Basis Sets Of Increasing Size Research Articles

An evaluation of correlation-consistent basis sets in calculating the structure and energetics of (H3Si)2O, H3SiOH, and H3SiO−

We studied the structure of disiloxane (H3Si–O–SiH3), silanol (H3Si–OH), and the silanol anion (H3Si–O−) with ab initio molecular orbital theory and the correlation consistent polarized basis sets of Dunning and co-workers. We present results for the correlation consistent polarized valence double zeta (cc-pVDZ), triple zeta (cc-pVTZ), and quadruple zeta [cc-pVQZ(-g)] basis sets. Optimized geometries and energies are given at both the restricted Hartree–Fock (RHF) level and with the inclusion of electron correlation by second order Mo/ller–Plesset perturbation theory (MP2). The correlation consistent basis sets provide a systematic expansion of the orbital basis set, with each set of additional functions adding a similar contribution to the correlation energy. We find that the calculated molecular properties show exponential convergence with increasing basis set size. These calculations answer long-standing questions regarding the structure and barrier to linearization of disiloxane. Results at the highest level of theory [MP2/cc-pVQZ(-g)] for disiloxane gave a Si–O–Si bond angle of 147.0°, a Si–O bond length of 1.641 Å, and a barrier to linearization of 0.4 kcal/mol. All of these values are in excellent agreement with experimental results. Similar calculations for silanol gave a Si–O bond length of 1.655 Å, an O–H bond of 0.955 Å, and a Si–O–H angle of 117.9°. The MP2/cc-pVQZ(-g) deprotonation energy (ΔE0) for silanol, calculated as the energy difference between silanol and its anion, is −366.6 kcal/mol. The effects of electron correlation at the MP4 level are studied in all three molecules using the cc-pVDZ and cc-pVTZ basis sets.

Quantum dynamics simulation with approximate eigenstates

We present a new semiclassical formalism for nonadiabatic dynamics of a quantum subsystem interacting with an explicit bath. The method is based on a stationary phase approach to the bath and a variational principle for the quantum transition amplitudes, for quantum systems represented by approximate wave functions. A new expression for the force exerted on a classical bath by a quantum subsystem is derived which, in the adiabatic limit, reduces to the gradient of the expectation value of the energy. Our new methods for adiabatic and nonadiabatic dynamics are applied to a test problem of vibrational relaxation. For adiabatic dynamics, we find that our new algorithm produces results which converge faster, with increasing basis set size, than calculations performed with the Hellmann–Feynman force; for a limited basis set, our new algorithm gives results that are in better agreement with exact results. For nonadiabatic dynamics, we also find that, in comparison to an earlier algorithm, our new algorithm produces results which converge more rapidly with increasing basis set size. In addition, we find that our new algorithm is more robust with respect to the size of the time step than the earlier algorithm, a result of the implementation of a nuclear coordinate dependent basis.

Dimethylcarbene: A Singlet Ground State?

Ab initio molecular electronic structure theory has been used to determine the energy separation between the lowest {sup 3}B{sub 1} and {sup 1}A states of dimethylcarbene. The geometries of both states have been optimized at the self-consistent Field(SCF) and the single and double excitation configurationinteraction (CISD) levels of theory using various basis sets. Single point energies at the coupled cluster with single and double excitations (CCSD) and the CCSD with perturbative triple excitations [CCSD(T)] levels of theory were determined at the CISD equilibrium geometries with the same basis set. Harmonic vibrational frequencies and infrared (IR) intensities were determined for both states at the SCF level of theory using all three basis sets and at the CISD level of theory - using the DZP and TZ2P basis sets. The energy separation between the lowest triplet state ({sup 3}B{sub 1}) and the lowest singlet state ({sup 1}A) for dimethylcarbene decreases with increasing basis set size and electron correlation. At the highest level of theory employed in this research, TZ2P+fCCSD(T), the singlet state is predicted to be lower in energy than the triplet state by 0.8 kcalmol{sup -1}. This energy separation becomes 1.4 kcal mol{sup -1} with the inclusion of zero-point vibrational energy(ZPVE)more » corrections. 35 refs., 2 figs., 4 tabs.« less

