Basis Set Of Gaussian Functions Research Articles

Efficient Constrained Density Functional Theory Implementation for Simulation of Condensed Phase Electron Transfer Reactions.

Constrained density functional theory (CDFT) is a versatile tool for probing the kinetics of electron transfer (ET) reactions. In this work, we present a well-scaling parallel CDFT implementation relying on a mixed basis set of Gaussian functions and plane waves, which has been specifically tailored to investigate condensed phase ET reactions using an explicit, quantum chemical representation of the solvent. The accuracy of our implementation is validated against previous theoretical results for predicting electronic couplings and charge transfer energies. Subsequently, we demonstrate the efficiency of our method by studying the intramolecular ET reaction of an organic mixed-valence compound in water using a CDFT based molecular dynamics simulation.

Phonon and electronic properties of the LiCaAlF6 crystal: Experiment and ab initio calculations

We have studied the IR polarized reflection spectra of LiCaAlF6 crystal in the range of 50–2000 cm–1 and have obtained parameters of dipole phonons. In order to calculate the electronic and vibrational properties of the crystal, we have applied the density functional method with the basis sets of Gaussian functions and plane waves. We have shown that the structure of electronic bands has a direct energy gap. The projected densities of electronic states of atoms, the Born effective charges, and the Mulliken populations have been found to be consistent with the ionic–covalent character of cation–fluorine interatomic bonds. The dielectric properties in high and low-frequency limits have been calculated. We have examined the longitudinal–transverse splitting of dipole modes and have revealed a phonon with an inverted splitting. The theoretical IR reflection and Raman spectra have been found to agree well with experiment. Based on the analysis of the dispersion of phonons in the Brillouin zone, we have revealed an effect of the “quasi-doubling” of the crystal cell along the z axis due to the competing interactions of atoms with nearest and next neighbors. We have found that phonons with frequencies higher than 500 cm–1 are separated by an energy gap and have predominantly stretching character of vibrations.

Reduction of molecular oxygen on the surface of transition metal complex oxide

Ab initio quantum‐chemical calculations have been carried out for the electronic structures of molecular clusters and adsorption complexes to model physical and chemical adsorption of molecular oxygen on the surface of nickel‐cobalt and iron‐cobalt mixed oxides (spinels). The quantum‐chemical calculations were done using the Hartree‐Fock‐Roothan self‐consistent field MO LCAO formalism in the 6–31 basis set of Gaussian functions. It was shown that the value of adsorption energy of hydrogen peroxide influences the mechanism of oxygen reduction: at lower adsorption energies oxygen is reduced by the two‐electron mechanism, which is followed by desorption of the peroxide molecule formed. At higher adsorption energies the reduction of oxygen occurs via the four‐electron mechanism up to water formation. An explanation was proposed that the catalytic reaction of oxygen reduction proceeds on average via a 3.7‐electron mechanism, which is confirmed experimentally.

Lattice dynamics of α-TeO2 in the DFT-LCAO-B3LYP approximation

Ab initio DFT analysis of phonon frequencies at the center of the Brillouin zone, dispersion of phonons, phonon state density, effective Born charges, and IR reflection and Raman spectra of α-TeO2 is performed in the basis set of Gaussian functions using the hybrid B3LYP pseudopotential. Inverted phonons were discovered in the TO–LO splitting of polar modes. The possibility of assigning the frequencies to vibrations of the TeO2 molecule is discussed. The anisotropy of effective Born charges is explained to be a result of the ion-covalent character of the Te–O bond.

Recovering four-component solutions by the inverse transformation of the infinite-order two-component wave functions

The two-component Hamiltonian of the infinite-order two-component (IOTC) theory is obtained by a unitary block-diagonalizing transformation of the Dirac-Hamiltonian. Once the IOTC spin orbitals are calculated, they can be back transformed into four-component solutions. The transformed four component solutions are then used to evaluate different moments of the electron density distribution. This formally exact method may, however, suffer from certain approximations involved in its numerical implementation. As shown by the present study, with sufficiently large basis set of Gaussian functions, the Dirac values of these moments are fully recovered in spite of using the approximate identity resolution into eigenvectors of the p(2) operator.

