Minimal Basis Set Calculations Research Articles

Sliced Basis Density Matrix Renormalization Group for Electronic Structure.

We introduce a hybrid approach to applying the density matrix renormalization group to continuous systems, combining a grid approximation along one direction with a finite Gaussian basis set for the remaining two directions. This approach is especially useful for chainlike molecules, where the grid is used in the long direction. For hydrogen chain systems, the computational time scales approximately linearly with the number of atoms, as we show with near-exact minimal basis set calculations with up to 1000 atoms. The linear scaling comes from both the localization of the basis and a compression method for the long-ranged two-electron interaction. For shorter hydrogen chains, we show results with up to triple-ζ bases.

Recoupled-Pair Bonding and 4-Electron 3-Center Bonding Units

Consideration is given to recoupled-pair bonding and the origin of electronic hypervalence for formulations of the bonding for symmetric 4-electron 3-center ((4e,3c)) bonding units with one overlapping atomic orbital per atomic center. Molecular orbital and valence bond theory for symmetric (4e,3c) bonding units is redescribed and applied to aspects of the bonding for SF(6) and CLi(6). The results of minimal basis set calculations for CLi(6) provide support for a hypothesis that two Li-C-Li (3e,3c) bonding units rather than two (4e,3c) bonding units are preferred for this molecule. Brief comments are also made on the use of [Formula: see text] and [Formula: see text] as valence bond structures for the three electron bond.

Symmetry dilemmas in oxocarbons

SCF minimal basis set calculations on oxocarbons demonstrate the occurrence of Hartree-Fock instabilities in these compounds.

Photoionization of C60 by large scale one-center density functional explicit continuum wave-function

The photoionization cross-section and asymmetry parameter profiles relative to the seven uppermost molecular orbitals of C60 are calculated by means of a density functional approach, based on the explicit continuum wave-function within a very large scale one center expansion in a radial B-spline basis set. The convergence with respect to the maximum angular momentum is analyzed. Strong giant resonances in the cross-section of individual states are found, their occurrence is rationalized on the ground of minimal basis set calculations. The asymmetry parameters are as well very structured, also at higher photon energy than the cross-section profiles. Good agreement between the present calculations and the available experimental data is found.

The correlation part of molecular binding energy of simple, covalently bonded molecules from minimal basis set ab initio calculations

Ab initio minimal basis set calculations, coupled with simple empirical formulae, allow for the estimation of the correlation contribution to the molecular binding energy for first and second row atoms in covalently bonded molecules.

Infrared and Raman spectra of 1,1-dibromodisilanes and STO-3G∗ calculations

Infrared and Raman spectra in the gas phase are reported for 1,1-Si 2H 4Br 2 and 1,1-Si 2D 4Br 2. With the help of STO-3G∗ calculations for these species and for Si 2H 5Br and Si 2D 5Br, nearly all the fundamentals of the dibromo compounds are assigned and reliable estimates made for the remainder, except the silyl torsions. Minimal basis set calculations of vibration frequency are useful if suitable scaling is applied, based on analogous compounds. Using substituent effects, harmonic local mode calculations and several impurity bands in the 1,1-dibromodisilane species, SiH stretching frequencies are predicted for tri-, tetra- and penta-bromodisilanes as well as for 1,2-dibromodisilane conformers.

Calculations of giant resonances and cross section profiles of valence ionizations of cubane by the LCAO Density Functional Stieltjes Imaging approach

Valence partial channel photoionization cross sections for each final symmetry of cubane have been evaluated at the local density level. The muffin-tin potential approximation is avoided by the use of large basis set LCAO calculations and the Stieltjes Imaging approach. The “giant resonances” which are expected from symmetry considerations have only actually been determined for outer valence ionizations, while they are not present in the inner valence. Minimal basis set calculations have been successfully used throughout the discussion in order to assess the position and the intensity of the transitions to virtual valence orbitals. Eventually, we analyze the total cross sections for each final state and their ratios, which might be compared with further experimental data that are not yet available. The previous partial final symmetry analysis allows the assignment of the features which could be experimentally observable,

Splicing I: Using mixed basis sets in ab initio calculations

AbstractThe effect of mixing (or “splicing”) extended and minimal basis sets on molecular properties such as geometries, Mulliken charges, dipoles, and internal rotation barriers was studied for several test molecules. The effect is gauged by comparison with full extended basis set calculations. It is found that splicing improves most properties relative to full minimal basis set calculations, and little accuracy is lost if the splicing is done in a judicious manner.

Dependence ofRHF properties of hydrogen and helium chains on the exchange lattice summations

An alternative configuration space scheme for ab initio polymer band structure calculations based on a Filon-type quadrature is proposed. This scheme avoids the explicit calculation and the storage of the “troublesome” Fourier transforms of the LCAO density matrix elements. Furthermore, the lattice sums (Coulomb and exchange) can be carried out up to infinity which removes the difficult problem of guessing limits to these summations. The potential of the proposed technique is illustrated by minimal basis set calculations on the infinite chains of H and He atoms.

