Murco N. Ringnalda

Pseudospectral localized Mo/ller–Plesset methods: Theory and calculation of conformational energies

We have developed an algorithm based upon pseudospectral ab initio electronic structure methods for evaluating correlation energies via the localized Mo/ller–Plesset methodology of Pulay and Saebo. Even for small molecules (∼20 atoms) CPU times are diminished by a factor of ∼10 compared to canonical MP2 timings for Gaussian 92 and the scaling is reduced from N4−N5 in conventional methods to ∼N3. We have tested the accuracy of the method by calculating conformational energy differences for 36 small molecules for which experimental data exists, using the Dunning cc‐pVTZ correlation consistent basis set. After removing 6 test cases on the grounds of unreliability of the experimental data, an average deviation with experiment of 0.18 kcal/mol between theory and experiment is obtained, with a maximum deviation of ∼0.55 kcal/mol. This performance is significantly better than that obtained previously with a smaller basis set via canonical MP2; it is also superior to the results of gradient corrected density func...

New pseudospectral algorithms for electronic structure calculations: Length scale separation and analytical two‐electron integral corrections

We describe improved algorithms for carrying out pseudospectral Hartree–Fock calculations; these algorithms are applicable to other ab initio electronic structure methodologies as well. Absolute energies agree with conventional basis set codes to within 0.25 kcal/mol, and relative energies agree to better than 0.1 kcal/mol for a wide variety of test molecules. Accelerations of CPU times of as large as a factor of 6.5 are obtained as compared to GAUSSIAN 92, with the actual timing advantage increasing for larger basis sets and larger molecules. The method is shown to be highly reliable and capable of handling extended basis sets.

Pseudospectral Hartree–Fock theory: Applications and algorithmic improvements

Several additions to the pseudospectral Hartree–Fock theory are described, including a localized least‐squares procedure, various numerical cutoff algorithms, and calculation of all integrals in the diatomic frame. This pseudospectral method is tested on 23 molecules, ranging in size from two to twenty atoms (200 6‐31G** basis functions). A direct comparison of accuracy and computational efficiency is made with the conventional electronic structure programs gamess, gradscf, gaussian 86, and gaussian 88. The pseudospectral code is shown to be up to nine times faster than any of the above programs for the molecules tested here; moreover, this timing advantage increases with molecular size, suggesting that ab initio calculations may soon be possible on large systems not accessible by the Roothaan–Hall procedure.

Pseudospectral generalized valence‐bond calculations: Application to methylene, ethylene, and silylene

The pseudospectral (PS) method for self‐consistent‐field calculations is extended for use in generalized valence‐bond calculations and is used to calculate singlet–triplet excitation energies in methylene, silylene, and ethylene molecules and bond dissociation and twisting energies in ethylene. We find that the PS calculations lead to an accuracy in total energies of ≤0.1 kcal/mol and excitation energies to ≤0.01 kcal/mol for all systems. With effective core potentials on Si, we find greatly improved accuracy for PS.

Pseudospectral contracted configuration interaction from a generalized valence bond reference

A multireference configuration interaction method is presented based upon pseudospectral integration and a novel generalized valence bond referenced contraction procedure. The combination of these approaches is shown to allow for unprecedented multiconfiguration self‐consistent‐field calculations on large molecules.

Pseudospectral Hartree–Fock calculations on glycine

The pseudospectral method for Hartree–Fock calculations is applied to the glycine molecule, a test case with 100 basis functions. Several algorithmic improvements are reported, including a Newton–Raphson convergence scheme, Fock matrix updating, a multigrid technique, and optional recalculation of integrals. The pseudospectral method is shown to accurately reproduce the Roothaan–Hall relative and total energies for three conformations of glycine. Timing results show the pseudospectral code to be substantially faster than conventional Hartree–Fock codes.

Saturation of the second hyperpolarizability for polyacetylenes

Abstract Polyacetylene (PA) polymers −(−CHCH−)N− lead to large second hyperpolarizabilities (γ) that increase with N. For small N the increase is quite rapid, eventually saturating (becoming linear in N) for N ⩾ Nsatγ. Both experimental and theoretical attempts have been made to estimate Nsatγ. In 1994 this led to two Science papers, one obtaining Nsatγ = 20 (semiempirical theory) and the other obtaining Nsatγ = 125 (experiment, but on a substituted disordered form of PA!). We report here ab initio calculations up through N = 49 (C98H100) and show that Nsatγ = 45 ± 5. The much larger experimental value, Nsatγ = 125, is explained in terms of the structural defects and disorder introduced by the synthetic method.

Efficient pseudospectral methods for density functional calculations

Novel improvements of the pseudospectral method for assembling the Coulomb operator are discussed. These improvements consist of a fast atom centered multipole method and a variation of the Head–Gordan J-engine analytic integral evaluation. The details of the methodology are discussed and performance evaluations presented for larger molecules within the context of DFT energy and gradient calculations.

Nuclear-magnetic-resonance shielding constants calculated by pseudospectral methods

We have developed an algorithm based upon pseudospectral (PS) ab initio electronic structure methods for evaluating nuclear magnetic shielding constants using gauge-including atomic orbitals (GIAOs) in the spin-restricted and spin-unrestricted formalisms of Hartree-Fock (HF) theory and density-functional theory (DFT). The nuclear magnetic shielding constants for both 1H and 13C calculated using PS methodology for 21 small molecules have absolute mean errors of less than 0.3 ppm in comparison with analytic integral results. CPU timing comparisons between PS methods and conventional methods carried out for seven large molecules ranging from 510 to 1285 basis functions demonstrate that the PS methods are an order of magnitude more efficient than the conventional methods. PS-HF was between 9 and 26 times faster than conventional integral technology, and PS-DFT (Becke three-parameter Lee-Yang-Parr) was between 6 and 21 times faster.

Pseudospectral Hartree-Fock gradient calculations

Techniques for the calculation of analytic first derivatives of the Hartree–Fock energy are reported, within the context of the pseudospectral ab initio method. Using these gradients, geometry optimization is carried out on several molecules at the 6‐31 G** level. The resultant geometries are compared to those from conventional ab initio molecular‐orbital calculations, and it is shown that bond lengths agree to within 0.003 A, while bond angles are within 1°.