Comparison of Theoretical Methods and Basis Sets for ab initio and DFT Calculations of the Structure and Frequencies of Normal Vibrations of Polyatomic Molecules

The dependence of the quality of calculation of the geometric parameters and frequencies of normal vibrations on the choice of the theoretical method and the basis set of Gaussian functions has been investigated within the framework of four approximations (DFT/B3LYP, HF, MP2, MP3), using benzene and s-triazine molecules as an example. It has been shown that the molecular parameters calculated using the basis set without polarization functions within the framework of any of the above theoretical methods agree poorly with the experimental data. It has been concluded that the use of the basis set 6-31G(d) within the framework of these methods with allowance for the electron correlation for calculating the geometric parameters and frequencies of normal vibrations of polyatomic cyclic compounds is most optimum in terms of the relation between the expenditure of time and the quality of the calculation. The coefficients of linear scaling of frequencies have been obtained by the DFT/B3LYP method for 22 basis sets that were tested on porphin, pyrrole, indene, and pyridine molecules. Atypically large errors in determining the frequencies of some benzene and s-triazine vibrations have been obtained in a number of quantum-mechanical calculations with large basis sets. The changes in the force field for these cases have been investigated with the example of the benzene molecule.

Determination of the 23Na nuclear quadrupole moment from molecular data for NaF and NaCl

High-level correlated calculations of the electric field gradient at Na in NaF and NaCl have been carried out with large basis sets of Gaussian functions. The singles and doubles coupled-cluster results corrected noniteratively for the effects of three-body clusters have been combined with microwave spectroscopic data to yield a new ‘molecular’ value of the nuclear quadrupole moment of 23Na, Q( 23Na) = 104 mb, whose uncertainty is expected to be not worse than about 1%. The present ‘molecular’ result for Q( 23Na) lies between the two currently most reliable values obtained from atomic spectra (107.1(2.1) mb) and muonic experiments (100.6(2.0) mb).

Relativistic all-electron ab initio calculations for the ground and excited states of the mercury atom

We present the results of relativistic all-electron ab initio calculations on the mercury atom, using the spin-free no-pair Hamiltonian in a Gaussian basis set expansion. Excitation energies, electron affinity and ionization potential were calculated using a multi-reference configuration interaction technique. The results are in good agreement with experimental data. A new basis set of Gaussian functions for the mercury atom is proposed.

A distributed Gaussian approach to the vibrational dynamics of Ar–benzene

A method for calculating the vibrational eigenstates of van der Waals clusters is presented and applied to argon–benzene. The method employs the linear variational principle with a nonorthogonal basis set of Gaussian functions in both the stretching and bending coordinates. These localized functions allow greater flexibility than the standard spherical harmonics or Wigner D functions and should be more efficient when the motion is confined to specific regions of the potential energy surface. Calculations are performed on several potential surfaces including two recent fits to a previously published ab initio calculation. Accurate results with rapid convergence are obtained here for the states of zero total angular momentum (J=0). The results agree with calculations recently performed on the same potential surfaces by a different method [J. Chem. Phys. 98, 5327 (1993)] and suggest a reassignment of the experimentally observed bands. An extension of the basis set to nonzero J is presented in the Appendix.

Quasirelativistic studies of molecular electric properties: Dipole moments of the group IVa oxides and sulfides

Dipole moments of SiO, GeO, SnO, PbO, and of the corresponding sulfides are computed by using a variety of high-level correlated methods and polarized basis sets of Gaussian functions. The contribution of relativistic effects has been accounted for by the first-order quasirelativistic approach based on mass-velocity and Darwin terms. The results for sulfides are in good agreement with experiment while for oxides seem to show a progressive deterioration with the increase of the heavy atom nuclear charge. The discrepancies between the calculated and experimental dipole moments for oxides have been carefully analyzed for the PbO molecule in terms of the basis set choice and reliability of the calculated electron correlation and relativistic corrections. The pattern of relativistic corrections computed in the present study is compared with that which follows from recent quasirelativistic and fully relativistic calculations of Dyall. Some complementary calculations of the dipole moment of PbSe and PbTe seem to indicate that both the polarized basis sets and computational methods used in this study should not fail to predict correct values of the dipole moment of PbO and other oxides of the group IVa atoms. The rather unexpected discrepancies have no plausible explanation within the range of methods employed in our study and offer a challenge for more advanced, fully relativistic molecular calculations at the correlated level of approximation.