Large Basis Set Calculations on Model Zerovalent Palladium Systems

Wave function based ab initio and nonlocal density functional calculations employing large basis sets have been performed on the model systems PdCO and PdPH3 in order to investigate the influence of the basis set and electron correlation on properties of the Pd-C and Pd-P metal-ligand bonds. Three relativistic effective core potentials (RECPs) on palladium were combined with various valence basis sets and ligand basis sets. Electron correlation was included using Moller-Plesset methods MPn (n = 2-4), configuration interaction including single and double excitations (CISD), quadratic configuration interaction (QCISD(T)), and coupled-cluster methods (CCSD and CCSD(T)). Full geometry optimizations were performed at all of these levels, and the results were compared to local and nonlocal density functional calculations using the same basis sets. Geometries of reasonable accuracy were obtained using a small-core pseudopotential with double ζ basis sets and polarization functions on the ligands with either the MP2 level of theory or nonlocal density functional theory. The reaction energy for the process Pd-PH3 + CO → PH3 + Pd-CO was also investigated and found to be less consistent than the geometries; levels of theory lower than CCSD(T) or QCISD(T) gave results which deviated significantly (>7 kJ/mol) from the values calculated at these levels. Convergence of the reaction energy with increasing basis set size required large basis sets with diffuse functions and polarization functions on the metal and ligands. © 1995 American Chemical Society.

Benchmark calculations with correlated molecular wave functions. VII. Binding energy and structure of the HF dimer

The hydrogen bond energy and geometry of the HF dimer have been investigated using the series of correlation consistent basis sets from aug-cc-pVDZ to aug-cc-pVQZ and several theoretical methods including Mo/ller–Plesset perturbation and coupled cluster theories. Estimates of the complete basis set (CBS) limit have been derived for the binding energy of (HF)2 at each level of theory by utilizing the regular convergence characteristics of the correlation consistent basis sets. CBS limit hydrogen bond energies of 3.72, 4.53, 4.55, and 4.60 kcal/mol are estimated at the SCF, MP2, MP4, and CCSD(T) levels of theory, respectively. CBS limits for the intermolecular F–F distance are estimated to be 2.82, 2.74, 2.73, and 2.73 Å, respectively, for the same correlation methods. The effects of basis set superposition error (BSSE) on both the binding energies and structures have also been investigated for each basis set using the standard function counterpoise (CP) method. While BSSE has a negligible effect on the intramolecular geometries, the CP-corrected F–F distance and binding energy differ significantly from the uncorrected values for the aug-cc-pVDZ basis set; these differences decrease regularly with increasing basis set size, yielding the same limits in the CBS limit. Best estimates for the equilibrium properties of the HF dimer from CCSD(T) calculations are De=4.60 kcal/mol, RFF=2.73 Å, r1=0.922 Å, r2=0.920 Å, Θ1=7°, and Θ2=111°.

Basis-set effects on computed acid-base interaction energies using the Dunning correlation-consistent polarized split-valence basis sets

Ab initio calculations have been performed at correlated levels of theory to investigate the convergence of the binding energies of hydrogen-bonded neutral, positive ion and negative ion complexes with systematic expansion of the basis set. For this study, the Dunning correlation-consistent polarized split-valence basis sets augmented with diffuse functions only on nonhydrogen atoms (aug'-cc-pVXZ, where X = D for double-split, T for triplesplit, and Q for quadruple-split) have been used. Computed hydrogen bond energies of all complexes converge with increasing basis set size, with satisfactory convergence occurring at aug'-cc-pVTZ. Binding energies are not sensitive to the presence of diffuse f functions in the aug'-cc-pVTZ basis set, and these f functions may be omitted. The presence or absence of diffuse d functions has little effect on the computed binding energies of neutral and positive ion complexes. However, these functions are important for describing the binding energies of the negative ion complexes. In contrast, quantitatively accurate proton affinities for corresponding neutral and anionic monomeric bases require the presence of both diffuse f and diffuse d functions in the aug'-cc-pVTZ basis set. For neutral and positive ion hydrogen-bonded complexes, MP4/aug'-cc-pVTZ binding energies are within 0.1 kcal mol −1 of CCSD+T(CCSD) binding energies, but may be as much as 1 kcal mol −1 smaller for the negative ion complexes.

