m-benzyne is 2.0 A and the profile of the potential energy surface along the C1-C3 distance is that of an asymmetric, single well, in agreement with previous density-functional theory and coupled cluster studies. In addition, the calculated CCSD(T) fundamental frequencies are in excellent agreement with the measured infrared frequencies, thus confirming the monocyclic form of m-benzyne. For tetrafluoro-m-benzyne, however, the increased eclipsing strain between the ring-external C-X bonds stabilizes the bicyclo[3.1.0]hexatriene form: the C1-C3 distance is calculated at the CCSD(T)/cc-pVTZ level to be approximately 1.75 A, which is in the range of elongated CC bonds. Computed harmonic vibrational frequencies compare reasonably well with the experimental neon-matrix difference spectrum and provide further evidence for the existence of a bicyclic form.

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.

Relative energies of the C2H2S2 isomers 1,2-dithiete and dithioglyoxal: Peculiar basis set dependencies of density functional theory and ab initio methods

Ab initio calculations at the levels of Hartree–Fock (HF), second order Møller–Plesset perturbation theory (MP2), coupled-cluster theory with singles, doubles, and estimated triple excitations [CCSD(T)], and density functional theory (DFT) using the functionals B3LYP and B3PW91 of the relative energies of the C2H2S2 isomers 1,2-dithiete (2a), and dithioglyoxal (2b) show a peculiar dependence of the results on the f-type polarization functions. The ab initio calculations with 6-31G(nd) basis sets with n=1–3 incorrectly predict that 2a is higher in energy than 2b. The relative energies at the MP2 and CCSD(T) levels change by more than 6 kcal/mol in favor of 2a if the basis set is augmented by one set of f functions. The DFT calculations also give a higher stability of 2a relative to 2b if f functions are included in the basis sets, but the change in the relative energy is only ∼2 kcal/mol. The large change in the relative energies which are calculated at MP2 and CCSD(T) are mainly due to the functions at sulfur, while the effect of the f functions in the DFT calculations is mainly due to the f functions at carbon.

Searches on the potential energy hypersurfaces of GeCH2, GeSiH2, and Ge2H2

Optimum geometries are computed at both the SCF level of theory and the level of second-order perturbation theory for several isomers on the potential energy hypersurfaces of GeCH2, GeSiH2, and Ge2H2, including linear structures, methylene-carbenelike structures, dibridged structures, and monobridged structures. In addition, harmonic vibrational frequencies are computed to characterize these structures as local minima or transition states. All computations employ basis sets of triple-zeta quality on valence electrons with d and f polarization functions on the heavy atoms and p functions on hydrogen. This investigation is the first systematic study to include all of these germanium systems and to employ f-type polarization functions in such a study. Previous investigations of ours indicate that large basis sets such as those employed in this study can, in part, compensate for the lack of a more advanced treatment of electron correlation. While a dibridged global minimum is confirmed for both Ge2H2 and GeSiH2 systems, the C2v isomer, methylenegermene, is found to be the most stable structure for GeCH2. © 1998 John Wiley & Sons, Inc. Int J Quant Chem 70: 925–932, 1998

Basis set and correlation effects on geometry of octahedral second-row transition-metal complexes

An extensive investigation of the basis-set effect on the predicted geometry of the redox pair [Ru(NH3)6]2+/3+ is presented. Basis sets where the core electrons have been replaced with a relativistic core potential as well as all-electron basis sets were tested. Best agreement with observations was obtained with the all-electron basis set MIDI augmented with a set of f-type polarization functions on the metal center. Other properties such as the vibration spectrum, the relative energy of the high-spin and low-spin states, and geometry changes upon oxidation/reduction of the central metal are discussed. The importance of electron correlation on the predicted geometry was estimated at the MP2, MP3, MP4(SDQ), CCSD, and CCSD(T) levels of theory. The MIDI(f) basis set is then used for other octahedral second-row transition-metal complexes and some other related complexes. The electronic spectrum of [Ru(NH3)6]2+ is also calculated using two different CI computational schemes. Surprisingly good agreement between the predicted electronic spectrum and the observed spectrum are obtained using one of the CI computational schemes. © 1996 John Wiley & Sons, Inc.

Electronic Structure and Properties of Trihalogen Cations X(3)(+) and XY(2)(+) (X, Y = F, Cl, Br, I).

Electronic structures, charge distributions, geometries, valence force constants, and vibrational frequencies of the homoatomic clusters F(3)(+), Cl(3)(+), Br(3)(+), and I(3)(+) and of the heteroatomic clusters ClF(2)(+), BrF(2)(+), IF(2)(+), BrCl(2)(+), ICl(2)(+), and IBr(2)(+) were determined. The self-consistent field approach extended by MP2-correlation energy or density-functional corrections was applied using various basis sets. It was found that d- and f-type polarization functions play a crucial role as in some other halogen compounds. The MP2 approach yields the most satisfactory results. The effect of the crystalline environment surrounding the Cl(3)(+), Br(3)(+), and I(3)(+) species is successfully simulated by a Madelung potential. Frequencies calculated in the crystal field are in reasonable agreement with the more reliable ones among the experimental results. Coupling force constants were determined. They are not consistent with some empirical rules. Bonding and charge distributions of the formally mixed-valence systems X(+)Y(2)(0) are discussed. X(+) behaves like a divalent chalcogen with high electronegativity. Each of the X(+)-Y bonds in XY(2)(+) is very similar to the bond in X-Y. We predict the experimentally unknown F(3)(+) to be stable in vacuum but not in the solid state. Structures and frequencies of XY(2)(+) species, which are as yet unknown, are also predicted.