Magnetic susceptibility of some derivatives of cellulose and their mixtures: Theory and experiment

AbstractThe calculations of the magnetic susceptibility (χ) of the selected derivatives of cellulose have been performed using the localized molecular orbitals with the basis set of Gaussian functions. The advantages of the variational procedure in the framework of the approximation of the additivity of the localized molecular fragments for the evaluation of the magnetic susceptibility and nuclear magnetic shielding (σ) and the comparison with the NMR of high‐resolution data have been discussed. Theoretical values for χ of the 50 sizable organic molecules have been presented. © 1992 John Wiley & Sons, Inc.

Matrix Dirac—Fock—Breit SCF calculations on heavy atoms using geometric basis sets of Gaussian functions

Matrix Dirac—Fock—Breit self-consistent field calculations have been performed on heavy atoms up to Rn using large geometric basis sets Gaussian-type functions. Results of the calculations on Yb, Hg, Pb and Rn are presented. For Hg, a number of Dirac—Fock—Breit calculations were performed in which Gaussian basis sets were systematically enlarged to demonstrate the effects of the basis-set size on the total Dirac—Fock and the Breit interaction energies.

Ground state electric properties of NaH

Several electric properties of the X 1Σ + electric ground state of NaH have been calculated by using high-level correlated methods and a large polarized basis set of Gaussian functions. The vibrational corrections to the dipole (μ) and quadrupole (θ) moments, to the electric field gradients at Na ( q(Na)) and H ( q(H)) and to the electric dipole (α) and quadrupole ( C) polarizabilities have been computed by using a highly accurate potential energy curve obtained from multireference CI calculations. At the experimental equilibrium bond distance R e = 3.56667 au the following results have been obtained: μ = 2.569 au, θ (c.m.) = −6.32 au, q(Na) = −0.23122 au, q(H) = 0.03595 au, α xx = 37.7 au, α zz = 50.8 au, C xx,xx = 199 au, C zz,zz = 472 au, C calculated values of q(Na) are used to predict the nuclear quadrupole coupling constants for some rovibrational levels of 23Na 1H.

Coupled Hartree-Fock calculations of the electric dipole polarizability and first hyperpolarizability of some “inorganic benzenes”

Extended basis sets of gaussian functions were used to calculate near Hartree-Fock estimates of the electric dipole polarizabilities, α, and first hyperpolarizabilities, β, of the “inorganic benzenes” B 3N 3H 6, B 3O 3H 3, B 3P 3H 3 and Al 3N 3H 6. Assuming that electron delocalization is responsible for the enhanced polarizabilities of aromatic systems, an aromaticity scale can be set up according to the trend of theoretical polarizabilities obtained in this work, i.e. α (B 3O 3H 3) < α (B 3N 3H 6 ) < α (C 6H 6 ), which is consistent with previous calculations of the degree of delocalization in these compounds.

Coupled Hartree-Fock calculations of magnetic properties of the benzene molecule: estimate of the hartree-fock limit for magnetic susceptibilities and

Five basis sets of gaussian functions have been developed to calculate magnetic properties of the benzene molecule within the framework of a coupled Hartree-Fock (CHF) approach exploiting the entire D 6h symmetry. Separate contributions provided by k, σ and π electrons have been evaluated in order to analyze the Pauling-London ring-current model. Our results are at variance with this classical model, as the contribution of k and σ electrons to the enhanced out-of-plane magnetic susceptibility is roughly 50% of the total value. In addition, k electrons provide a deshielding of proton comparable with that of π electrons. The HF limits for electric dipole polarisability, magnetic susceptibility and magnetic shielding of hydrogen and carbon nuclei have been estimated.