Magnetic Susceptibility Anisotropy, Molecular Quadrupole Moment, and the Sign of the Electric Dipole Moment in OCCCS: A High-Resolution Microwave Fourier Transform Study Combined with IGLO Calculations

The molecular Zeeman effects of 16O12C12C12C32S and 16O12C12C12C34S have been observed by microwave Fourier transform spectroscopy in magnetic fields up to 20 000 G. The magnetic susceptibility anisotropy of the OCCCS molecule is ξ||-ξ⊥ = −18.740(6) 10−6 erg G−2 mol−1. The molecular g⊥ values for the two isotopomers obtained from the J = 3 → J = 2 transitions are g⊥(32S) = −0.013604(14) and g⊥(34S) = −0.013370(30). These data yield the sign of the molecular electric dipole moment which has −OCCCS+ polarity. Combining g⊥ and the rotational constant B gives the molecular electric quadrupole moment referred to the molecular center of mass as Q||(16O12C12C12C32S) = −1.97(3) DÅ. For ξ||-ξ⊥ ab initio calculations were carried out by the IGLO method. Their results compare well with the experimental value, although the system seems to be unusually demanding as can be seen from the untypical slow convergence of the result with increasing basis set size. Conventional coupled Hartree-Fock calculations with moderately sized basis sets are approximately 200 units off the experimental value. Comparative calculations on tricarbonoxide show that the basis set dependency is much less pronounced in this molecule.

Unusually large effects of single excitations on the geometry of radical species and limiting spin-projection invariance of some correlated methods

For a number of radical species with heavy spin contamination, including BO, CCH, CN, CO +, NO, N 3, and BN, it is shown that single excitations have a large effect, up to several hundredths of an Å, on calculated bond distances. The effect decreases with increasing basis set size. Harmonic frequencies may be affected by as much as 200 cm −1. It is also shown that CCSD, CISD, CID, and CCD energies are effectively invariant under single spin annihilation when no major higher contaminants are present. It can be concluded that for species with heavy spin contamination, CISD is presently the method to be preferred over MP2 and even spin-projected MP2.

Near-Hartree-Fock assessment of reorganization effects in ionic states of acetylene

Calculations on acetylene 2Πu and 2Πg ions and the 1Σg neutral ground state using a series of wavefunctions with increasing basis set size converge to an estimated Hartree-Fock vertical ionization energy near 10.0 eV and an estimated Hartree-Fock vertical electron affinity near −4.2 eV. The calculations reveal that the near-Hartree-Fock σ orbitals change strongly with the state of ionization leading to σ-electron energy errors (for transferring ground state σ orbitals to the ions) of − 4.5 eV for the cation and + 3.2 eV for the anion. Each carbon atom is calculated to lose only about 0.34 e upon π-electron ionization and to gain about 0.42 e on π-electron capture. Consequently there is poor transferability of the ground state HF σ core to the ionic states so that π-electron energy changes of + 3.2 eV for the cation and − 3.8 eV for the anion are incurred. The error incurred by transferring π orbitals from the ground state to the ions with frozen σ core is −0.8 eV for the cation and − 0.35 eV for the anion. The σ- and π-orbital reorganization effects largely cancel on going to the ions producing gross reorganization energy changes of − 1.3 eV in the cation and − 0.55 eV in the anion. Comparison with C(sp2)→C+ and ethylene π-electron ionization indicate that aside from extensive σ-π cancellation reorganization effects are not transferable between these species. At least double zeta level basis sets are necessary for physically meaningful descriptions of ionic processes.

Computation of vibrational-rotational energy levels of diatomic potential curves

The radial portion of the nuclear motion wave function is obtained by expanding its eigenfunctions in a truncated harmonic oscillator basis set. The method was tested giving results as good as or better than numerical integration or Dunham analysis. In addition, the method yields explicit wave functions in a useful form. The accuracy of solutions and the rate of convergence with increasing basis set size has been investigated for several methods of determining the parameters which specify a particular basis set.