Model calculations on Zn(II)/Cd(II) interaction with nucleic bases

The relative stability of binding sites for Zn(II) to guanine have been reported so far only on the basis of minimal basis set calculations, so that reinvestigation using a more accurate method seemed desirable

Potentials of an alternative scheme for ab initio polymer band structure calculations. Illustration on the chain of hydrogen atoms

AbstractAn alternative scheme for ab initio polymer band structure calculations based on a Filon‐type quadrature is proposed. This scheme avoids the explicit calculation and the storage of the “troublesome” Fourier transforms of the LCAO density matrix elements and is a first step towards a better control of the convergence of the different lattice sums appearing in the configuration space LCAO‐SCF‐CO method. The potential of the proposed technique is illustrated by a minimal basis set calculations on an infinite chain of H atoms.

Simple generation of an approximate internally correlated wave function from the Hartree-Fock approximation and its valence-bond decomposition.

If ${C}_{I}^{\mathrm{ex}}$ and ${C}_{I}$ are the coefficients of, respectively, the exact and single-determinant wave functions of an extended system on the valence-bond (VB) single determinant ${\ensuremath{\Phi}}_{I}$, the scaling effect ${\ensuremath{\lambda}}_{I}$=${C}_{I}^{\mathrm{ex}}$/${C}_{I}$ of the internal correlation has been empirically shown to follow approximately the law ${\ensuremath{\lambda}}_{I}$=exp(${\mathrm{kE}}_{I}$) where ${E}_{I}$=〈${\ensuremath{\Phi}}_{I}$\ensuremath{\Vert}H\ensuremath{\Vert}${\ensuremath{\Phi}}_{I}$〉 [see Lepetit, Oujia, Malrieu, and Maynau, preceding paper, Phys. Rev. A 39, 3274 (1989)]. The theoretical foundation of such a law is derived by using a mixed molecular-orbital valence-bond perturbation expansion. This law suggests a single-parameter approximate wave function, \ensuremath{\psi}= \ensuremath{\Sigma} ${C}_{I}$exp(${\mathrm{kE}}_{I}$)${\ensuremath{\Phi}}_{I}$. The calculation of an upper bound of the energy is obtained by optimizing k. The method has been tested for \ensuremath{\pi} systems of conjugated hydrocarbons treated through Pariser-Parr-Pople or Hubbard Hamiltonians, giving approximately 90% of the correlation energy, and on a few ab initio valence minimal basis-set calculations of small ${\mathrm{Li}}_{\mathrm{n}}$ clusters, with similar accuracy. The method works as well on open-shell problems and on excited states of both neutral and ionic VB character. This work rationalizes and simplifies (by a reduction to a single parameter) a similar proposal due to Stollhoff and Fulde [Z. Phys. B 26, 257 (1977); 29, 231 (1978); J. Chem. Phys. 73, 4548 (1980)].

RHF energy band shapes for metallic chains: Dependence on the summation of exchange contributions. An illustration on the linear chain of hydrogen atoms

Minimal basis set (STO-3G) calculations on the metallic infinite chain of hydrogen atoms, (-H-)x, performed within the same computational framework as currently used for more realistic model systems, are reported to illustrate the dependence of the RHF energy bands on the summation of exchange contributions. The numerical results show the gradual decay of the density of states at the Fermi level as the number of terms in the exchange lattice sums is increased and rather convincingly verify the predictions of previous formal analyses.

Basis sets and restricted Hartree-Fock instabilities in thiocarbonyls

While calculating zero-field splitting terms for the lowest triplet state of 4H-pyran4-thione, at the experimental geometry, it was found that the ground state was unstable with respect to an unrestricted Hartree–Fock perturbation. The smallest fragment of the molecule retaining this instability was found to be diatomic CS. The instability is dependent on the basis set used for the calculation. The instability and its relationship to basis set, equilibrium geometry, and the importance of polarization functions for second row elements has been explored for CS and H2CS as a function of internuclear distance. Minimal basis set calculations involving second row elements may be particularly prone to such instabilities.

Hyperconjugative interactions in halogen-substituted carbonyls: ultraviolet photoelectron spectroscopy of ω-halogenoacetophenones

The HeI and HeII photoelectron spectra of the para-substituted ω-halogenoacetophenones Y-C6H4COCH2X [Y = NO2, CN, H, OCH3, N(CH3)2; X = H, Cl, Br, I] are assigned on the basis of the composite-molecule approach, substituent effects, and intensity variations observed on changing the wavelenght of the ionizing radiation. Ab initio minimal basis set calculations using the pseudo-potential method have been used to calculate the most stable conformation of acetophenone and its ω-bromo and ω-iodo derivatives. The first band of the iodine derivatives shows peculiar energy and intensity variations on changing the para-substituent. These findings have been ascribed to an easier interaction of the iodine lone-pair orbitals with the substrate owing to their lower ionization energy values and larger size with respect to the other halogens.