Diborane, Dialane, and Digallane: Accurate geometries and vibrational frequencies

Optimum equilibrium geometries, harmonic vibrational frequencies, and infrared intensities within the double harmonic approximation are computed for diborane, B{sub 2}H{sub 6}, dialane, Al{sub 2}H{sub 6}, and digallane, Ga{sub 2}H{sub 6}, at both the SCF level of theory and the second-order perturbation theory [E(2)] using three large basis sets: 6-311G(d,p), 6-311G(2d,2p), and 6-311G(2df,2p). In particular, the results obtained with the latter basis set make this present work the first study to include f-type polarization functions in a systematic investigation of the molecular structure and properties of all three molecules in the series. Because of the good agreement of the present theoretical results with experimental data and with previous theoretical studies which employed a higher treatment of electron correlation, this study serves to show that large basis sets can in part compensate for the lack of a more advanced treatment of electron correlation in these electron-deficient systems. In addition, this study establishes the level of basis set needed for future work on these systems including a thorough description of the total electronic density at a correlated level.

A set of d-polarization functions for pseudo-potential basis sets of the main group elements AlBi and f-type polarization functions for Zn, Cd, Hg

A set of five-component d-type polarization functions has been optimized for the main group elements AlBi at the energetically lowest lying s 2p n electronic states for use with the effective core potentials of Hay and Wadt at the CISD level of theory. Also a set of f-type polarization functions is suggested for the elements Zn, Cd and Hg.

A set of f-polarization functions for pseudo-potential basis sets of the transition metals ScCu, YAg and LaAu

A Set of seven-component f-type polarization functions has been optimized for use with the pseudo-potentials of Hay and Wadt at the CISD level of theory for the transition metals ScCu, YAg, LaAu in the energetically lowest-lying s 1 d n electronic state.

Electronic states and potential energy surfaces of silver dihydride: comparison with gold dihydride

Complete active space MCSCF (CASSCF) followed by second-order configuration interaction (SOCI) and multireference single plus double configuration interaction (MRSDCI) which include excitations from the d shells are carried out on the two low-lying states of AgH{sub 2} ({sup 2}B{sub 2} and {sup 2}A{sub 1}). The bending potential energy curves of the two states with bond lengths optimized for all angles are presented. The {sup 2}B{sub 2} surface contains a double minimum with acute and obtuse H-Ag-H angles. The {sup 2}A{sub 1} surface contains a large barrier for the insertion of an Ag({sup 2}S) atom into H{sub 2} to form the linear {sup 2}{Sigma}{sup +} state of AgH{sub 2}. The excited Ag({sup 2}P) atom spontaneously inserts into H{sub 2} to form an acute-angled weak complex of Ag with H{sub 2} and another more stable {sup 2}B{sub 2} state with obtuse bending angle. The d shell correlation lowers the {sup 2}B{sub 2} obtuse-angled structure significantly. The potential energy surfaces and electronic states of AgH{sub 2} are compared with those of AuH{sub 2}. Relativistic mass-velocity effects are significant for AuH{sub 2} in comparison to AgH{sub 2}, while d correlation effects are more significant for AgH{sub 2} in comparison to AuH{sub 2}. The Mullikenmore » population analyses of the electronic states of AgH{sub 2} reveal considerable 5p participation. The bending potential energy surfaces of the {sup 2}B{sub 2} and {sup 2}A{sub 1} states of both the molecules cross, which would lead to avoided crossing of the {sup 2}E{sub {1/2}} components if the spin-orbit term is included. The effect of f-type polarization functions is also investigated by carrying out MRSDCI calculations which included the ten-component f functions in the basis sets.« less

An analysis of the electron density distribution in the free and polarized H2O molecule as calculated in the local density approximation

The Xα version of the LD approximation has been applied to H2O, resulting in a dipole moment and dipole polarizability of CI quality when augmenting the basis set with d- and f-type polarization functions. The behavior of the electron density upon placing the molecule in a small external homogeneous electric field has been investigated and depicted in the form of difference density maps.

F-Type functions in the orbital basis for calculating molecular interactions involving d electrons Cr 2 and Mo 2

Ab initio calculations on the ground electronic states of Cr 2 and Mo 2 show that f-type polarization functions in the orbital bases contribute 0.93 and 1.4 eV to the SCF energies of these molecules at their respective R e. These contributions vary rapidly with the internuclear separation and have a strong effect on the calculated R e, 0.06 A in Cr 2 and 0.08 A in MO 2. Previous studies have indicated that this effect can be expected to carry over to and may even be magnified considerably in correlated wavefunctions. The effects of f functions must be present, to a significant degree, in all systems involving d bonding. Results of previous theoretical calculations on Cr 2 and Mo 2 are analyzed in light of the present finding and the results of recent spectroscopic experiments.