The dipole moment of AuH

A finite-field perturbation approach is used to study the relativistic and relativistic-correlation contributions to electric properties of AuH. The relativistic terms in the molecular Hamiltonian are approximated by the so-called Cowan–Griffin perturbation operator whose first-order contributions are evaluated in a large basis set of Gaussian functions. The electron correlation contribution is accounted for by using the many body perturbation theory methods. Both the relativistic and electron correlation effects as well as the mixed relativistic-correlation contributions are shown to be important in accurate predictions of the dipole moment of AuH. According to the present study the dipole moment of the 1Σ+ ground electronic state of AuH calculated at the experimental equilibrium bond distance of 2.880 bohr is found to be in the range between 0.6–0.7 a.u. The quadrupole moment of AuH is shown to have positive sign in the relativistic-correlated treatment while its negative value is predicted in nonrelativistic calculations. The parallel component of the dipole polarizability tensor is found to be equal to about 44. a.u. It is also shown that the electric property values of AuH are strongly affected by the electron correlation effects involving the next-to-valence shell of the Au atom. The valence approximation gives quite unrealistic results for both the electron correlation and relativistic contributions to electric properties of AuH.

Electronic Structure and Properties of the O2+2, SO2+ and S2+2 Diatomic Dications

AbstractMultiply charged ions show novel energetic features which can potentially have useful photophysical properties. In order to investigate these interesting type systems, energy interaction curves for the ground and excited electronic states of O2+2, SO2+, and S2+2 have been generated by the ab initio complete active space multiconfiguration self‐consistent field (CAS‐MCSCF) method. The calculations were carried out in a triple‐zeta sp plus double‐zeta d Gaussian function basis set using compact effective potentials to replace the core electrons. In order to gauge the accuracy of the results, analogous calculations were carried out on the valence isoelectronic N2 and NO+ systems for which experimental information is available for comparison of geometric and spectroscopic properties. Diverse high energy spectroscopy experiments on O2+2 are interpreted and reconciled using the calculated ground and excited state energy interaction curves. Special attention is paid to the 3Σ+u state, whose location and character have been particularly puzzling. Almost all the dication molecular states studied show the characteristic avoided crossing of diabatic states which gives a trapped equilibrium structure and a barrier to dissociation. These features make the dication kinetically stable, but thermodynamically unstable with an exothermic dissociation energy. The spectroscopy experiments on O2+2 show that these states are experimentally attainable.

A b i n i t i o potentials and pressure second virial coefficients for CH4–H2O and CH4–H2S

A b initio Hartree–Fock (HF) and second-order many-body perturbation theory (E2) were used to generate data for pair potentials of the mixtures CH4–H2S and CH4–H2O. The points were fit with site–site functions consisting of terms for interactions of the following types: exponential repulsion and R−6 and electrostatic attraction. The basis sets of Gaussian functions were developed by systematically adding polarization functions to maximize the zeroth-order dipole polarizability; the counterpoise method was used to correct basis set superposition error. The best well depths calculated for CH4–H2S and CH4–H2O were −0.0227 and −0.0215 eV, respectively (with no experimental results available for comparison). The potentials were evaluated by examining errors in the dipole polarizabilities and pressure second virial coefficients.

Kinetically balanced geometric Gaussian basis sets for relativistic atoms

We present Dirac–Hartree–Fock (DHF) atomic structure results for many-electron atoms (Z=2–86) using kinetically balanced geometric basis sets of Gaussian functions. There is no ‘‘variational collapse’’ or bound failure if we impose the condition of kinetic balance between the large and the small component spinors along with proper boundary conditions for bound state orbitals. Furthermore, with a finite-size nucleus model, the DHF total energy for atoms converges more rapidly to the numerical Dirac–Fock (DF) limit with a smaller number of basis functions than those calculations where a point nucleus is assumed. By systematically extending the geometric basis sets, we have obtained the DHF total energies for all atoms(up to Z=86) within a few millihartrees of the numerical (DF) limit, with smooth convergence from above.

Semi-local pseudopotential calculations for the adiabatic potentials of alkali-neon systems

Pseudopotential calculations have been performed to obtain the adiabatic potentials fore the ground state and for several excited states of alkali-neon systems. Both the alkali ion-valence electron and Ne-valence electron interactions are represented by semi-local l-dependent pseudopotentials. Standard variational calculations were made in a basis set of Gaussian functions. The accuracy of the calculated potentials is assessed by comparison with the available experimental data and with results of other calculations. Overall agreement has been obtained. This indicates that a significant improvement in calculations of the adiabatic potentials of alkali-rare gas atoms can be achieved by applying an l-dependent pseudopotential technique.