Quantum chemical conformational analysis of the catalytic triad in α-chymotrypsin

Abstract We have applied a recently developed method for the conformational analysis of the Asp-102, His-57 and Ser-195 catalytic triad of α-chymotrypsin. The method is based on the semiempirical CNDO/2 parametrization and makes use of a bond orbital framework allowing a considerable reduction in computing time. The enzyme active site is modelled by the HCONHCH(CH 2 COO − )CONH 2 …HCONHCH(CH 2 Im)CONH 2 …HCONHCH(CH 2 OH)CONH 2 system containing 58 atoms and 157 valence orbitals (Im stands for imidazole). We also studied a model where the imidazole of His-57 is protonated. In this form, which can be compared to experiment, our method predicts conformations for the His-57 and Asp-102 side chains close to those obtained by X-ray diffraction studies. In the neutral form which exists under physiological conditions two stable conformations (A: x 1 = 84°, x 2 = 90° and A′: x 1 = 168°, x 2 = −81°) were located for the Ser-195 side chain. A very shallow minimum, B ( x 1 = −66°, x 2 = 0°) was also detected. Ab initio minimal basis set calculations on suitable small models indicate that, in agreement with the CNDO/2 results, conforamtions A and A′ have about the same energy. The effect of hydration was modelled by one and two attached water molecules. Conformation A which is close to the one supposed to exist at physiological pH values, is stronger stabilized by hydration than conformation A′. We compare our results to other experimental and theoretical data. Possible consequences of the conformational properties on the enzymatic mechanism are also discussed.

Quantum chemical conformational analysis of the catalytic triad in α-chymotrypsin

We have applied a recently developed method for the conformational analysis of the Asp-102, His-57 and Ser-195 catalytic triad of α-chymotrypsin. The method is based on the semiempirical CNDO/2 parametrization and makes use of a bond orbital framework allowing a considerable reduction in computing time. The enzyme active site is modelled by the HCONHCH(CH 2COO −)CONH 2 ⋯ HCONHCH(CH 2Im)CONH 2 ⋯ HCONHCH(CH 2OH)CONH 2 system containing 58 atoms and 157 valence orbitals (Im stands for imidazole). We also studied a model where the imidazole of His-57 is protonated. In this form, which can be compared to experiment, our method predicts conformations for the His-57 and Asp-102 side chains close to those obtained by X-ray diffraction studies. In the neutral form which exists under physiological conditions two stable conformations (A: χ 1 = 84°, χ 2 = 90° and A′: χ 1 = 168°, χ 2 = −81°) were located for the Ser-195 side chain. A very shallow minimum, B (χ 1 = −66°, χ 2 = 0°) was also detected. Ab initio minimal basis set calculations on suitable small models indicate that, in agreement with the CNDO/2 results, conformations A and A′ have about the same energy. The effect of hydration was modelled by one and two attached water molecules. Conformation A which is close to the one supposed to exist at physiological pH values, is stronger stabilized by hydration than conformation A′. We compare our results to other experimental and theoretical data. Possible consequences of the conformational properties on the enzymatic mechanism are also discussed.

Theoretical study of the properties of methyl radical

A detailed ab initio study of the structure and properties of methyl radical in its ground electronic state is presented. The primary focus is on the spin density distribution and its dependence on basis set, wave function model, and molecular geometry. By using a natural orbital analysis that provides an unambiguous decomposition into core and valence contributions, interesting theoretical and computational results are found that clarify the relationships among CI, UHF, and PUHF models. In particular, it appears that the better agreement with experiment for the PUHF model as compared to UHF is simply fortuitous. A large and negative core contribution found in the 13C isotropic hyperfine coupling constant explains why minimal basis set calculations always greatly overestimate this property, regardless of what wave function model is used. All the models studied give good results for anisotropic hfc and for the vibrational corrections to isotropic hfc, although not for the isotropic hfc themselves. Through comparison to the ab initio results, some conditions are revealed where semiempirical methods such as INDO should fail. The dependence of potential energy and various charge density properties on molecular geometry is also studied.

CI calculations on metallic and molecular hydrogen rings

To evaluate the importance of correlation effects in metallic and insulating polymers self-consistent field (SCF) and configuration interaction (CI) calculations were performed for equidistant (metallic) and alternant (insulating) hydrogen rings. Two main effects–increasing the number of electrons and changing the distance between the hydrogen atoms–were studied. Minimal basis set calculations were performed for 6-, 10-, 14-, 22-, and 30-membered rings, potential curves for the metallic and insulating H14 system have been computed with a double-zeta basis supplemented by polarization functions. The correlation energy of one-dimensional metallic hydrogen is estimated to be about 0.84 eV/atom compared with 0.54 eV in H2. For molecular hydrogen a van der Waals minimum was found for separation of two H2 molecules in the ring of about 5.5 a.u. The calculated value for the energy minimum suggests nonpairwise-additive contributions to the van der Waals interaction energy of seven H2 molecules. Finally, the pressure to induce a transition from the molecular to the metallic phase was calculated to be about 1.8 Mbar both on the SCF and CI level.

Comment on simulations of liquid ammonia based on quantum mechanical potential functions

Monte Carlo simulation of liquid ammonia is reported. An initial potential function of the dimer was generated from minimal basis set calculations. The potential was uniformly scaled by a factor of 1.3 and the energy of the liquid was computed.(AIP)